Mechanistic Modelling in Pig and Poultry Production

MECHANISTIC MODELLING

IN PIG AND POULTRY

PRODUCTION

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MECHANISTIC MODELLING

IN PIG AND POULTRY

PRODUCTION

Edited by

R. Gous

University of KwaZulu-NatalPietermaritzburgSouth Africa

T. Morris

University of ReadingReadingUK

and

C. Fisher

ConsultantMidlothianScotland

CABI is a trading name of CAB International

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A catalogue record for this book is available from the Library of Congress, Washington, DC.

ISBN-10: 1–84593–070–3ISBN-13: 978–1-84593–070–7

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Contents

List of Contributors vii

Preface ix

Acknowledgements xi

1 An Introduction to Modelling in the Animal Sciences 1T.R. Morris

2 Scientific Progress and Mathematical Modelling: DifferentApproaches to Modelling Animal Systems

6

J. France and J. Dijkstra

3 Basic Concepts Describing Animal Growth and Feed Intake 22N.S. Ferguson

4 The Effects of Social Stressors on the Performance of Growing Pigs

54

I.J. Wellock, G.C. Emmans and I. Kyriazakis

5 Modelling Populations for Purposes of Optimization 76R.M. Gous and E.T. Berhe

6 Advancements in Empirical Models for Prediction and Prescription

97

W.B. Roush

7 The Problem of Predicting the Partitioning of Scarce Resources during Sickness and Health in Pigs

117

I. Kyriazakis and F.B. Sandberg

8 Nutrient Flow Models, Energy Transactions and Energy Feed Systems

143

J. van Milgen

v

9 Evaluating Animal Genotypes through Model Inversion 163A.B. Doeschl-Wilson, P.W. Knap and B.P. Kinghorn

10 Considerations for Representing Micro-environmental Conditions in Simulation Models for Broiler Chickens

188

O.A. Blanco and R.M. Gous

11 Using Physiological Models to Define Environmental Control Strategies

209

M.A. Mitchell

12 Modelling Egg Production in Laying Hens 229S.A. Johnston and R.M. Gous

13 Comparison of Pig Growth Models – the Genetic Point of View 260P. Luiting and P.W. Knap

14 Mechanistic Modelling at the Metabolic Level: a Model of Metabolism in the Sow as an Example

282

J.P. McNamara

15 The Place of Models in the New Technologies of Production Systems

305

D.M. Green and D.J. Parsons

Index 325

vi Contents

Contributors

E.T. Berhe, Animal and Poultry Science, School of Agricultural Sciences andAgribusiness, University of KwaZulu-Natal, Private Bag X01, Scottsville 3209,South Africa.

O.A. Blanco, Animal and Poultry Science, School of Agricultural Sciences andAgribusiness, University of KwaZulu-Natal, Private Bag X01, Scottsville 3209,South Africa.

J. Dijkstra, Animal Nutrition Group, Wageningen Institute of Animal Sciences,Wageningen University, Marijkeweg 40, 6709 PG Wageningen, TheNetherlands.

A.B. Doeschl-Wilson, Sygen International, Scottish Agricultural College, BushEstates, Penicuik, Edinburgh, EH26 0PH, UK.

G.C. Emmans, Animal Nutrition and Health Department, Scottish AgriculturalCollege, West Mains Road, Edinburgh, EH9 3JG, UK.

N.S. Ferguson, Maple Leaf Foods Agresearch, 150 Research Lane, Guelph,Ontario, Canada, N1G 4T2.

J. France, Centre for Nutrition Modelling, Department of Animal and PoultryScience, University of Guelph, Guelph, Ontario, Canada, N1G 2W1.

D.M. Green, University of Oxford, Department of Zoology, South Parks Road,Oxford, OX1 3PS, UK.

R.M. Gous, Animal and Poultry Science, School of Agricultural Sciences andAgribusiness, University of KwaZulu-Natal, Private Bag X01, Scottsville 3209,South Africa.

S.A. Johnston, Animal and Poultry Science, School of Agricultural Sciences andAgribusiness, University of KwaZulu-Natal, Private Bag X01, Scottsville 3209,South Africa.

B.P. Kinghorn, Sygen International, Scottish Agricultural College, Bush Estates,Penicuik, Edinburgh, EH26 0PH, UK.

P.W. Knap, PIC International Group, Ratsteich 31, D-24837 Schleswig, Germany;and Sygen International, Scottish Agricultural College, Bush Estates, Penicuik,Edinburgh, EH26 0PH, UK.

vii

I. Kyriazakis, Animal Nutrition and Health Department, Scottish AgriculturalCollege, West Mains Road, Edinburgh, EH9 3JG, UK.

P. Luiting, PIC International Group, Ratsteich 31, D-24837 Schleswig, Germany.J.P. McNamara, Department of Animal Sciences, Washington State University, PO

Box 646351, Pullman WA 99164-6351, USA.M.A. Mitchell, Roslin Institute, Roslin, Midlothian, EH25 9PS, UK.T.R. Morris, School of Agriculture, Policy and Development, The University of

Reading, New Agriculture Building, PO Box 237, Reading, RG6 6AR, UK.D.J. Parsons, Cranfield University, Silsoe, Bedford, MK45 4HS, UK.W.B. Roush, USDA-ARS Poultry Research Unit, Mississippi State, MS 39762,

USA.F.B. Sandberg, Animal Nutrition and Health Department, Scottish Agricultural

College, West Mains Road, Edinburgh, EH9 3JG, UK.J. van Milgen, INRA – UMR SENAH, Domaine de la Prise, 35590 Saint-Gilles,

France.I.J. Wellock, Animal Nutrition and Health Department, Scottish Agricultural

College, West Mains Road, Edinburgh, EH9 3JG, UK.

viii Contributors

Preface

This volume records the proceedings of a conference held in South Africain April 2005 with the title ‘Recent Advances in Pig and Poultry Modelling’.The Conference, organized by the University of KwaZulu-Natal and theSouth African Branch of the World’s Poultry Science Association, broughttogether scientists from several countries and from different modellingtraditions to share their ideas and recent developments. The paperspublished here create a permanent record of these deliberations.

The Conference was held at the Ithala Game Reserve in KwaZulu-Natalfrom 13–16 April 2005 and was attended by 65 delegates. Ithala offered anunusual and stimulating location for the meeting and scientific sessions wereinterspersed with the viewing of wild game and the exploration of a verybeautiful wild bush. A team of staff and students from the Department ofAnimal and Poultry Science, University of KwaZulu-Natal, Pietermaritzburg,led by Professor Rob Gous, ensured that the requirements for a successfulmeeting were fully met. Several companies supported the Conference bysponsorship as shown under Acknowledgements.

The meeting had three main aims: to provide a discussion and recordof recent developments in the mechanistic modelling of pig and poultryproduction systems; to provide a written record of these discussions; andto mark the contribution of retiring Professor Trevor Morris of theUniversity of Reading to the field of animal modelling and systems.

Mechanistic modelling of animal systems has already provided a greatdeal of understanding of the underlying principles of pig and poultrynutrition and production. This is an ongoing process and a review at thistime is particularly appropriate. Notable amongst these papers is theconsideration of new components of the animal production process, suchas social stressors and disease. Also the understanding of some newsystems, such as the physiological control of egg production in hens, hasbenefited greatly from the development of a modelling approach. Theintegration of modelling into the wider aspects of animal production

ix

systems is an area that is developing quite rapidly at this time. On the moregeneral questions of animal modelling, many different philosophies andapproaches are viable and the reader will find a reflection of this diversityin these pages. The day-to-day application of modelling in managementdecision-making is still some way off but the progress towards this ideal isreflected in this book.

Professor Trevor Morris led the way in the application of quantitativemethods in poultry production and nutrition. Mainly using statisticalmethods but always with a clear view of the underlying mechanisms, formany years he showed the benefits of combining the results of differentexperiments into a set of simple and applicable quantitative rules. Whilstthis is some way from modern, computer-based mechanistic modelling,these earlier ideas undoubtedly showed the way and, in particular, trainedand motivated many students who later became modellers. ProfessorMorris is now retired and this volume is warmly dedicated to him inrecognition and appreciation of his work and contribution. It will be anappropriate testament to his work if this volume encourages some younganimal scientists to see how the application of modelling techniques andideas can enhance their own work.

R.M. Gous

x Preface

Acknowledgements

Financial support for this symposium is gratefully acknowledged from:

AviagenDegussaEFG Software (Natal)Elsevier PublishingMaple Leaf FoodsUniversity of KwaZulu-NatalWorld’s Poultry Science Association

xi

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1 An Introduction to Modelling inthe Animal Sciences

T.R. MORRIS

School of Agriculture, Policy and Development, The University of Reading,New Agriculture Building, PO Box 237, Reading, RG6 6AR, [email protected]

Scientists and engineers use models to represent parts of what they regardas the real world; to help them to convey to others an understanding of theway in which things work and, sometimes, to help them to makepredictions about the consequences of alternative courses of action.

Some models are pictorial and none the less useful for that. We coulddraw a diagram of the digestive system of a pig that would be helpful inexplaining how the animal converts its food into components that can beabsorbed, leaving a residue to be excreted. Note that the diagram does notneed to look much like the real guts of a pig and, indeed, a colourphotograph of an alimentary tract, although more ‘accurate’ than a simpleline drawing, is actually less suitable for our purpose. A single photographwould not reveal the teeth, the salivary glands, the bile duct, the pancreasand the hepatic portal vein. For similar reasons, an accurate scale map ofthe London underground railway system, showing all its tracks, stations andplatforms might be valuable to a maintenance engineer but is not helpful tothe visitor trying to find his or her way around London. The map whichdoes appear on the walls of London underground stations is a muchsimplified diagram, showing the relationships between stations on a givenline (but not their real geographical locations) and the interconnectionsbetween lines, which are distinguished by the use of colour codes. Thismodel is the work of an electrical engineer who knew how to draw a circuitdiagram and applied his skill to the problem of making the planning of ajourney as simple as possible. What these examples tell us is that modelshave to be sufficient for their purpose and, therefore, that we must definethe purpose carefully before setting out to construct a model.

A diagram of a pig’s digestive system and a map of an undergroundsystem are examples of models which represent something in the realworld, but they do not involve equations. Wordsworth (1798) wrote that‘poetry is emotion recollected in tranquillity’ and we might argue that

© CAB International 2006. Mechanistic Modelling in Pig and Poultry Production (eds. R. Gous, T. Morris and C. Fisher) 1

‘science is observation encapsulated in equations’. The aim of mostscientific research is (or should be) to reduce a mass of observational detailto equations which have powerful predictive value. Galileo could (and did),like others before him, construct models of the solar system which werehelpful when explaining the relative motion of the sun and its planets; butNewton explained why the planets moved in elliptical orbits around thesun and provided equations capable of predicting their future positions.The hypothesis, later derived from Einstein’s work, that the ultimatefuture of the sun itself (not just our sun – any sun) is limited by naturalprocesses (as distinct from divine judgement), does not detract from thevalue of Newton’s equations for any planetary predictions that we mortalsmight wish to make. The proposition that light travels in straight lines hasbeen shown to be false by quantum theory, but it still works on the smallscale of our solar system and will do well enough for landing a man on themoon (and bringing him home again). The validity of any particular modelcan only be judged in relation to the purpose it is intended to serve.

The early history of the application of models in animal agriculturewas well reviewed by Baldwin and Hanigan (1990). Two strands becameinterwoven with very fruitful results. On the one hand there were the earlymodels of energy and protein utilization due to Kellner (1909) and Armsby(1917), later codified by Brody (1945). On the other hand, there was thework of economists who sought predictive models for systems and, in ourparticular case, for agricultural systems. These economic models wereusually designed to maximize profit in a particular system or to minimizecosts. The use of linear programming to maximize profit within a farmbusiness, and the application of the same linear programming metho-dology to minimizing the ingredient cost of a diet for a particular set of nu-trient specifications and raw materials, were early examples of economicmodelling applied to agriculture.

Fawcett, an economist, wrote in 1973 that ‘much effort is now beingapplied to simulation techniques for the purpose of designing optimalprocesses, but simulation is no substitute for mathematical analysis’.Whittemore and Fawcett (1974, 1976) were subsequently among the first tocombine the thinking of economists and animal nutritionists to produce, intheir case, a simulation model for the growing pig. Meanwhile, Morris(1968) had quantified the response of laying hens to changes in dietaryenergy concentration and had shown how this could lead to optimizingenergy level in relation to any particular set of ingredient prices (Morris,1969). Fisher and Wilson (1974) did the same thing for the energy content ofbroiler diets. These last were examples of quantitative models, derivedempirically and not based upon any direct understanding of the mechanismsat work.

A model of the laying hen’s response to amino acid intake (Fisher et al.,1973), on the other hand, was explicitly derived by considering the uti-lization of the limiting amino acid for the synthesis of egg and bodyproteins. Here, theory and experimental data fitted neatly together.McDonald and Morris (1985) subsequently argued that, since the theory

2 T.R. Morris

could be shown to fit all the available experimental data for lysine,methionine, tryptophan, isoleucine and valine, it should be adopted as thepreferred method of calculating responses to these and other amino acids,rather than undertaking more experiments.

The potential of good models to obviate the need for furtherexperiments seems often to have been overlooked. Workers will often planan experiment to answer a particular question about the response of onecurrent genotype to nutrient or environmental inputs, without stopping toconsider how this might help to predict the response of future genotypes(and tomorrow is part of the future) to a somewhat different array of inputvariables. Worse, they may use the results of such trials to list ‘requirements’for current genotypes (e.g. Chiba, 1999; Leeson and Summers, 1999). Thisignores the important proposition that ‘nutrient requirements’ cannot bedefined for groups of chickens or pigs for three reasons. First, the responseof any group of animals to increasing inputs of any limiting variable iscurvilinear (Morris, 1983): this means that an optimum input can bedetermined, but it should not be labelled a ‘requirement’. Secondly, theresponse curve will shift with changes in the potential output of the groupof animals being considered. Thirdly, the position of the optimum on thecurve will shift with changes in the cost of the input or the value of theoutput. Thus it is possible to produce equations defining curves whichrepresent the mean response of groups of animals (with defined potential)to various inputs, but this cannot lead to a calculation of the optimum doseuntil prices have also been defined. The marriage of economic thinking andnutritional knowledge, which took place some 30 years ago, is indissoluble.

The scope of this publication has been limited to mechanisticmodelling, a term which seems to have been introduced by Thornley andFrance in 1984. By this we mean models which are quantitative and whichaim to represent the underlying mechanisms that produce end results.This is in contrast to other quantitative models, which use equationsderived from observations in the real world, but not necessarilyrepresenting any understanding of the causal mechanisms at work. Forexample, we might construct an epidemiological model showing how therisk of heart attack in a given population is affected by factors such assmoking, excess body weight or physical exercise. This would be a gooddescription of the historical data analysed and might be a valuablepredictor of future risk but does not require any understanding of howthese risk factors actually alter the frequency of heart attacks in apopulation. Conversely, a team of doctors might establish quite convincingexplanations of the causal connection between excess energy intake,atherosclerosis and myocardial infarction, but would not, from that evidence,be in a position to predict how many heart attacks would be avoided by adefined reduction in body mass index.

Causal, or mechanistic, models are much to be preferred when we canfind them. This is because they are much more likely to be robust and toapply to situations outside the range of conditions actually tested. You cantravel the universe with an equation such as E = mc2 and expect it to be

Introduction to Modelling in Animal Sciences 3

obeyed everywhere. However, there are many cases where we are not yetin a position to build a causal model from fundamental components andwe must therefore, for the time being, rely on empiricism in those cases.Two examples will illustrate this point. We know that changes in photo-period have marked effects on the rate of sexual development in pulletsand we can trace changes in the concentration of gonadotrophic hormonesin the blood, following an increase or decrease in photoperiod. We areconfident that the brain responds to photoperiod by altering the flow of areleasing hormone from the hypothalamus to the pituitary gland, which inturn adjusts the flow of gonadotrophins to the ovary. However, thisknowledge does not put us in a position to write equations representingthe effect of a stated series of photoperiods during rearing upon the age atwhich the pullet will lay her first egg. We can, however, provide quiterobust empirical equations to predict age at first egg for any specifiedpattern of photoperiod applied during rearing (Lewis et al., 2002, 2003). Itis perhaps going too far to say that this particular gap between theory andempiricism will never be bridged, but it seems unlikely that a fullmechanistic model would have any better predictive capability than thepresent empirical one; and so it may be that further effort to quantify themechanism is not justified. A second example is the response to addedcopper in a diet. A small amount of copper (about 6 mg/kg diet) is neededfor metabolic purposes, but this level is supplied by almost all natural diets.If copper sulphate is added to raise copper levels to 50–100 mg/kg, growthrate of pigs and baby chicks is enhanced. This effect is attributed tomodification of the gut flora in a manner that is beneficial to the hostanimal. At higher concentrations, copper begins to be toxic and growth isdepressed. All these effects, copper deficiency at very low levels, copper asa growth promoter in the medium range and copper toxicity at high doses,can be demonstrated and quantified by appropriate trials, but this does notlead to a theory connecting the cause to the effects in a mechanistic model.On the other hand, we could produce a well researched response curve,which could be reliably used to predict the effect of adding coppersulphate to pig and poultry diets.

There are many more examples available where we have no immediateprospect of being able to develop a good mechanistic model, even thoughwe believe that we understand a good deal about the mechanisms involved.Empirical modelling is therefore not to be despised if it is the best availabletool for solving a particular problem. What is not acceptable is the use ofempirical modelling where others have already developed a mechanisticmodel capable of resolving the particular question being approachedempirically. I believe that the modelling of growth and development inpigs and poultry has now reached a sufficiently advanced state thatempirical models in this area can no longer be justified.

4 T.R. Morris

References

Armsby, H.P. (1917) Nutrition of Farm Animals. Macmillan, New York.Baldwin, R.L. and Hanigan, M.D. (1990) Biological and physical systems: animal

sciences. In: Jones, J.G.W. and Street, P.R. (eds) Systems Theory Applied toAgriculture and the Food Chain. Elsevier Science, Barking, UK, pp. 1–21.

Brody, S. (1945) Bioenergetics and Growth. Hafner, New York.Chiba, L.I. (1999) Feeding systems for pigs. In: Theodoru, M.K. and France, J.

(eds) Feeding Systems and Feed Evaluation Models. CAB International,Wallingford, UK, pp. 181–209.

Fawcett, R.H. (1973) Towards a dynamic production function. Journal ofAgricultural Economics 20, 543–549.

Fisher, C., Morris, T.R. and Jennings, R.C. (1973) A model for the description andprediction of the responses of laying hens to amino acid intake. British PoultryScience 14, 469–484.

Fisher, C. and Wilson, B.M. (1974) Response to dietary energy concentration bygrowing chickens. In: Morris, T.R. and Freeman, B.M. (eds) EnergyRequirements of Poultry. Constable, Edinburgh, UK, pp. 151–184.

Kellner, O. (1909) The Scientific Feeding of Animals. Translated by Goodwin, W.Duckworth, London.

Leeson, S. and Summers, J.D. (1999) Feeding systems for poultry. In: Theodoru,M.K. and France, J. (eds) Feeding Systems and Feed Evaluation Models. CABInternational, Wallingford, UK, pp. 211–237.

Lewis, P.D., Morris, T.R. and Perry, G.C. (2002) A model for predicting the age atsexual maturity for growing pullets of layer strains given a single change inphotoperiod. Journal of Agricultural Science, Cambridge 138, 441–448.

Lewis, P.D., Morris, T.R. and Perry, G.C. (2003) Effect of two opposing changes inphotoperiod upon age at first egg in layer-hybrid pullets. Journal of AgriculturalScience, Cambridge 140, 373–379.

McDonald, M.W. and Morris, T.R. (1985) Quantitative review of amino acid intakesfor young laying pullets. British Poultry Science 26, 253–264.

Morris, T.R. (1968) The effect of dietary energy level on the voluntary calorieintake of laying birds. British Poultry Science 9, 285–295.

Morris, T.R. (1969) Nutrient density and the laying hen. In: Swan, H. and Lewis,D. (eds) Proceedings of the Third Nutrition Conference for Feed Manufacturers.University of Nottingham, Nottingham, UK, pp. 103–114.

Morris, T.R. (1983) The interpretation of response data from animal feeding trials.In: Haresign, W. (ed.) Recent Advances in Animal Nutrition – 1983. Butterworths,London, pp. 2–23.

Thornley, J.H.M. and France, J. (1984) Role of modelling in animal research andextension work. In: Baldwin, R.L. and Bywater, A.C. (eds) Modelling RuminantNutrition, Digestion and Metabolism; Proceedings of Second International Workshop.University of California Press, Davis, California, pp. 4–9.

Whittemore, C.T. and Fawcett, R.H. (1974) Model responses of the growing pig tothe dietary intake of energy and protein. Animal Production 19, 221–231.

Whittemore, C.T. and Fawcett, R.H. (1976) Theoretical aspects of a flexible modelto simulate protein and lipid growth in pigs. Animal Production 22, 87–96.

Wordsworth, W. (1798) Preface. In: Wordsworth, W. and Coleridge, S.T. (eds)Lyrical Ballads. Longmans, London.

Introduction to Modelling in Animal Sciences 5

2 Scientific Progress andMathematical Modelling: Different Approaches to Modelling Animal Systems

J. FRANCE1 AND J. DIJKSTRA2

1Centre for Nutrition Modelling, Department of Animal and Poultry Science,University of Guelph, Guelph, Ontario, Canada, N1G 2W1;2Animal Nutrition Group, Wageningen Institute of Animal Sciences,Wageningen University, Marijkeweg 40, 6709 PG Wageningen, [email protected]

Introduction

A general understanding of science influences the scientific questions thatare asked, the choice of problems for scientific investigation and also howthese are attacked. A more widespread understanding of this topic mightenable a greater contribution to be made for the same effort. This chapterattempts to describe what science is, how it progresses, the role and practiceof mathematical modelling and different approaches to modelling animalsystems. This is done with particular reference to animal science, withexamples from poultry and pigs. It represents, of course, a personal view.

Nature and Progress of Science

The zoologist E.O. Wilson has stated that science is ‘the reconstruction ofcomplexity by an expanding synthesis of freshly demonstrated laws’(Wilson, 1978). This contrasts with the view of the famous engineer andphysicist Ernst Mach that science is a minimal problem (Mach, 1942).Mach’s widely-accepted principle is cogently stated by the biologist andgeneticist J.B.S. Haldane who wrote ‘in scientific thought we adopt thesimplest theory which will explain all the facts under consideration andenable us to predict new facts of the same kind’ (Haldane, 1927). However,the philosopher Karl Popper, who has much to say on the nature of science

© CAB International 2006. Mechanistic Modelling in Pig and Poultry Production 6 (eds. R. Gous, T. Morris and C. Fisher)

(Popper, 1968), stresses the importance of predictive ability rather thansimplicity or complexity. All this may be distilled into the statement thatscience is about the correspondence of our ideas with the real world:

Ideas ↔ Real World (2.1)

In Eqn 2.1 ideas means such things as concepts, hypotheses or theories,and the real world means the world contacted through our senses, extendedor not by instrumentation. Ideas are connected to the real world by meansof experiments. Often theoretical prediction (deduced from a scheme ofideas or model) is compared with experimental data. If the experiments(the interactions with the real world) are quantitative and numbers aremeasured, the ideas should similarly be expressed numerically in order tomake a proper connection. To express ideas quantitatively, it is necessaryto use mathematics.

Most practising scientists share the views of Thomas Kuhn (1963) thatscientific progress is largely evolutionary, in contrast to those of Karl Popper(1968) that science progresses entirely by a series of revolutions orcatastrophes. Kuhn argues that most scientists are conservative, seeking toapply accepted methods and theories to new problems. When inconsistenciesin experimental data build up and some new paradigm is offered, a scientificrevolution occurs and more and more scientists abandon the old paradigmin favour of the new one. Indeed, there is little doubt that from time to timerevolutions do occur, usually by the replacement of a theory by a moreembracing alternative theory. In trying to understand a particularphenomenon, current theory must be taken as the starting point. An attemptis made at connecting the corpus of current scientific knowledge to theproblem which concerns some aspect of the real world. This attempt to makea connection will usually fail at the desired level of precision. However, afterperhaps repeating the experiment and modifying or extending the theory,some success may be achieved. The scientist will then be better able to makepredictions and will feel he has arrived at a better understanding of theproblem. Going round this cycle (Fig. 2.1) again and again, the concepts andideas become more articulated and more precise, and are matched to natureat more points and with more precision. It is stressed that movement isalways in the direction of increasing precision. At some point in the cycle itwill become necessary to use mathematics or mathematical modelling forformulating the ideas and for making the connection between theory andexperiment. Thus, a set of mathematical equations or a model can be viewedsimply as an idea, a hypothesis or a relationship expressed in mathematics.

Role and Practice of Mathematical Modelling

Modelling is a central and integral part of the scientific method. Asphrased eloquently by Arturo Rosenbluth and Norbert Weiner,

the intention and result of a scientific inquiry is to obtain an understanding andcontrol of some part of the universe. No substantial part of the universe is so

Scientific Progress and Mathematical Modelling 7

simple that it can be grasped and controlled without abstraction. Abstractionconsists in replacing the part of the universe under consideration by a model ofsimilar but simpler structure. Models, formal or intellectual on the one hand, ormaterial on the other, are thus a central necessity of scientific procedure.

(Rosenbluth and Weiner, 1945)

Models therefore provide us with representations that we can use.They provide a means of applying knowledge and a means of expressingtheory and advancing understanding (i.e. operational models and researchmodels). They are simplifications not duplications of reality. To quote froman editorial that appeared in the Journal of the American Medical Association,

a model like a map cannot show everything. If it did it would not be a modelbut a duplicate. Thus the classic definition of art as the purgation of superfluitiesalso applies to models and the model-makers problem is to distinguishbetween the superfluous and the essential.

(Anon, 1960)

This is, of course, an affirmation of Occam’s Razor, that entities are not tobe multiplied beyond necessity.

To appreciate fully the role of mathematical modelling in the biologicalsciences, it is necessary to consider the nature and implications oforganizational hierarchy (levels of organization) and to review the types ofmodels that may be constructed.

Organizational hierarchy

Biology, including pig and poultry science, is notable for its manyorganizational levels. It is the different levels of organization that give riseto the rich diversity of the biological world. For animal science, a typical

8 J. France and J. Dijkstra

Fig. 2.1. Nature and progress of science.

scheme for the hierarchy of organizational levels is shown in Table 2.1.This scheme can be continued in both directions and, for ease ofexposition, the different levels are labelled …, i + 1, i, i – 1, …. Any level ofthe scheme can be viewed as a system, composed of subsystems lying at alower level, or as a subsystem of higher level systems. Such a hierarchicalsystem has some important properties:

1. Each level has its own concepts and language. For example, the terms ofanimal production such as plane of nutrition and liveweight gain have littlemeaning at the cellular level.2. Each level is an integration of items from lower levels. The response ofthe system at level i can be related to the response at lower levels by areductionist scheme. Thus, a description at level i – 1 can provide amechanism for responses at level i.3. Successful operation of a given level requires lower levels to functionproperly, but not vice versa. For example, a microorganism can beextracted from the caecum of a pig and grown in culture in a laboratory, sothat it is independent of the integrity of the caecum and the animal, butthe caecum (and hence the animal) relies on the proper functioning of itsmicrobes to function fully itself.

This organizational hierarchy helps to explain three categories of model:teleonomic models which look upwards to higher levels, empirical modelswhich examine a single level, and mechanistic models which look downwards,considering processes at a level in relation to those at lower levels. A moredetailed classification of models is given in Thornley and France (2006).

Teleonomic modelling

Teleonomic models (see Monod, 1975, for a discussion of teleonomy) areapplicable to apparently goal-directed behaviour, and are formulatedexplicitly in terms of goals. They usually refer responses at level i to theconstraints provided by level i + 1. It is the higher level constraints that,via evolutionary pressures, can select combinations of the lower levelmechanisms, which may lead to apparently goal-directed behaviour at leveli. Currently, teleonomic modelling plays only a minor role in biological


Table 2.1. Levels of organization.

Level Description of level

i + 3 Collection of organisms (herd, flock)i + 2 Organism (animal)i + 1 Organi Tissuei – 1 Celli – 2 Organellei – 3 Macromolecule

modelling, though this role might expand. It has hardly been applied toproblems in animal physiology though it has found some application inplant and crop modelling (Thornley and Johnson, 1989).

Empirical modelling

Empirical models are models in which experimental data are used directly toquantify relationships, and are based at a single level (e.g. the whole animal)in the organizational hierarchy discussed above. Empirical modelling isconcerned with using models to describe data by accounting for inherentvariation in the data. Thus, an empirical model sets out principally todescribe, and is based on observation and experiment and not necessarily onany preconceived biological theory. The approach derives from thephilosophy of empiricism and adheres to the methodology of statistics.

Empirical models are often curve-fitting exercises. As an example,consider modelling voluntary feed intake in a growing pig. An empiricalapproach to this problem would be to take a data set and fit a linearmultiple regression equation, possibly relating intake to liveweight,liveweight gain and some measure of diet quality.

We note that level i behaviour (intake) is described in terms of level iattributes (liveweight, liveweight gain and diet quality). As this type ofmodel is principally concerned with prediction, direct biological meaningusually cannot be ascribed to the equation parameters and the modelsuggests little about the mechanisms of voluntary feed intake. If the modelfits the data well, the equation could be extremely useful though it isspecific to the particular conditions under which the data were obtained,and so the range of its predictive ability is limited.

Mechanistic modelling

Mechanistic models are process-based and seek to understand causation. Amechanistic model is constructed by looking at the structure of the systemunder investigation, dividing it into its key components, and analysing thebehaviour of the whole system in terms of its individual components andtheir interactions with one another. For example, a simplified mechanisticdescription of intake and nutrient utilization for our growing pig mightcontain five components, namely two body pools (protein and fat), twoblood plasma pools (amino acids and other carbon metabolites) and adigestive pool (gut fill), and include interactions such as protein and fatturnover, gluconeogenesis from amino acids and nutrient absorption. Thusthe mechanistic modeller attempts to construct a description of the systemat level i in terms of the components and their associated processes at leveli – l (and possibly lower), in order to gain an understanding at level i interms of these component processes. Indeed, it is the connections that


inter-relate the components that make a model mechanistic. Mechanisticmodelling follows the traditional philosophy and reductionist method ofthe physical and chemical sciences.

Model evaluation

Model evaluation is not a wholly objective process. Models can beperceived as hypotheses expressed in mathematics and should therefore besubject to the usual process of hypothesis evaluation. To quote Popper,

these conjectures are controlled by criticism; by attempted refutations, whichinclude several critical tests. They may survive these tests, but they can neverbe positively justified … by bringing out our mistakes it makes us understandthe difficulties of the problem we are trying to solve.

(Popper, 1969)

A working scientific hypothesis must therefore be subjected to criticism andevaluation in an attempt to refute it. In the Popperian sense, the termvalidation must be assumed to mean a failed attempt at falsification, sincemodels cannot be proved valid, but only invalid. Validation is thus bestavoided.

Following Popper’s analysis, the predictions of a model should becompared with as many observations as possible. However, there is often alack of suitable data to compare predictions with observations, because theavailable data were used to estimate model parameters and hence cannot beused to evaluate the model independently, or because the entities simplyhave not or cannot be measured experimentally. We refute the opinion ofsome referees and editors that a model is valuable if and only if itspredictions are fully accurate. The evaluation of research models dependson an appraisal of the total effort, within which mathematical modellingserves to provide a framework for integrating knowledge and formulatinghypotheses. For applied models, evaluation involves comparison of theresults of the new model and of existing models, in a defined environment(the champion-challenger approach). In all cases, the objectives of amodelling exercise should be examined to assess their legitimacy and towhat extent they have been fulfilled.

Mathematical Approaches

At this point in our discussion, it is important to give a correct picture of thenature of mathematics. Mathematics is often seen as a kind of tool, as thehandmaiden of science and technology. This view fails to acknowledge orreflect the potential role of mathematics in science and technology as anintegral part of the basic logic underlying the previewing and developmentalimagination which drives these vital disciplines. The use of the word tool todescribe mathematics is, we submit, pejorative. Tools operate on materials in acoercive way by cutting, piercing, smashing, etc. Mathematics is used in a


completely non-coercive way, by appealing to reason, by enabling us to see theworld more clearly, by enabling us to understand things that we previouslyfailed to understand.

Mathematics itself is an umbrella term covering a rich and diversediscipline. It has several distinct branches, e.g. statistics (methods ofobtaining and analysing quantitative data based on probability theory),operational research (methods for the study of complex decision-makingproblems concerned with best utilization of limited resources) and appliedmathematics (concerned with the study of the physical world and includinge.g. mechanics, thermodynamics, theory of electricity and magnetism). Themathematical spectrum is illustrated in Fig. 2.2.

Statistics has had a major influence on research in animal science andin applied biology generally, and is well understood by biologists. This ishardly surprising given that many of the techniques for the design andanalysis of experiments were pioneered in the 1920s to deal with variabilityin agricultural field experiments and surveys caused by factors beyond thecontrol of investigators such as the weather and site differences. Otherpertinent branches of mathematics, such as applied mathematics andoperational research, are less well understood. In the rest of this chapter,we explore a key paradigm from each of these three branches, viz. theregression and the linear programming (LP) paradigms from statistics andoperational research, respectively, and the rate:state formalism of appliedmathematics (biomathematics).

Regression paradigm

Linear multiple regression models pervade applied biology. The mathe-matical paradigm assumes there is one stochastic variable Y and q deter-ministic variables X1, X2, …, Xq, and that E(Y | X1, X2, …, Xq), the expectedvalue of Y given X1, X2, …, Xq, is linearly dependent on X1, X2, …, Xq:

and the variance V(Y | X1, X2, …, Xq) is constant:

Y is known as the dependent variable, X1, X2, …, Xq as the independentvariables, and the equation:

Y X X Xq q= + + + +β β β β0 1 1 2 2 ... ,

V( )Y X X Xq1 22, , ,... .= σ

E ) ... (2.2)(Y X X X X X Xq q q1 2 0 1 1 2 2, , , ,... = + + + +β β β β


Statistics Operationsresearch

Appliedmathematics

Numericalanalysis

Puremathematics

← Empirical modelling →← Mechanistic modelling

Fig. 2.2. Mathematical spectrum.

as the regression equation. The parameters are the partialregression coefficients.

It is convenient to write Eqn 2.2 in the form:

where the x– i’s are computed from the n observations (y1, x11, x21, …, xq1),

(y2, x12, x22, …, xq2), …, (yn, x1n, x2n, …, xqn) as, e.g. The sum

of squares of the yj’s from their expectations is therefore:

and the least squares estimates of the parameters are thesolutions of the normal equations:

Parameter β0 can be determined knowing β0. A linear multiple regressionmodel is linear in the parameters . A non-linear model thatcan be transformed into a form which is linear in the parameters (e.g. bytaking natural logarithms) is said to be intrinsically linear. Draper andSmith (1998) is recommended reading on regression methods.

Many of the models applied in pig and poultry science are systems oflinked regression equations, e.g. current feed evaluation systems.

LP paradigm

An LP problem has three quantitative aspects: an objective; alternativecourses of action for achieving the objective; and resource or otherrestrictions. These must be expressed in mathematical terms so that thesolution can be calculated. The mathematical paradigm is:

where Z is the objective function and the Xj’s are decision variables. The cj’s,aij’s and bi’s (bi � 0) are generally referred to as costs, technological

X j qj ≥ =0 1 2; , , , , [non-negativity constraints]...

a X b i mij jj

q

i=

∑ ≥ ≤ =1

1 2or ; , [constraints], , ... ,

min , [objective]Z c Xj jj

q

==

∑1

� � �1 2, , , ... q

∂∂

= ∂∂

= ∂∂

= = ∂∂

=S S S S

q˜ .� � � �0 1 2

0 ...

˜ ...β β β β0 1 2, , , , q

S y x x x x x xq j j j q qj qj

n

( , , , ) ( ) ( ) ( ) ,˜ ... ˜ ...� � � � � � �0 1 0 1 1 1 2 2 22

1

= − − − − − − − −[ ]=

∑

x x njj

n

1 11

==

∑ .

E( ( ) ( ) ( ))Y X X X X x X x X xq q q q1 2 0 1 1 1 2 2 2, , , ,... ˜ ...= + − + − + + −� � � �

� � �1 2, , ,... q


coefficients and right-hand-side values, respectively. The paradigm isgenerally solved using a simplex algorithm (see Thornley and France, 2006).

This formalism is much less restrictive than it first appears. Forexample, maximization of an objective function is equivalent to minimizingthe negative of that function; an equality constraint can be replaced byentering it as both a � and a � constraint; and any real variable can beexpressed as the difference between two positive variables. Also, there arevarious extensions of this paradigm that allow, e.g. examination of the waythe optimal solution changes as one or more of the coefficients varies(parametric programming); nonlinear functions of single variables to beaccommodated (separable programming); decision variables to take integervalues (integer programming); the objective of an activity or enterprise tobe expressed in terms of targets or goals rather than in terms of optimizinga single criterion (goal programming); and multiple objective functions tobe considered (compromise programming). Further description of thesetechniques can be found in Thornley and France (2006).

Typical applications in pig and poultry production include:formulating feed compounds and least-cost rations; allocating stock tofeeding pens; and deciding on the amounts of fertilizer to apply to land.

Rate:state formalism

Differential equations are central to the sciences and act as the cornerstone ofapplied mathematics. It is often claimed that Sir Isaac Newton’s greatdiscovery was that they provide the key to the ‘system of the world’. Theyarise within biology in the construction of dynamic, deterministic, mechanisticmodels. There is a mathematically standard way of representing such modelscalled the rate:state formalism. The system under investigation is defined attime t by q state variables: X1, X2, …, Xq. These variables represent propertiesor attributes of the system, such as visceral protein mass, quantity of substrate,etc. The model then comprises q first order differential equations whichdescribe how the state variables change with time:

where S denotes a set of parameters, and the function fi gives the rate ofchange of the state variable Xi.

The function fi comprises terms which represent the rates of processes(with dimensions of state variable per unit time), and these rates can becalculated from the values of the state variables alone, with of course thevalues of any parameters and constants. In this type of mathematicalmodelling, the differential equations are constructed by direct application ofscientific law based on the Cartesian doctrine of causal determinism (e.g. thelaw of mass conservation, the first law of thermodynamics) or by applicationof a continuity equation derived from more fundamental scientific laws. The

dd

( , , ..., ; ); , , ..., , (2.3)Xt

f X X X S i qii q= =1 2 1 2


rate:state formalism is not as restrictive as first appears because any higher-order differential equation can be replaced by, and a partial differentialequation approximated by, a series of first-order differential equations.

If the system under investigation is in steady state, solution to Eqn 2.3 isobtained by setting the differential terms to zero and manipulatingalgebraically to give an expression for each of the components and processesof interest. Radioisotope data, for example, are usually resolved in this way,and indeed, many of the time-independent formulae presented in the animalscience literature are derived likewise. However, in order to generate thedynamic behaviour of any model, the rate:state equations must be integrated.

For the simple cases, analytical solutions are usually obtained. Suchmodels are widely applied in digestion studies to interpret time-course datafrom marker and in vitro experiments, where the functional form of thesolution is fitted to the data using a curve-fitting procedure. This enablesbiological measures such as mean retention time and extent of digestion inthe gastro-intestinal tract to be calculated from the estimated parameters.

For the more complex cases, only numerical solutions to the rate:stateequations can be obtained. This can be conveniently achieved by using oneof the many computer software packages available for tackling suchproblems. Such models are used to simulate complex digestive andmetabolic systems. They are normally used as tactical research tools toevaluate current understanding for adequacy and, when currentunderstanding is inadequate, help identify critical experiments. Thus, theyplay a useful role in hypothesis evaluation and in the identification of areaswhere knowledge is lacking, leading to less ad hoc experimentation. Also, amechanistic simulation model is likely to be more suitable for extrapolationthan an empirical model, as its biological content is generally far richer.Recent examples of this type of model include the simulation of nutrientpartitioning in growing pigs to predict anatomical body composition(Halas et al., 2004) and the simulation of calcium and phosphorus flows inlayers to evaluate feeding strategies aimed at reducing P excretion to theenvironment in poultry manure (Dijkstra et al., 2006).

Sometimes it is convenient to express a differential equation as anintegral equation; for example Eqn 2.3 may be written:

where Xi(0) denotes the initial (zero time) value of Xi. Integral equationsarise, not only as the converse of differential equations, but also in theirown right. For example, the response of a system sometimes depends notjust on the state of the system per se but also on the form of the input.Input P and output U might then be related by the convolution (orFaltung) integral:

U t P x W t x x P t W tt

( ) ( ) ( )d ( ) ( ),= − =∫0

*

X X f X X X S t i qi i i q

t

= + =∫( ) ( , , ..., ; )d ; , , ..., ,0 1 21 20


where x is a dummy variable ranging over the time interval zero to thepresent time t during which the input has occurred, and W is a weightingfunction which weights past values of the input to the present value of theoutput. The symbol * denotes the convolution operator. Integral equationsare much less common in biology than differential equations though theyoccur as convolution integrals in areas such as tracer kinetics. Furtherdiscussion of these issues can be found in Thornley and France (2006).

Application of the rate:state formalism is illustrated with reference tococcidiosis, an intestinal disease in chickens caused by protozoan parasitesof the genus Eimeria. The life cycle of E. tenella, a typical species thatinvades the caecum, is depicted in Fig. 2.3.


Fig. 2.3. Life cycle of E. tenella: (a) sporulated oocyst; (b) sporozoite being liberated fromoocyst and sporocyst; (c) sporozoite; (d) trophozoite parasitizing an epithelial cell; (e) earlyschizont; (f) mature first-generation schizont; (g) first-generation merozoite parasitizing anotherepithelial cell; (h, i) second-generation schizonts; (j) rupture of second-generation schizont; (k)second-generation merozoite may parasitize other epithelial cells (l) for a third asexual cycle, ormay parasitize an epithelial cell (m) to become a female gametocyte (q); merozoite parasitizingan epithelial cell (n) and becoming a male gametocyte (o); (p) liberated microgametes unite withmacrogamete (r), which develops into oocyst (s) and is liberated in the faeces by host (t),sporulation (u) of oocyst occurs in outside environment (source: Reid, 1984).

The main features of this complex life cycle are: (i) the exogenousdevelopment of newly excreted oocysts in the litter to become infectioussporulated oocysts; and (ii) programming of the parasite to undergocontrolled replication within the intestinal mucosa, with a time delaybetween each stage. Endogenous development occurs from the eightsporozoites released from each oocyst which then undergo a maximum ofthree cycles of sexual divison (schizogony) with known multiplication rates.Each of the three generations of schizonts contains a different butrelatively constant number of protozoan forms known as merozoites.Merozoites released from third generation schizonts give rise to the sexualphases of the cycle, forming either male microgametes or femalemacrogametes. Fertilization of the macrogametes results in zygotes which,after the development of a protective wall, are released as unsporulatedoocysts. A much simplified version of this life cycle is shown in Fig. 2.4.

The system as represented is defined at time t by five state variables: X1,X2, …, X5. These variables represent the number of oocysts per bird in thelitter (X1), the number of oocysts inside a single bird (X2), the number ofsporozoites inside a bird (X3), the number of schizonts inside a bird (X4),and the number of zygotes inside a bird (X5). The model then comprisesfive first order differential equations given by Eqn 2.3 with q = 5. The solidarrows between boxes represent flows (per unit time) between the differentstages of the life cycle included in the model. Time delays are incorporatedto allow for stages not explicitly or inadequately represented. The modelcan be solved using an appropriate set of parameter values (S) to give valuesof the state variables over time, and to simulate the effects of interventionstrategies such as the use of vaccine oocysts in the feed (Fig. 2.4).

A second application of the formalism is demonstrated by consideringthe synthesis of milk fat and lactose, two of the principal constituents of


Zygotes,X5

Oocysts in litter,

X1

Ingestedoocysts,

X2

Totalschizonts,

X4

Sporozoites,X3

Merozoites

Time delay

Vaccineoocysts

Time

Timedelay

Fig. 2.4. Simplified representation of the life cycle of E. tenella for use as a model (fromParry et al., 1992).

milk, in the mammary gland of the lactating sow. The biochemicalpathways involved are shown in Fig. 2.5.

Triacylglycerols comprise over 97% of the lipids in milk. Biosynthesisof fatty acid precursors occurs in the mitochondria, that of fatty acids,glycerol, and other related intermediates in the cytosol, and that oftriacylglycerol in or near the endoplasmic reticulum. The primary pathwayfor fatty acid synthesis is glucose through glycolysis to pyruvate, followedby oxidative decarboxylation to form acetyl CoA. Acetyl CoA, together withoxaloacetate (OAA), may be further oxidized to CO2 in the citric acid cycle(Fig. 2.5). Lactose is a disaccharide composed of one molecule of glucoseand one of galactose. The synthetic pathway is glucose-1-P to uridinediphosphate (UDP)-glucose to UDP-galactose, then UDP-galactose plusglucose to lactose (Fig. 2.5).

A highly simplified version of these pathways is shown in Fig. 2.6. Thesystem as represented is defined at time t by five state variables: X1, X2, …,X5. These variables (in mols) represent the precursors fatty acids (X1) andglucose (X2), the intermediate fatty acyl CoA (X3), and the products milk fat


Fig. 2.5. Biochemical pathways involved in the synthesis of milk fat and lactose in themammary gland of the lactating sow (source: J.P. Cant, personal communication).

(X4) and lactose (X5). The model then comprises five first order differentialequations given by Eqn 2.3 with q = 5, as for the simplified representationof the life cycle of E. tenella (Fig. 2.4). The solid arrows between boxesrepresent flows (mols per unit time) between the state variables of themodel. An acetyl CoA transaction is incorporated to generate ATP formetabolic transactions via its oxidation. The model can be used to simulatea complete lactation and to help develop practical feeding strategies.

These two applications illustrate the power of differentials and therate:state formalism in providing quantitative, dynamic descriptions ofbiological life cycles and biochemical pathways, which are central to pigand poultry science.

Conclusions

The first step in the application of scientific precepts to a problem is toidentify objectives. Next, appropriate information is collated to generatetheories and hypotheses which are subsequently tested against observations(Fig. 2.1). Mathematical models, particularly process-based ones, provide auseful means of integrating knowledge and formulating hypotheses. Thusmathematical modelling is an integral part of a research programme, withthe experimental and modelling objectives highly inter-related.

The mathematical expression of hypotheses in models forms a centralrole in a research programme. Kuhn (1963) stressed the importance ofresearch performed by scientists within a scientific discipline, which slowlybut steadily increases knowledge, and the more rapid progress which fromtime to time is achieved by efforts of scientists in a true interdisciplinarymanner. Progress in modelling depends on a variety of approaches andideas. Thus, while further refinements of models may provide knowledge


Fatty acids,X1

Glucose,X2

Fatty acyl CoA,X3

Milk fat,X4

Milk lactose,X5

Oxidation

Fig. 2.6. Simplified milk fat and lactose synthesis for use as a model (adapted fromPettigrew et al., 1992).

that is of value in its own right, that value is greatly enhanced if theserefinements can be related to the interaction between observationsresulting from experiments and from simulations. Modelling increases theefficiency and effectiveness of experiments with animals and enhancesprogress in understanding and controlling pig and poultry production.

Biological research, if it is to remain truly relevant, must beundertaken at several levels of generality, e.g. cell, tissue or organ, wholeorganism, population. There is much more to biology than just molecularscience. Hopefully, the molecular chauvinism that seems to havedominated biological research thinking (and hence funding) for much ofthe last quarter century is finally at an end. This chapter has identifieddifferent modelling approaches, i.e. teleonomic, empirical and mechanisticmodelling, and different mathematical paradigms drawn from differentbranches of mathematics. No approach or paradigm is advocated as beinguniversally superior; no one has a monopoly on wisdom. It is noteworthyand pleasing that papers on pig and poultry modelling were read at thepresent workshop and also formed a significant part of a recently held 5-yearly farm animal modellers workshop (Kebreab et al., 2006). It is, afterall, a truism that those modelling pig nutrition have things to learn fromtheir counterparts working, for example, in poultry nutrition, and viceversa. Thus scientific pluralism, not just across animal species but alsoacross levels of generality and types of modelling, should be a pillar forfuture development of the activity of pig and poultry modelling.

Peering into a crystal ball and attempting to foretell what lies ahead isusually a futile task. To quote Baldwin (2000): ‘previewing the future is anequivocal process’. We think it sufficient to conclude by saying that a futurefocus for pig and poultry modelling based on scientific pluralism, withemphasis on solving biological problems rather than applying mathematicaltechniques, offers a fruitful way ahead.

Acknowledgement

We thank Dr John Thornley for many useful discussions on this topic overa number of years.

References

Anon (1960) Working models in medicine. Journal of the American Medical Association174, 407–408.

Baldwin, R.L. (2000) Introduction: history and future of modelling nutrientutilization in farm animals. In: McNamara, J.P., France, J. and Beever, D.E.(eds) Modelling Nutrient Utilization in Farm Animals. CABI Publishing,Wallingford, UK, pp. 1–9.

Dijkstra, J., Kebreab, E., Kwakkel, R.P. and France, J. (2006) Development of adynamic model of Ca and P flows in layers. In: Kebreab, E., Dijkstra, J., Gerrits,W.J.J., Bannink, A. and France, J. (eds) Nutrient Digestion and Utilization in FarmAnimals: Modelling Approaches. CABI Publishing, Wallingford, UK, pp. 192–210.


Draper, N.R. and Smith, H. (1998) Applied Regression Analysis, 3rd edn. Wiley, NewYork.

Haldane, J.B.S. (1927) Science and theology as art forms. In: Possible Worlds. Chatto& Windus, London.

Halas, V., Dijkstra, J., Babinszky, L., Verstegen, M.W.A. and Gerrits, W.J.J. (2004)Modelling of nutrient partitioning in growing pigs to predict their anatomicalbody composition. 1. Model description. British Journal of Nutrition 92,707–723.

Kebreab, E., Dijkstra, J., Gerrits, W.J.J., Bannink, A. and France, J. (eds) (2006)Nutrient Digestion and Utilization in Farm Animals: Modelling Approaches. CABInternational, Wallingford, UK, viii+480 pp.

Kuhn, T.S. (1963) The Structure of Scientific Revolutions. University Press, Chicago,Illinois.

Mach, E. (1942) The Science of Mechanics, 9th edn. Open Court, LaSalle, Illinois.Monod, J. (1975) Chance and Necessity. Collin metabolism of lactating sows. Journal of

Animal Science 70, 3742–3761.Popper, K.R. (1968) The Logic of Scientific Discovery. Hutchinson, London.Popper, K.R. (1969) Conjecture and Refutations. The Growth of Scientific Knowledge, 3rd

edn. Routledge & Kegan Paul, London.Reid, W.M. (1984) Coccidiosis. In: Hofstad, M.S. (ed.) Diseases of Poultry, 7th edn.

Iowa State University Press, Ames, Iowa, pp. 784–846.Rosenbluth, A. and Weiner, N. (1945) The role of models in science. Philosophical

Science 12, 316–321.Thornley, J.H.M. and France, J. (2006) Mathematical Models in Agriculture, 2nd edn.

CAB International, Wallingford, UK, 886 pp.Thornley, J.H.M. and Johnson, I.R. (1989) Plant and Crop Modelling. Oxford

University Press, Oxford, UK.Wilson, E.O. (1978) On Human Nature. Harvard University Press, Cambridge,

Massachusetts.


3 Basic Concepts DescribingAnimal Growth and Feed Intake

N.S. FERGUSON

Maple Leaf Foods Agresearch, 150 Research Lane, Guelph, Ontario,Canada, N1G [email protected]

Introduction

The simulation of animal growth potentially provides a way of predictinganimal performance and the subsequent effects on the production of pork,over a wide range of conditions with an accuracy that would otherwise beimpossible to accomplish. In addition, limiting factors within the porkproduction system can be identified, nutrient requirements predicted,meat quantity and quality estimated, more effective financial andmanagement decisions made, and the consequences of genetic selectionpredicted. Fundamental to any model predicting animal growth andvoluntary feed intake, is the theory describing how the animal grows andhow it interacts with its environment. The accuracy of defining thesebiological responses depends on the nature of the theory and howinclusive and/or exclusive it is of our understanding of animal growth ingeneral. The basic theory proposed in this chapter has been well definedand described in the literature, as well as successfully implemented in anumber of modelling applications (Ferguson et al., 1994; Emmans andKyriazakis, 1999; Wellock et al., 2003a,b). Essentially, it is driven by anadequate description of: (i) an animal in some state of being; (ii) theenvironment in which the animal exists; (iii) the type and quantity of feedgiven; and (iv) the health status. The combination of these componentsprovides the framework for predicting growth responses to a wide varietyof production scenarios and the numerous commercial applicationsthereafter (Fig. 3.1).

The following are the key assumptions and premises of the proposedtheory:


1. The animal will always attempt to achieve its potential rate of growthwhich is defined by its current state and genetic potential;2. The amount of feed eaten will be the lesser of what the diet can offer toachieve potential growth and the capacity of the gut, within the constraintof maintaining heat balance;3. Health status and stocking density are possible constraints on potentialgrowth;4. Predicted responses are of the average individual.

With an accurate description of the genotype, the potential growth rate ofthe animal may be predicted. When the nutritional and environmentalinputs are inadequate the animal will fail to achieve its potential growth; theextent to which it is constrained will be defined by a set of rules governingthe partitioning of nutrients according to the most limiting factor (e.g. aminoacid, energy, disease challenge, gut capacity, maintaining heat balance, etc.).The corollary to this suggests that the nutrient and environmental inputsrequired to achieve potential growth can be determined. Based on thisapproach, an adequate description of the genotype, the feed, health status,physical and social environment are required.

Basic Concepts Describing Animal Growth and Feed Intake 23

Animal

MaintenanceGrowth

RequirementsFeed

Desired IntakePotential Growth

ConstrainedIntake and Growth

Actual Intake and Growth

Grading

NutrientRequirements

PhysicalEnvironment

SocialEnvironment

GutCapacity

Carcass NutritionalManagement Manure

Economics LCF/Optimize Feed Budgets N and P

RESOURCES

CONSTRAINTS

Fig. 3.1. Framework of the processes involved in modelling growth and feed intakeand the subsequent commercial application (after Emmans and Oldham, 1988).

Animal Description

There is a plethora of mathematical functions describing the pattern ofpotential growth through various phases of life (Gompertz, 1825;Robertson, 1923; Brody, 1945; Von Bertalanffy, 1957; Parks, 1982; Black etal., 1986; Bridges et al., 1986; France et al., 1996). However, not all areappropriate, nor do they all meet the criteria for the framework proposedin this chapter. Wellock et al. (2004) examined these numerous functionsand concluded that the Gompertz function is a ‘suitable descriptor ofpotential growth’ because of its simplicity, accuracy and ease of application.According to this function, growth will reach a peak at approximately0.368 of the animal’s mature weight and will then decline to zero atmaturity. But a description of the potential growth of an animal must alsodeal with the systematic changes occurring in both chemical and physicalcomposition of the body. The detailed theory of how these parametersinteract to determine the daily rate of growth has previously beendocumented by Ferguson et al. (1994), Emmans and Kyriazakis (1999) andWellock et al. (2003a) and therefore only an overview will be presented inthis chapter. In summary, the Gompertz function is used to determine thepotential protein growth rate from which the growth of the remainingchemical components of the body (lipid, moisture and ash) can bedetermined. This is achieved using allometric relationships betweenprotein and lipid, moisture and ash (Emmans and Fisher, 1986; Moughanet al., 1990). Based on this approach, the inherent characteristics requiredto describe the animal (genotype) are:

1. The rate of maturing (B);2. The mature body protein weight (Pm);3. The inherent fatness or lipid:protein ratio at maturity (LPRm); and4. The allometric coefficients defining the relationships between proteinand water (the water:protein ratio, WPRm), and protein and ash(ash:protein ratio, APRm) at maturity. According to Emmans andKyriazakis (1995) these are constant for a number of breeds.

An important assumption here, is that the rate of maturing is similar acrossall four chemical components (protein, lipid, water and ash). Ferguson andKyriazis (2003) provided evidence to corroborate this assumption.Genotypes, therefore, will differ in a number of respects that affect theirpotential growth curves, including mature protein size, maturecomposition (fat, moisture and ash) and the rates of maturing.

Potential protein growth

Body protein weight over time is determined from the function:

Pt = Pm x e–e ln(–lnuo) – (Bxt) (kg/day),

24 N.S. Ferguson

where Pt = body protein weight at time t (kg)Pm = mature body protein weight (kg)uo = degree of maturity at birth (Pt0/Pm)B = rate of maturing constant (day�1)t = age (days);

while the rate of potential protein growth (pPD) is defined by:

pPD = B � Pt � ln (Pm/Pt) (g/day),

with maximum pPD (pPDmax), determined as:

pPDmax = B � 1/e � Pm (g/day).

The equations above indicate that the rate at which an animal growswill depend almost entirely on its current state and two inherentcharacteristics, B and Pm (Taylor, 1980). Potential protein deposition (pPD)will only be realized if the animal is able to ingest sufficient quantities ofenergy and the first limiting amino acid, and if the environment issufficiently cool to allow the animal to lose the subsequent heat produced.Otherwise, actual protein deposition rate (PD) will be lower than pPD.Examples of estimated constants for different sexes and strains of pigsderived from the literature and experiments are shown in Table 3.1.

Fat growth

It has been widely acknowledged that an animal has an inherent potentialrate of protein growth, as defined by its maximum rate of growth under


Table 3.1. Growth parameters from various literature sources.

Literature source and pig type B Pm LPRm WPRm APRm (/day) (kg) (kg/kg) (kg/kg) (kg/kg)

Ferguson and Gous (1993)LW � Landrace – entire males

(South Africa) 0.0107 38.7 2.60 3.30 0.21Ferguson and Kyriazis (2003)LW � Landrace – entire males

(South Africa) 0.0114 40.0 1.80 3.17 0.22Ferguson (2004, unpublished results)Commercial � Duroc – mixed sexes

(Canada) 0.0142–0.0156 33.0–34.0 2.0–2.3 3.40 0.21Knap (2000b)Commercial – mixed sexes (UK) 0.009–0.0170 31.0 1.4–4.7Kyriazakis et al. (1990)LW � Landrace – entire males (UK) 0.0150 35.0 2.50 3.05 0.19Wellock et al. (2003b)LW � Landrace � Pietrain – mixed sexes

(France) 0.0175 35.0 2.50 3.05 0.19

ideal conditions (Webster, 1993; Schinckel and de Lange, 1996; Moughan,1999; Schinckel, 1999; Knap et al., 2003). However, lipid growth does notappear to have a potential limit, because of its dependence on nutrition, butrather a desired (preferred) rate of fat deposition. Emmans (1981) alludedto the concept of a ‘desired lipid growth’ to quantify the relationshipbetween protein and fat growth and voluntary feed intake. In subsequentpapers by Kyriazakis and Emmans (1992a,b, 1999) and Ferguson andTheeruth (2002), there is evidence indicating that pigs that are fatter than‘normal’, will attempt to correct this deviation once the limiting conditionhas been removed. Normal, in this case, is defined as the body fat content ofpigs, with a similar body protein content, grown under ideal dietary andenvironmental conditions. This desired or preferred fatness is bestdescribed in relation to body protein in the form of a lipid:protein ratio atmaturity (LPRm) and, during growth, an allometric coefficient relating lipidcontent to protein (bl) (Emmans and Kyriazakis, 1999). The desired bodyfatness (dLt), at a point in time, is therefore defined as:

dLt = LPRm � Pm � (Pt/Pm)bl (g/day),

where bl = 1.46 � LPRm0.23 (after Emmans, 1997).

The preferred rate of fat deposition (dLD) can therefore be described as:

dLD = pPD � LPRm � bl � (Pt/Pm)bl-1 (g/day).

At any age, dLD can be predicted merely as a function of the currentprotein weight of the animal. However, the actual rate of fat deposition(LD) and body fat content (Lt) will be dependent on other nutritional andenvironmental factors, including the quantity and quality of foodconsumed, the protein:energy ratio in the diet, environmental conditions,and the state of the animal. With an estimate of dLt, it becomes possible todetermine any compensatory growth responses. Any differences betweenLt and dLt will result in larger or lower daily fat gains. For example,feeding a poor quality diet (e.g. low protein:energy) will result in excess fatdeposition while restricting feed intake will be associated with a leaneranimal. Compensatory responses are determined by adding the desired fatgrowth (dLD) and the difference between actual body fat (Lt) andpreferred body fat content (dLt):

LD = dLD + (dLt – Lt)/1000 (g/day).

If the animal is fatter than desired then LD on the following day will be less,in order to compensate for the extra fat deposited the previous day(Kyriazakis et al., 1991; Ferguson and Theeruth, 2002). Provided it is possiblethe animal will deposit less fat on the following day. Similarly, if the animal isleaner than expected, for a given protein content, then LD would be higherthan dLD. An important corollary to the concept of maintaining a desiredlevel of fatness is that at all times the animal can utilize body fat reserves, to agreater or lesser extent, to supplement dietary ME, when the need arises.The use of body fat reserves is limited to periods when dLD is less than or

26 N.S. Ferguson

equal to 0. It is therefore possible to obtain significant protein growth ratesat the expense of fat growth, which would not be possible if a minimum lipidto protein ratio was used (Moughan et al., 1987; Pomar et al., 1991).

Moisture and ash growth

As the allometric coefficient describing the relationship between bodyprotein and body moisture content is not unity, the method of determiningmoisture deposition (WD) is similar in approach to that of determining fatgrowth viz.

WD = PD � WPRm � bw � (Pt/Pm)bw-1 (g/day),

where bw = 0.855 (range from 0.83 to 0.90)

after Emmans and Kyriazakis (1995) and Moughan et al. (1990).The relative proportion of ash varies little between sexes and strains,

with the rate of ash growth (AD) proceeding at a constant proportion ofprotein growth (Moughan et al., 1990; Ferguson and Kyriazis, 2003)between 0.19 and 0.22 such that:

AD = 0.20 � PD (g/day).

Live weight gains

Empty body weight gains (EBWTg) for each day will be calculated fromthe sum of the four components, after all other constraints or conditionshave been met, including environmental

EBWTg = PD + LD + AD + WD (g/day).

the empty body weight gains are added to the empty body weight at thestart of the day to give the empty body weight at the end of the day.

To translate empty into total body weights, gut fill has to be considered.Gut fill is determined from the equation of Whittemore (1998):

Gut fill = 1.05 + 0.05 � (0.008 � crude fibre � 1000 – 40) (g/day),

where crude fibre (CF) is a dietary input value, the daily live weight gains(ADG) are calculated as:

ADG = EBWTg � Gut fill (g/day).

Body weight at any given time (BWTt ) becomes:

BWTt = BWT(t-1) + ADG/1000 (kg/day).

Similarly for each body component, their weights equal the sum of theirstarting weight and growth rate for each day. Whether the animal is able toachieve its potential growth rate each day is dependent on the feed beingoffered, the health status and on the environment in which it is housed.


Prediction of Voluntary Feed Intake

The principle behind predicting voluntary feed intake assumes that ananimal will eat what it needs to grow to its potential, within the constraintsof gut volume, health, social stresses and environmental temperature (Fig.3.1). The basic concept was first proposed by Emmans (1981) and hassubsequently been incorporated into a number of simulation models thatpredict voluntary feed intake in growing pigs (Ferguson et al., 1994; Knap,1999; Wellock et al., 2003a). For a more detailed explanation of theprinciples, refer to Kyriazakis and Emmans (1999).

Desired feed intake

The basic premise on which the prediction of voluntary feed intake isbased is that a pig will attempt to consume an amount of feed daily thatwill satisfy its requirements for both energy and protein. Unlike the morepopular assumption that animals ‘eat for energy’ (Schinckel and de Lange,1996), the theory of desired feed intake considers the possibility thatanimals may ‘eat for protein’ (Ferguson et al., 2000a,b). Therefore, thedesired feed intake will be the quantity of the diet needed to satisfy therequirement for the most limiting of either energy or an amino acid, undernon-limiting circumstances.

Energy most limiting

To determine energy requirements for growth and maintenance, use ismade of the ‘Effective Energy’ system proposed by Emmans (1994, 1997).The effective energy required (EER) by the animal is described as follows:

EER = Em + 50 � PD + 56 � LD (kJ/day),

where Em = Maintenance energy requirement (kJ/day)= (1.63 � Pt � Pm�0.27) � 1000.

The definition of Em is not the same as the ‘typical’ classification thatequates maintenance energy requirements with fasting heat productionbecause it removes the effect of the energy lost from the synthesis andexcretion of nitrogen in the urine during fasting. Maintenancerequirements also need to be adjusted for activity and health status. Thiswill be discussed in more detail later: suffice it to say that activity anddisease can increase Em by as much as 0.15 and 0.20, respectively. Inaddition, disease can also reduce the level of activity.

The effective energy content (EEC) of a feed may be described as theamount of energy available for maintenance and tissue deposition afterdeducting energy losses resulting from digestion and defecation. The effectof fermentation heat losses is considered negligible. The EEC is calculatedas follows:

28 N.S. Ferguson

EEC = MEc – 4.67 � dCP – 3.8 � IOM + k � 12 � dCL (kJ/day),

where ME = Metabolizable Energy of the feed (kJ/g)

MEc = ME corrected for zero nitrogen retention (MEc = ME –5.63 � dCP)

IOM = Indigestible organic matter or indigestible carbohydratecomponent (g/kg)

dCP = Digestible crude protein content of the feed (g/kg)

k = Proportion of dietary fat retained as body fat (assumedbetween 0.3 and 0.8)

dCL = digestible crude lipid content of the feed (g/kg).

The feed intake that will allow the potential energy requirements to be metin a thermoneutral environment with no social deviances (dFIe), iscalculated as:

dFIe = EER/EEC (g/day).

Protein (amino acid ) most limiting

If protein, or more precisely an amino acid, is the first limiting nutrient in thefeed then the desired feed intake will be based on the protein (amino acid)requirement and the concentration of dietary protein (available amino acid).Similar to energy requirements, protein requirement is the sum of idealmaintenance and potential protein growth, and their respective efficiencies ofutilization. Recent publications have provided evidence to justify theseparation of maintenance protein requirement into its various constituentsand the inclusion of the different amino acid profiles (Table 3.2), to accountfor more specific protein losses, including protein turnover, gut andintegument losses (Moughan, 1999; Boisen et al., 2000; Whittemore et al.,2001c; Green and Whittemore, 2003; de Lange, 2004). In addition, if aminoacid requirements are to be expressed in terms of ‘standardized’ ilealdigestible values then, by definition, the endogenous losses from the gutunassociated with the feed must be included in the requirements. Moughan(1999), Boison et al. (2000) and Green and Whittemore (2003) provide adetailed exposition of the determination of maintenance proteinrequirements. In summary, the individual ideal maintenance constituents are:

1. Protein that is deaminated and not reused, which is estimated to be 0.06of total protein turnover. This is divided into two components, proteinturnover associated with maintaining (PLm) and retaining (PLnm) proteintissue. Both these processes involve different amino acid profiles (Table3.2) and therefore need to be determined independently.

PLm = 8 � Pt/Pm0.27 (g/day)

PLnm = 0.06 � (PD/0.23 x Pm/(Pm–Pt)) – PLm (g/day).


2. Integument protein losses (PLsh) which, according to Moughan (1999),may be quantified as:

PLsh = 0.105 � BWT0.75 (g/day).

3. Total protein endogenous gut loss (PLel) includes losses from bothsecretions (PLsec) and physical effects (PLpe) of the feed on the intestinallining. The latter gastrointestinal lining losses are a result of the passage offood and the lack of reabsorption of these amino acids. The inclusion ofboth sources of gut loss is important when the supply of amino acids isexpressed in standardized ileal digestible terms (AmiPig, 2000). Intestinaldisease is likely to increase PLel significantly, but the exact extent of theeffect is unknown. If the cost of disease on maintenance protein is to beconsidered, it is proposed that PLel could be increased by as much as 0.20,depending on the severity of the disease. According to Moughan (1999),Whittemore et al. (2001b) and de Lange (2004):

PLsec = 0.57 � BWT0.75 (g/day)

PLpe = 15 g per kg DM intake (g/day)

or PLpe = 1.19 � BWT0.75 (g/day)

PLel = (PLsec + PLpe) � (1 + DiseaseEffect) (g/day).

4. The ideal protein requirement for maintenance (Pmaint) is the sum ofthe four constituents and the efficiency of utilization of absorbed proteinfor maintenance (em). Under conditions of normal health em is assumed tobe 0.95, such that:

Pmaint = (PLm + PLnm + PLsh + PLel)/em (g/day).

With these metabolic functions placing demands on different amino acids, itis necessary to have a specific profile for each amino acid. Table 3.2 providessuggested amino acid profiles for the various functional requirements.

Boisen et al. (2000) indicated that maintenance protein losses are highin methionine, cysteine and threonine and therefore requirements forthese amino acids must be increased accordingly. Table 3.2 shows thesignificantly higher M+C, Thr and Trp coefficients for PLm, relative to

30 N.S. Ferguson

Table 3.2. Profiles of the amino acid coefficients (expressed as mg/g protein) used for the variousconstituents of protein requirements (after Green and Whittemore, 2003 and de Lange, 2004).

Lys M+C Thr Trp Ile Leu P+T His Val

Protein Deposition (PD) 70 37 38 10 35 75 63 30 45Maint Turnover (PLm) 65 75 90 17 49 45 79 21 44Non Maint Turnover (PLnm) 66 32 38 10 34 75 63 28 45Skin and Hair Loss (PLsh) 43 55 32 9 24 50 47 12 36Endogenous gut losses (PLel) 54 54 46 23 36 60 96 21 63

coefficients for PD. A consequence of these differences in requirements forindividual amino acids, is that there is no longer a constant proportionbetween each other and, therefore, relating the requirements of the aminoacids to lysine is no longer appropriate nor correct (de Lange et al., 2001;de Lange, 2004). For example, Thr:Lys ratio can be 0.64 in pigs < 20 kgbut increase to 0.70 in finisher pigs (>100 kg).

The ideal protein requirement for growth (Pg) is a function of pPDand the efficiency of ideal protein utilization (eg). A certain amount ofinefficiency does exist when dietary available amino acids are convertedinto body tissue, with the result that ideal protein requirements need to beadjusted before being stated as actual requirements. Efficiency of proteinutilization according to Kyriazakis and Emmans (1992b) is a function ofdietary energy and digestible protein such that eg = 0.0112 � ME/dCPwith a maximum of 0.814. However, there is evidence to suggest that themaximum is closer to 0.85 (Ferguson and Gous, 1997; Green andWhittemore, 2003). An important assumption with using this function isthat eg is constant across sexes, strains and breeds of pigs and amino acids(Kyriazakis et al., 1992b). Pg can therefore be calculated as:

Pg = pPD/eg (g/day).

Total ideal protein requirement (Preq) is the sum of maintenance andgrowth:

Preq = Pmaint + Pg (g/day).

To determine the amount of feed required to satisfy potential growth, theavailable ideal protein content of the feed has to be known. This isdetermined by multiplying the digestible protein content of the diet (dCP)by the value of the protein relative to an ideal balance (BV). The BV valueis the ratio of the proportion of the most limiting amino acid in digestibledietary protein over the proportion of the same amino acid in ideal bodyprotein. Therefore, the desired feed intake to satisfy ideal proteinrequirements (dFIp) is:

dFIp = Preq / (dCP � BV) (g/day).

Constrained feed intake

A potentially limiting factor, preventing an animal attaining its potentialrate of growth is the interaction between the capacity of the gut and thebulk density of the diet. There is a limit to the volume of food an animalcan ingest, which is determined partly by the size of the animal and partlyby the indigestible components of the diet. For example, a young pig fed ahigh fibre diet will have a lower feed intake than an older pig. This limitedintake capacity is referred to as the constrained feed intake. Using thisconcept of a bulk constraint (Tsaras et al., 1998) is a more rationalapproach to determining dietary constraints than that of imposing fixed


maximum feed intake limits based on animal size (Black et al., 1986)irrespective of the actual dietary constituents. Kyriazakis and Emmans(1995) and Whittemore et al. (2001a, 2003) have proposed the use of waterholding capacity as a means of estimating the bulk constraint of a diet.Unfortunately estimates of water holding capacity for diets are not readilyavailable and therefore an alternative approach is proposed using the IOMcontent (indigestible component) of the diet to predict the bulk density ofthe diet (BLKDN):

BLKDN = 0.36 + (0.857 + form) � IOM,where IOM = OM – digOM (kg/kg)

OM = organic matter (1-ash)DigOM = digestible organic matter (Noblet et al., 2004)form = physical form of the feed where with pellets: form = 0.0;crumbles: form = 0.01; mash: form = 0.02.

The maximum feed intake on any one day or constrained feed intake (cFI)is determined by the following equation, which also incorporates arudimentary adjustment for breed differences in appetite capacity:

cFI = ((�26.78 + (171.34 � Pt) + (�2.3316 � Pt2) )/ BULKDN) �AdjustBlk (g/day),

where AdjustBlk = appetite factor depending on genotype.

The equation considers both the size effect of the animal and theindigestible component of the diet, in determining a constrained intake. Inthis case, the contribution of size is a quadratic function of protein weight.

Actual feed intake

The desired feed intake (dFI) of the pig in a thermal neutral environmentwould be the larger of dFIe and dFIp while the actual daily feed intake(aFI) would be the lesser of dFI and cFI. For a perfectly balanced diet,dFIe would equal dFIp. The decision-making process to determine aFI isillustrated in Fig. 3.2.

Consequences of feed intake on growth

There are three possible pathways to consider, each with their ownconsequences on protein and fat growth assuming the physicalenvironment is not limiting.

1. When energy is most limiting, such that aFI = dFIe

This is the simplest case where the animal consumes enough energy andprotein to satisfy both pPD and dLD. High protein diets will reduce theEEC of the diet.

32 N.S. Ferguson

2. When protein is most limiting, such that aFI = dFIp

With protein (or more specifically) an amino acid limiting, the excessenergy consumed above that for pPD and maintenance will be deposited asextra fat (Ferguson and Theeruth, 2002). The additional fat deposited willresult in the pig being fatter than its preferred level of fatness. Thefollowing day the animal will attempt to compensate by depositing less fatin order to return to its desired state. It could only achieve this if theconstraining factor, which had caused it to deposit more fat, were removed.In this case, it would mean increasing the concentration of the limitingamino acid. Associated with the increase in fat deposition is the amount ofheat produced by the animal. If the heat produced is greater than thatwhich could be lost to the environment then additional constraints areplaced on growth rate and feed intake. This will be discussed in moredetail in the environmental section below.

3. When intake is constrained by gut capacity, such that aFI = cFI

Voluntary intake is likely to be constrained by the gut capacity in youngpigs (< 50 kg, Whittemore et al., 2003) and/or when the nutrient density ofthe diet is low (high bulk diet). In cases such as these, the question becomeswhich nutrient becomes the most limiting? This is an importantconsideration as it determines whether the animal can attain pPD or not. Ifenergy was the most limiting then the animal may still be able to consumesufficient protein to sustain pPD but not dLD. Biological processes dictate


dFIe dFIp

Diet details

Feed bulk

cFIdFI

greater

Pig description

Potential growthDesired fatness

Gut capacity

Actual FI

lesser

Fig. 3.2. Decision-making process to determine actual daily feed intake.

that energy should be allocated first to maintenance functions and then toprotein and lipid growth. If there is insufficient energy for pPD then PDwill be reduced to:

PD = eg � ((cFI � BV � dCP) – Pmaint ) (g/day).

Finally, any remaining energy will be deposited as fat (LD). This amountwill be less than desired resulting in a reduction from the animal’s desiredlevel of body fatness, such that:

LD = [(cFI � EEC) – (50 � PD)] / 56 (g/day).

If protein is more limiting than energy, then dietary protein is allocatedaccording to priority with maintenance first and then the remainder togrowth. The limited amount of dietary protein available for growth willmean that PD is less than pPD and the energy that would have been used forpPD (pPD-PD) is deposited as fat. The amount of fat deposited will dependon the constrained feed intake; it may be higher or lower than dLD.

Compensatory responses

The work by Kyriazakis and Emmans (1991), de Greef (1992), Tsaras et al.(1998) and Ferguson and Theeruth (2002), provides substantialexperimental support for the previously discussed compensatory growththeory. These authors found that when young pigs were made fatter, byeating a poor quality diet (low CP:ME ratio), and then were placed on ahigh protein diet, they deposited fat at a much slower rate, than pigs thatwere leaner. These data corroborate the idea of a preferred level of fatnessand the desire of the pig to maintain this level (Fig. 3.3).

The implication of this compensation is that pigs will adjust theirvoluntary intake to maintain pPD but at the expense of LD once thecausative factor has been removed. It is therefore possible for negative LDto occur simultaneously with a positive PD, provided there is enough fat tolose. A minimum amount of body fat is essential for sustaining life, and isoften expressed in terms of a minimum body lipid:protein ratio (L:Pmin).Wellock et al. (2003a) assumed a L:Pmin ratio of 0.1 but this was notsubstantiated. In practice, it is highly improbable that pPD will continueunabated when the ratio of body lipid:protein decreases below 0.3, even inyoung pigs who already have a low L:P ratio (Stamataris et al., 1991).

Physical Environment

Crucial to the prediction of voluntary feed intake and deposition of proteinand fat tissue is the influence of the surroundings of the animal. There area number of physical factors that affect the amount of heat the animal canproduce and lose from its body. The interactions between the environment,animal and diet are regulated by how much heat the animal can lose to itsenvironment. Therefore, to include the physical environmental effects on

34 N.S. Ferguson

feed intake it is necessary to compare the daily heat production (THP) withthe maximum (THLmax) and minimum (THLmin) daily heat loss limits. IfTHP falls within these upper and lower bounds then growth and feedintake are unaffected by the thermal environment. However, should THPextend beyond these boundaries, there will be changes in predicted feedintake and body composition (Fig. 3.4).

Any external stimuli that can affect the temperature the animal actually‘feels’ at its level will influence the rate of heat loss from the animal(Whittemore, 1983). This includes factors such as ventilation, the type of floormaterial and the insulation of the house. Therefore, ambient temperatureneeds to be adjusted accordingly, to reflect an ‘effective’ temperature (Te).

Calculation of THLmin and THLmax

Total heat loss (THL) is the sum of the non-evaporative (or sensible, SHL)and evaporative heat loss (EHL) components. Therefore, to determineTHLmax and THLmin the minimum and maximum amounts of SHL andEHL, respectively, have to be determined.

Evaporative heat loss (EHL)

Evaporative heat loss is minimal (EHLmin) and is constant for a particularlive weight at low temperatures (Black et al., 1986, 1999). The maximumEHL is normally constant, and several times greater than EHLmin, but athigh temperatures the animal will wet its skin and therefore a greateramount of EHL occurs (Fig. 3.5) (Knap, 2000a).


Desired

Change diet

Improve diet

Removerestriction

Restrictintake

Protein weight (kg)

Lipi

d w

eigh

t (kg

)

Fig. 3.3. The compensatory responses in fatgrowth when animals are made either fatteror leaner than their preferred or desired levelof fatness.

Fig. 3.4. The relationship betweentemperature and total heat loss, and themaximum (THLmax) and minimum (THLmin)bounds within which growth and feed intakeare unaffected.

THLmin

THLmax

Temperature

Bounds for totalheat lossTo

tal H

ea

t L

oss

}

The following descriptions of EHLmin and EHLmax are modifiedfunctions from Bruce and Clarke (1979), Black et al. (1986) and Knap(2000a). Minimum EHL is defined as:

EHLmin = (8+0.07 � BWT) � (0.09 � BWT0.67) (Watts/day).

The maximum EHL is more complicated as it includes an additionalamount of heat loss from evaporation of wet skin. Without losing any heatfrom wet skin, the maximum EHL (EHLhot) is determined as:

EHLhot = (12+100 � BWT-0.33) � humidityfactor � 0.09 � BWT0.67

(Watts/day),where humidity factor = 1.36 – (Waterair/35.9)Waterair = water content of the air calculated from relative humidity (g/kg).

The extra heat lost from the pig wetting its skin is calculated as:

EHLwet = ((45.4 � Vel0.6) � BWT-0.13 � (Abs-Waterair)) � 0.35 � 0.09 �BWT0.67 (Watts/day),where Vel = air speed (m/s)Abs = water content of the air at 100% Relative Humidity (g/kg).

Maximum EHL can be calculated as:

EHLmax = EHLhot + EHLwet (Watts/day).

Sensible or non-evaporative heat loss (SHL)

Sensible heat loss (SHL) depends on the temperature gradient between theenvironmental temperature and the surface of the pig. It is dominantunder cold conditions and diminishes at a constant rate with increasingtemperature. To incorporate the effects of behavioural and physiologicalchanges, such as huddling, vasoconstriction and vasodilation, associatedwith environmental stimuli, the model determines a maximum (SHLmax)and a minimum (SHLmin). The general theory of how SHL changes withtemperature is illustrated in Fig. 3.6.

36 N.S. Ferguson

Temperature

Sen

sibl

e he

at lo

ss (

SH

L)

SHLmin

SHLmax

Above thermoneutral temperature

Temperature

EHLmax

EHLminEva

pora

tive

heat

loss

(E

HL)

Fig. 3.5. Relationship between evaporativeheat loss and temperature.

Fig. 3.6. Relationship between sensible(non-evaporative) heat loss and temperature.

The amount of heat lost through SHL depends on the slope of the linein Fig. 3.6 (HLslope), the temperature difference between the animal and itsimmediate surroundings, and the surface area from which the heat is lost.Therefore, SHL can generally be defined as:

SHL = HLslope � (Body Temperature – Te) � BWT0.67 (kJ/day),where HLslope = 48Te = effective temperature.

A minimum amount of heat can be stored by allowing body temperature toincrease from 38 to 40.5 when temperatures exceed the upper bound of thethermoneutral range. If the animal is hot or cold then certain anatomicaland behavioural changes occur, resulting in the core body temperatureeither rising (40.5°C, SHLmax) or remaining constant at 38°C (SHLmin),respectively. The SHL component contributes very little towards heatproduction at high temperatures, because sensible heat loss depends on thedifference in temperature between the environment and the surface of thepig (Mount, 1975). At an effective temperature of 40.5°C, SHL will be zero.

THLmax and THLmin

Maximum total heat loss is the sum of EHLmax and SHLmax while THLmincomprises EHLmin and SHLmin.

Comparison of THL with THP

The final stage in determining the effects of the thermal environment ongrowth and feed intake is to compare the heat produced (THP) by the pigwith THLmax and THLmin. The THP is calculated as the difference betweenthe energy consumed and that retained for protein and fat deposition:

THP = (aFI � ME) – (23.8 � PD) – (39.6 � LD) (kJ/day).

Comparing THL with THP determines whether the animal is too hot, coldor thermoneutral, and enables the appropriate voluntary intake andgrowth responses to be calculated.

Responses to environmental constraints

1. THP > THLMAX. When the amount of heat the animal produces is greaterthan the maximum that can be lost to the environment then the pig iseffectively ‘hot’ and, therefore, will attempt to reduce THP, such that THP= THLmax. There are three ways of doing this, depending on thedifference between heat loss and heat produced. First, activity levelsdecline and therefore maintenance energy requirements will decrease.According to Knap (2000a) this reduction can be as much as 7.5%.Secondly, LD can increase to improve the efficiency of energy utilizationand therefore reduce the heat burden. Thirdly, and most often, feed intakedeclines to maintain the energy balance:


aFI = dFIe – (THP – THLmax)/ME (g/day).

The impact this has on PD and LD depends on whether there is stillsufficient protein consumed to meet pPD, given that PD is determined by:

PD = eg � ( (aFI � BV � dCP) – Pmaint) (g/day).

Fat deposition (LD) may increase or decrease depending on the severity ofthe reduction in aFI, and is calculated from the difference between energyintake and the energy retained for PD and lost as heat.

LD = {(aFI x ME) – THP – (23.8xPD)} / 39.6 (g/day).

In most cases, LD will decline rather than increase (Close, 1989). 2. THP < THLMIN. If the amount of heat lost to the environment is greater thanthe amount produced then the animal is cold and extra heat (coldthermogenesis) will be required to maintain body temperature and ensureTHP = THLmin. The energy difference between THLmin and THP, underthermoneutral conditions, will cause maintenance requirements to increaseand therefore feed intake will increase by:

ExtraFI = (THLmin – THP)/ME (g/day).

The only constraint on ExtraFI, is the bulk constraint, cFI. If (ExtraFI + aFI)> cFI then feed intake will decline to cFI, and PD and LD will be adjustedaccordingly, as previously discussed under Constrained Feed Intake.

The lower and upper critical temperatures, which define thethermoneutral boundary, as well as the ideal or comfortable temperature,can be determined from THP and the various minimum and maximumheat loss components.

Social Environment

Under commercial growing conditions the environment within which thepig exists is far from ideal, and changes over the growing period. Factorscontributing to this changing environment include disease challenges,decreasing air quality, reduced feeder space, high stocking density andother social stresses. Of these factors only the influences on performance ofstocking density, and to a lesser extent disease, have been quantified(Kornegay and Notter, 1984; Hyun et al., 1998; Black et al., 1999; Morganet al., 1999; Knap, 2000a).

Stocking density

Recent evidence suggests that stress associated with high stocking densityresults in a reduction in protein growth, irrespective of feed intake, such thatthe amount of feed consumed is driven by the lower PD requirement and not

38 N.S. Ferguson

vice versa (Chapple, 1993; Baker and Johnson, 1999; Morgan et al., 1999;Matteri et al., 2000; Ferguson et al., 2001). Based on these findings and withinthe current context, it is reasonable to assume that stocking density exerts itseffect by reducing protein growth through a lower rate of maturing. Whenthe amount of space per pig declines below a minimum value then the rate ofmaturity will be reduced accordingly. The function used to implement thiseffect is based on the surface area of the pig and the amount of space available(kg0.67/m2) (StDen). The adjusted rate of maturity (Badj) is calculated as:

Badj = B � (1 – ((StDen –25) /50)) (/day),

where StDen = (pigs/pen � BWT0.67) / pen size (kg0.67/m2).

Disease or health and well-being status

Disease affects the growth performance and feed intake of growing pigs,the response depending on the source and severity of infection (Baker andJohnson, 1999; Greiner et al., 2000; Escobar et al., 2002). The possibleeffect that health status has on growth under commercial conditions isillustrated in Fig. 3.7. Although animals may show no signs of clinicaldisease, the sub-clinical disease challenge can reduce performance.

The main effects of sub-clinical disease appear to be an increasedmaintenance requirement, reduced nutrient digestibility, reduced proteingrowth and feed intake (Black et al., 1999; Knap, 2000a). How these aremediated is not clear. Within the proposed modelling framework, the question becomes what factors, be they animal or dietary, are likely to beaffected by disease or health status, and how are they adjusted in a simple


Age (days)

Live

wei

ght (

kg)

50 75 100 125 150 175 200 22510

30

50

70

90

110

130

At 110 kg

8 days longer to market

18 days longer to market

PoorGoodOptimal

Fig. 3.7. Effects of sub-clinical disease challenge on changes in live weight over time. Thehealth status of the pig is indicated by Optimal, Good and Poor.

but meaningful way. Logic would dictate that of the animal parameters,mature protein weight is unlikely to be affected, except under a severedisease challenge, but the rate at which it achieves this will be adverselyaffected. With little evidence to support or disprove this theory, it isproposed that a proportional reduction in B, relative to the degree ofdisease challenge or health status, be adopted to account for the reductionin protein deposition and subsequent feed intake. In addition, maintenanceprotein and energy requirements will be increased, while activity levels willbe reduced.

Reduction in rate of maturity

The model uses a health profile to adjust B. This profile represents thehealth status, well-being and barn conditions post weaning (Fig. 3.8) andcan be modified depending on the health status of the animal. Based onretrofitting data, typical values for high health pigs grown undercommercial conditions are in the range 0.96–1.00, while for diseased pigsthe value could be as low as 0.80.

The health coefficient from the profile is used to reduce B andtherefore PD, LD and feed intake accordingly. The poorer the healthstatus the more severe the reduction in PD, LD, live weight and feedintake. Although simplistic in design, and arguably scientifically naïve, theapplication of this approach under commercial conditions has shown toimprove significantly the accuracy of prediction (Fig. 3.9).

Increase in maintenance requirements

Black et al. (1999) suggest that maintenance energy be increased by asmuch as 0.30 and protein deposition decreased by 0.10 as a consequenceof disease. With insufficient data to justify a 30% increase in maintenanceenergy, a more conservative 20% increase is proposed. Although there are

40 N.S. Ferguson

0

0.2

0.4

0.6

0.8

1.0

1.2

0 5 10 15 20 25 30 35 40

Weeks after weaning

Hea

lth c

oeffi

cien

ts

Fig. 3.8. Health profile illustrating the changes in health and well-being status post weaning.

no data to justify similar effects on maintenance protein, for the sake ofbrevity, the same increase is applied, such that:

Maint_adj = 1/Health_status,where Maint_Adj <= 1.20 and >= 1.0.

Maintenance protein (particularly endogenous protein losses) and energyrequirements are increased by multiplying Pmaint and Em by theadjustment factor. Simultaneously, activity levels are reduced between 1.25(healthy) and 1.00 (sick), depending on the health status. A reduction inactivity will reduce maintenance energy requirements but not enough tocompensate for the increase due to disease. A consequence of the increasedmaintenance requirement, reduced B value and a lower feed intake will bea reduction in PD and LD.

Commercial example

Comparative data from a number of different commercial production unitswithin Canada were used. The main cause of the differences inperformance between units was the health and well-being status of thepigs. The data were separated according to the performances of the best(High) and worst (Low) health status units, and were compared against themodel predictions. To simulate the differences in health conditions, thehealth status coefficients of the Low health units were assumed to be 0.9


–10.0

–7.5

–5.0

–2.5

0.0

2.5

5.0

7.5

10.0

21 35 49 63 77 91 105 119 133 147 164

Age (days)

Dev

iatio

ns fr

om a

ctua

l wei

ght (

%)

No health adjustment With health adjustment 95% Confidence limits

Fig. 3.9. Comparison of the deviations from actual live weight over time between predictedresults, which include and exclude health status adjustments.

times the High health units over the live weight range of 6 to 108 kg. Thegrowth rate and feed intake results are shown in Figs 3.10a and b.

The similarity between actual versus predicted suggests that theproposed approach does not produce unrealistic results and is sufficientlysensitive to differentiate between animals differing in health status.However, it would be inappropriate and too simplistic to assume that theprocess is valid as a means of quantifying the complex effects of specifichealth challenges. Nevertheless, the results indicate that it is a reasonableattempt to incorporate the adverse effects of reduced health status ongrowth and feed intake.

Testing Model Theory

Critical to any model is the need to test the underlying theories that driveor control the modelling process. This is not an easy exercise, as an

42 N.S. Ferguson

(a)

(b)

300

400

500

600

700

800

900

Gro

wth

rate

(g/d

ay)

High health(6–29 kg)

Low health(6–29 kg)



500

800

1100

1400

1700

2000

2300

Feed Inta

ke (

g/d

ay)





Fig. 3.10. Comparison of (a) growth rates and (b) feed intakes, between Actual ( ) andPredicted (�), for High versus Low health status producers.

accurate prediction under one set of circumstances does not mean that it is‘valid’ (Black, 1995). However, confidence in the validity of the model maybe gained when accurate predictions, for a number of diversecircumstances, are consistently obtained. Unfortunately, there is no specificway in which models can be validated other than by comparing thesimilarities in the model predictions with experimental outcomes. Thethree key components of the proposed model that need to be tested arethe growth and intake responses when energy is limiting, when protein(amino acid) is limiting and when ambient temperatures change.

Responses when energy is limiting

Nursery pigs

To evaluate the effect of Effective Energy content in young nursery pigs,data from a recent trial (Ferguson, 2005 unpublished results) were used.Five energy levels, ranging from 13.00 to 13.82 MJ/kg, were fed to pigsbetween 12 and 25 kg live weight. The animal definition parameters usedwere: B = 0.0142, Pm = 33.0kg, LPRm = 2.30, WPRm = 3.40, APRm =0.20. The results of the comparison between actual and predicted growthrates and feed intakes are shown in Figs 3.11a and b. Given that youngpigs (< 30 kg) cannot eat sufficient to satisfy their high relative potentialgrowth irrespective of the nutrient density of the diet (Whittemore et al.,2001a), this comparison, in many respects, evaluates the ability of themodel to define the gut capacity and the effects of this constraint onpredicted performance. From Figs 3.11a and b, the results would suggestthat the method proposed in this chapter is sufficiently robust to predictfeed intake and performance within the 95% confidence interval of actualresults.

The higher predicted feed intake value at 13.00 MJ/kg was the result ofthe reduced efficiency of protein utilization associated with a lowME:digestible CP ratio (65 MJ/kg). As the minimum ratio, below which theefficiency of protein utilization will decline, is 73 MJ/kg (Kyriazakis andEmmans, 1992b) there will an increased demand for dietary protein tocompensate for the reduced efficiency of utilization. The increasedrequirement for protein has resulted in an increase in voluntary feedintake. Therefore, the slightly higher predicted ADFI at 13.00 MJ/kg wouldsuggest either an overestimation of the gut capacity or that the equationpredicting efficiency of protein utilization is underestimating the efficiencyin low ME:dCP diets. However, as the overestimation was within the 95%confidence limits, there is no justification for rejecting the status quo.

Grower-Finisher pigs

The data from Campbell et al. (1985) were used to compare the responsesto energy intake in grower pigs between 48 and 90 kg live weight. Theparameters used to describe the castrate genotype were: B = 0.0125, Pm


= 28.0 kg, LPRm = 4.0, WPRm = 3.00, APRm = 0.20. The lysine:energyratio was reported to be in excess of that required for maximum proteindeposition on ad libitum feed intake, therefore energy was always the mostlimiting nutrient. A summary of the differences between the predictedoutcomes from the model and actual data is shown in Figs 3.12a,b and c.

The most noticeable differences (> 1 standard deviation) wereconfined to PD and LD at very low energy intakes (55% of ad libitumintakes) where the model overestimated PD and underestimated LD.These differences are due, in part, to the difficulty in establishing therelationship between protein and fat deposition when energy is severelylimiting (restricted intakes) and secondly, in the inadequate description ofthe environmental conditions given in the scientific paper. Without a

44 N.S. Ferguson

(b)

(a)

–10

–8

–6

–4

–2

0

2

4

6

8

10

13.00 13.23 13.48 13.72 13.82Effective energy content (MJ/kg)

Dev

iatio

n fr

om A

ctua

l AD

G v

alue

s (%

)

–10

–8

–6

–4

–2

0

2

4

6

8

10

Dev

iatio

n fr

om A

ctua

l AD

FI v

alue

s (%

)

13.00 13.23 13.48 13.72 13.82Effective energy content (MJ/kg)

Fig. 3.11. Comparison of the deviations in (a) growth rates (ADG) and (b) feed intakes(ADFI), between Actual and Predicted in response to Effective energy in nursery pigs. (—)95% Confidence interval.


200

400

600

800

1000

20 25 30 35 40 45

DE Intake (MJ/day)

AD

G (

g/da

y)

(a)

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

20 25 30 35 40 45

DE Intake (MJ/day)

Feed:G

ain

(b)

proper measure of the housing conditions, a number of assumptions hadto be made (e.g. air temperature, insulation, relative humidity) andtherefore any one of these may not have held true. The differences inprotein, fat, water and ash content of the empty body at 90 kg live weightin pigs on ad libitum intake, were +5.3, �14.1, +8.0 and 3.2%, relative toexperimental results.

Fig. 3.12a. Comparison of actual (�) versus predicted (—) responses in growth rate (ADG)to digestible energy intake (DE Intake), in pigs grown from 48 to 90 kg live weight. Data fromCampbell et al. (1985). Bars represent 1 standard deviation.

Fig. 3.12b. Comparison of actual (�) versus predicted (—) responses in feed:gain ratio todigestible energy intake (DE Intake), in pigs grown from 48 to 90 kg live weight. Data fromCampbell et al. (1985). Bars represent 1 standard deviation.

Responses when protein is limiting

This evaluation was conducted to measure the effectiveness of the modelwhen crude protein or an amino acid is first limiting. The first testcompared the outcome of the model with two experiments (A and B)published by Gatel et al. (1992). Experiment A investigated the response inweaned piglets (between 8 and 26 kg) to increasing protein and amino acidconcentrations, with the amino acid:protein ratio remaining constant foreach of the six treatments. Experiment B investigated the growth responsesto increasing amino acid levels but keeping protein constant; hence anincreasing amino acid:protein ratio. The animal description parametersused were: B = 0.0137, Pm = 35 kg, LPRm = 3.0, WPRm = 3.02, APRm =0.20. The second test compared differences in total lysine content as well asdifferences in amino acid:energy ratios, using data from Kyriazakis et al.(1990) for pigs grown between 12 and 30 kg. The animal descriptionparameters used were: B = 0.0135, Pm = 48 kg, LPRm = 3.0, WPRm =3.4, APRm = 0.20. Although this experiment was primarily concerned withthe effects of choice feeding on performance in young pigs, it does provideresponses to single feeding systems that differ in their dietary crude protein(total lysine) content only. The results of the comparison are summarized inFigs 3.13 a, b and c. The results clearly show the similarity betweenpredicted and actual responses to increasing dietary amino acids. Very fewof the predicted values were outside of the range of 1 standard deviationabove or below the mean. This allows for a greater degree of confidence inthe model, and support for the underlying theory of growth and feedintake regulation, especially when protein and/or an amino acid is firstlimiting, as is often the case in the young growing pig.

46 N.S. Ferguson

0

50

100

150

200

250

300

350

400

20 25 30 35 40 45

DE Intake (MJ/d)

PD

and

LD

(g/

d)

(c)

Fig. 3.12c. Comparison of actual versus predicted responses in protein deposition (PD) (�, —)and lipid deposition (LD) (�, ....) to digestible energy intake (DE Intake), in pigs grown from 48to 90 kg live weight. Data from Campbell et al. (1985). Bars represent 1 standard deviation.


300

400

500

600

700

800

0.5 0.7 0.9 1.1 1.3 1.5 1.7Total lysine content (%)

AD

G (

g/d

ay)

(a)

Fig. 3.13. (a) Comparison of responses in growth rates (ADG) to total lysine content in the diet.(b) Comparison of responses in feed intake to total lysine content in the diet. (c) Comparison ofresponses in feed:gain (FCR) to total lysine content in the diet. Gatel Expt A, Actual (�),Predicted (—); Gatel Expt B, Actual (�), Predicted (....); Kyriazakis Actual (�), Predicted (– –).Bars represent 1 standard deviation.

600

700

800

900

1000

1100

0.5 0.7 0.9 1.1 1.3 1.5 1.7

Total lysine content (%)

Fee

d In

take

(g/d

ay)

(b)

1.00

1.25

1.50

1.75

2.00

2.25

0.5 0.7 0.9 1.1 1.3 1.5 1.7

Total lysine content (%)

FC

R (

g/g)

(c)

Responses to ambient temperature

To test the effects of the thermal environment, the data from Rinaldo andLe Dividich (1991) were selected. This study examined the performance ofgrowing pigs between 10 and 30 kg live weight when kept in one of fourdifferent temperatures, 12, 18.5, 25 and 31.5°C. The animal descriptionparameters used were: B = 0.0150, Pm = 35 kg, LPRm = 3.0, WPRm =3.3, APRm = 0.20. The differences between actual and predicted aresummarized in Fig. 3.14a and b. The only significant difference betweenthe model predicted and the reported results was in daily growth rates(ADG) at 12°C, which in turn affected the feed:gain ratio. The very lowADG observed by Rinaldo and Le Dividich (1991) is contrary to what isfound in most published literature on growth responses at lowtemperatures, where ADG remains constant at low temperatures (Nienaberet al., 1987; Ferguson and Gous, 1997; Wellock et al., 2003b). Noexplanation is given for the reduced growth rate reported in thepublication by Rinaldo and Le Dividich (1991).

Conclusions

The theory of growth and feed intake described in this chapter is based onthe proposition that an animal eats to grow to its potential, and if anythingprevents it attaining this growth, then it will grow according to what it haseaten. Foremost, therefore, is the need to predict desired feed intake andhow the subsequent interactions with the animal and its environmentinfluence the actual voluntary feed intake. Energy that is available formaintenance and productive purposes, after removing the heat increment

48 N.S. Ferguson

400

600

800

1000

1200

1400

8 12 16 20 24 28 32Ambient temperature (°C)

AD

G a

nd fe

ed in

take

(g/

day)

(a)

1

1.5

2

2.5

3

8 12 16 20 24 28 32

Ambient temperature (°C)

Fee

d:ga

in

(b)

Fig. 3.14a. Comparison of actual versuspredicted responses in growth rate (ADG) (�, ....) and feed intake (�, —) to ambienttemperature, in pigs grown from 10 to 30 kglive weight. Data from Rinaldo and Le Dividich(1991). Bars represent 1 standard deviation.

Fig. 3.14b. Comparison of actual versuspredicted responses in feed:gain (�, —) toambient temperature, in pigs grown from 10to 30 kg live weight. Data from Rinaldo andLe Dividich (1991). Bars represent 1standard deviation.

of eating and digestion, is compared with the requirements to predictvoluntary food intake. In addition, the response of the animal is to the firstlimiting nutrient rather than energy alone. Changes in the chemicalcomposition of the animal are based on nutrient and physical and socialenvironmental interactions as well as the current physiological state of theanimal. This includes the effects of health status and pig space. Live weightchanges are determined first, by predicting potential protein growth usingthe Gompertz growth function, and secondly, by calculating the remainingcomponents of the body through established allometric relationships withbody protein content. However, the exact change in body composition isgoverned by the desire to maintain an inherent body state, to which theanimal will attempt to return wherever possible. The constraining factorsmost likely to cause any deviations from normal growth will be: the gutcapacity, the physical and social environment, and the first limitingnutrient. When the model described here was used to predict results ofpreviously published data, the results produced were, with few exceptions,within the 95% confidence limits of the published data, suggesting thatboth the theory and the logic of the model appear to be valid. Where therewere incidences of departure from reality, they were associated withextreme conditions, which do not normally occur in commercial practice.

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52 N.S. Ferguson

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4 The Effects of Social Stressors onthe Performance of Growing Pigs

I.J. WELLOCK, G.C. EMMANS AND I. KYRIAZAKIS

Animal Nutrition and Health Department, Scottish Agricultural College,West Mains Road, Edinburgh, EH9 3JG, [email protected]

Introduction

Different published approaches to pig simulation modelling have advancedour understanding of pig performance under a wide range ofenvironmental conditions. They range from the first relatively simpleattempt to model pig growth by Whittemore and Fawcett (1974, 1976),where predictions were based upon empirical equations, to more recentand elaborate attempts such as those made by Black et al. (1986),Whittemore and Green (2002) and Pomar et al. (2003). These latter modelscontain various combinations of empirical and mechanistic equationsusually with an underlying biological basis. Attempts to predict feed intake,although still not universal, are more frequent in recent modelling attempts(e.g. Black et al., 1986; Bridges et al., 1992; Ferguson et al., 1994) and morefactors have been considered and introduced as model inputs. Stressors inthe physical environment, such as ambient temperature, humidity, airvelocity and floor type have been comprehensively modelled (e.g. Bruceand Clark, 1979; Black et al., 1986; Wellock et al., 2003a,b) allowingpredictions of performance under varying conditions to be made. Factorswhich may act as social stressors, which include group size (N), spaceallowance (SPA, m2/BW0.67), feeder space allowance (FSA, feeders/pig), andmixing on the other hand, have been largely ignored. This is mainly due toa lack of quantitative data on which to build models and a lack ofunderstanding of how such stressors affect performance. Effects of theinfectious environment are yet to be included in a systematic way.

The objective of this chapter is to describe how the effects of socialstressors on the performance of growing pigs can be quantified and toshow how these relationships, including variation between genotypes intheir ability to cope (AB), can be incorporated into a more general piggrowth model. The consequences of introducing individual variation intothe model are investigated and the difficulties of estimating parameter


values, with particular regard to AB, are described. Finally, the practicalimplications of AB in relation to production, welfare and genetic selectionare discussed along with potential future model developments.

Modelling the Effects of Social Stressors

The influence of social stress on pig performance, although undeniable, isfrequently underestimated and, in pig growth modelling, generallyignored. Black (2002) noted that ‘current pig models do not predict wellthe effects of stress encountered by pigs reared in commercialenvironments’. Only the pig growth model of NRC (1998) includes a socialstressor effect on performance, with SPA directly affecting dietary energyintake. The adjustment is calculated from one of three equations accordingto body weight (BW) and is added to dietary energy intake. However, thisis considered to be ‘a crude estimate [which] should be used with caution’particularly at the ‘lower end of the three weight classes’ (NRC, 1998).

Kornegay and Notter (1984) developed linear regression equationsrelating average daily feed intake (ADFI, kg), average daily gain (ADG, kg)and feed conversion ratio (FCR, kg/kg), to SPA and N for pigs in threeweight ranges. More recently Turner et al. (2003) did the same, using thesame three weight ranges (Table 4.1). This latter exercise was over a muchlarger data set and included group sizes of up to 120 as opposed to amaximum of 33 in the analysis of Kornegay and Notter (1984). Whilst theseequations give some insight into how N and SPA may affect performance,they are difficult to interpret and implement and fail to predict interactionsbetween the type of pig and the environment in which it is kept. Forexample, the equations of Kornegay and Notter (1984) and Turner et al.(2003) predict an ADG of zero when group size reaches 338 and 1363,respectively, in growing pigs. This seems unrealistic, since pigs in groups of

Effects of Social Stressors on Performance of Growing Pigs 55

Table 4.1. Equations from Kornegay and Notter (1984) and Turner et al., (2003)relating group size (N) to average daily gain (ADG, kg), average daily feed intake(ADFI, kg) and feed conversion ratio (FCR).

Kornegay and Notter (1984) Turner et al. (2003)

Weaner period (7.6 to 21.1 kg)ADG = 0.4178 – 0.0037N (R2 = 0.97) ADG = 0.416 – 0.00036N (R2 = 0.97)ADFI = 0.8317 – 0.092N (R2 = 0.97) ADFI = 0.618 – 0.00051N (R2 = 0.98)FCR = 1.9535 – 0.0051N (R2 = 0.94) FCR = 1.650 + 0.00004N (R2 = 0.96)

Grower period (26.6 to 53.5 kg)ADG = 0.6407 – 0.0019N (R2 = 0.43) ADG = 0.654 – 0.00048N (R2 = 0.90)ADFI = 1.5950 – 0.0025N (R2 = 0.87) ADFI = 1.790 – 0.00005N (R2 = 0.90)FCR = 2.4974 + 0.0037N (R2 = 0.94) FCR = 2.750 + 0.00179N (R2 = 0.97)

Finisher period (44.1 to 92.3 kg)ADG = 0.7497 – 0.0012N (R2 = 0.82) ADG = 0.715 – 0.00009N (R2 = 0.99)ADFI = 2.3748 + 0.0032N (R2 = 0.92) ADFI = 2.340 + 0.00033N (R2 = 0.84)FCR = 3.2182 + 0.0060N (R2 = 0.72) FCR = 3.329 + 0.00104N (R2 = 0.97)

up to 2000 are now kept in profitable pig production enterprises, and is aconsequence of the range of data used in the empirical analysis.

Developing a Model

To develop a mechanistic model for predicting the effects of social stressorson pig performance it is necessary to do the following three things: (i)determine the mechanism by which social stressors affect performance, thisis needed to integrate social stressor effects into a model in a mechanisticway; (ii) quantify the effects of the individual social stressors; and (iii)integrate these social stressor effects into an overall growth model. Thesethree steps are discussed below in turn.

How social stressors affect performance

Integrating the effects of social stressors in the form of mechanisticequations into a growth model poses the problem of describing how socialstressors affect pig performance. Unlike physical environmental stressors(e.g. thermal environment) which affect pig performance in an ordered wayvia known mechanisms (e.g. Bruce and Clark, 1979) the way in which socialstressors act is not clear. Amongst the possible mechanisms are: (i) a directreduction in appetite (Matteri et al., 2000); (ii) a reduction in the capacity todeposit protein and attain potential growth (Chapple, 1993); and (iii)increased metabolic demands diverting resources from the growth process(Elsasser et al., 2000) resulting in a reduction in the efficiency of feed use.

Chapple (1993) used the AUSPIG simulation model developed byBlack et al. (1986) to investigate how changes induced by social stressorsobserved in experiments may come about in order to try and elucidate themechanism of how social stressors lead to a depression in performance. Hefound that a reduction in intake alone, i.e. a direct reduction in appetite,could not explain the experimental observations. The effect of reducingintake was predicted to result in leaner pigs with a lower backfat thickness,but observations showed that an increase in group size resulted in anincrease in P2 backfat depth. A reduction in the pig’s ability to depositbody protein was required in order to simulate the experimental result.Consequently, Chapple suggested that the stressors associated with rearingpigs in groups are mediated through biochemical growth factors thatdown-regulate lean tissue growth, resulting in a reduction in feed intake. Ithas been suggested that physiological factors such as growth hormone(MacRae and Lobley, 1991), plasma cortisol (von Borell et al., 1992),insulin-like growth factor or cytokines (Chapple, 1993) may be responsible.

Experiments where an increased protein supply to crowded pigs did notovercome their decreased performance relative to non-crowded pigs(Edmonds et al., 1998; Ferguson et al., 2001) also support the mechanismsuggested by Chapple (1993). For example, Edmonds et al. (1998) found thatcrowded pigs with lower feed intakes required a substantially lower quantityof amino acids than their uncrowded counterparts when expressed as a

56 I.J. Wellock et al.

percentage of the diet. If the mechanism was a direct reduction in appetiteor increased metabolic demands it would be expected that the crowded pigswould have a requirement equal to or greater than the uncrowded pigs.

Although not simulated by Chapple (1993), a reallocation of resources isunlikely to be the mechanism responsible as, providing no other constraint ispresent, it is assumed that an animal will eat to meet its requirement for thefirst limiting resource (Emmans and Fisher, 1986). Thus it is expected thatany increase in resource demands would be met by compensatory feed intake.Consequently, it is suggested that a down regulation in lean tissue growth,which may also be described as a decrease in the animal’s ability to attain itspotential, is the most suitable mechanism to incorporate into a model todescribe the detrimental effects of social stressors on pig performance.

Representing the effects of individual social stressors: functional form andparameter estimation

The relationship between social stressors and performance is describedhere by conceptual equations derived on biological grounds that are thenparameterized using experimental data. Rather than predicting values forthe model output variables, such as ADFI and ADG by an empiricaladjustment (e.g. Kornegay and Notter, 1984; Turner et al., 2003), theapproach used here integrates the chosen functional forms into a generalgrowth model as mechanistic equations. By this means any interactionsthat exist between the type of pig and its environment can be exploredand, at least in principle, predicted.

In order to test the chosen functional forms for their relevance, and toenable realistic quantitative values to be assigned to the parameters,experimental data must be used (Table 4.2). To avoid the various problemsof using a strictly empirical approach, several measures were taken,including the following: (i) using only experiments where all variablesother than the one of interest were controlled for, to try and avoid theconfounding effect of other variables; (ii) using more biologically relevantmethods where possible, for example, by relating space allowance to BWrather than simply area per pig; (iii) taking differences in live weight intoaccount. Relative daily gain (R) was used as the measure of performancerather than daily gain, thus eliminating the need for separate equationsaccording to BW and allowing a greater amount of information to beincluded in the analysis; (iv) accounting for differences in the potential ofpigs used; (v) accounting for differences between the experiments andgiving appropriate weighting for the number of replications in eachexperiment; and (vi) checking that the equations used are sensible whenextrapolated over the full range of interest.

Space allowance

Decreasing the space allowance available to a group of pigs depressesintake and growth (e.g. Edwards et al., 1988; Hamilton et al., 2003). This


may be due to an increase in the frequency of antagonistic encounters thatmay to an extent depend on breed. It appears that there is a critical value,(SPAcrit, m2/BW0.67) below which performance becomes depressed. It isassumed that above SPAcrit, there is no effect on performance and thatwhen SPA reaches another crucial value (SPAmin, m2/BW0.67), growth is nolonger able to occur (see Fig. 4.1). SPAmin is reached when the pen is fullyoccupied and sets the minimum value for SPA within the model, 0.019m2/BW0.67 (Petherick, 1983). When SPAmin < SPA < SPAcrit, relative dailygain, RSPA, in relation to that recorded at a SPA > SPAcrit, is calculated as:

RSPA = b1 + g1.f.(SPA) (4.1)

b1 and g1 determine SPAcrit and the extent of performance depressionbelow SPAcrit. They are affected by genotype as discussed below. SPA =Area/BWq where Area is m2/pig and q is the body weight scalar assumed tobe 0.67 (Petherick, 1983). As there appears to be no clear biologicalexpectation for the shape of the functional form, f, between SPAcrit andSPAmin, the logarithmic relationship was chosen (Table 4.2) after inspectionof the experimental data. The value assigned to SPAcrit was 0.039m2/BW0.67. To account for the greater space requirements of pigs housedon solid floors, SPA in Eqn 4.1, is decreased by 25% in agreement withWhittemore (1998), when pigs are housed on solid floors.

Group size

There appears to be an effect of grouping per se as individually housed pigshave been widely shown to outperform their group-housed counterparts(e.g. Gonyou et al., 1992) and most experiments report a decrease in


Table 4.2. Parameter values for the conceptual equations relating the major social stressorsto pig performance estimated from experimental data in the literature (reproduced fromWellock et al., 2003c, Table 1).

Equationa Parameter 1 Parameter 2 Parameter 3

1 RSPA = b1 + g1 ln (SPA) b1 = 168.49 g1 = 21.48(9.62)b (2.65)b –

2 RN = b2 – g2 ln (N) b2 = 100c g2 = 3.6971(0.69)b –

3 EN = (x1.(N-1)).EMaint x1 = 0.0075 – –5 FRmax = (g3.BW1) / (1000.WHC) g3 = 2.85 – –7 RMix = b3 – g4.BW – ((g5.BW).ln.(t)) b3 = 100c g4 = 0.6 g5 = 0.188 EMix = (x2 – (x3.ln.(t))).EMaint x2 = 1.15 x3 = 0.050 –

a RSPA, RN and RMix represent the relative daily gain as a percentage of maximal performancein relation to space allowance (SPA, m2/BW0.67), group size (N) and mixing (Mix),respectively. EMaint, EN and EMix represent the energy expenditure (MJ/d) due to maintenance,group size and mixing, respectively. FRmax is the maximal feeding rate (kg/min) and WHC isthe water holding capacity (kg/kg) of the food used as a measure of its bulk.b Values in parenthesis are standard errors. c Denotes fixed parameter values.

performance as N increases (e.g. Wolter et al., 2001; Hyun and Ellis, 2001).Increasing N by a fixed number has a greater influence on smaller groupsthan larger ones, because the social hierarchy of small groups is disruptedto a greater degree than that of large groups that appear to lack socialstructure (Arey and Edwards, 1998; Turner et al., 2001). A logarithmicform is used to represent the relationship (Fig. 4.2):

RN = b2 – g2.ln.(N) (4.2)

RN is the daily gain as a proportion of that of a singly housed counterpart.The value of the constant b2 is set to 100 and the value of g2 is assumed todiffer between breeds (see below). Calculated parameter values are givenin Table 4.2.

Although the evidence for greater activity in larger groups is equivocal,the literature does indicate such a trend (e.g. Petherick et al., 1989; Turneret al., 2002). Consequently, energy expenditure is increased as N increases.This increase, EN, is calculated as a proportion of maintenance energyrequirements (Emaint, MJ/day) and included in the calculation of dailyenergy requirements. It is assumed that EN will not increase indefinitelyand so a proposed maximum is set at Nm. When N < Nm:

EN = (x1.(N�1)).Emaint (4.3)

The value of x1 will differ between genotypes as discussed later. When N�Nm, Nm replaces N in Eqn 4.3. To account for a twofold increase inactivity as N increases to Nm, a value of 0.0075 was assigned to x1. A valueof 21 was assigned to Nm.

Feeder space allowance

Intake is reduced when the number of feeder spaces available to a groupof pigs falls below a critical value (FSAcrit, feeder spaces/pig), and continuesto decrease as FSA decreases further (e.g. Nielsen et al., 1995). FSAcrit is


SPA, m2/BW0.67

0

1

SPAcrit

SPAmin

RS

PA

Fig. 4.1. Effect of space allowance on the relative daily gain (RSPA) in relation to that recordedat SPA > SPAcrit. SPAcrit represents the point below which space becomes limiting resulting ina depression in performance and SPAmin represents the minimum amount of space requiredfor a given animal. Both SPAcrit and SPAmin are affected by body weight and genotype.

reached when all of the pigs in the group can no longer satisfy theirdesired feed intake (FId, kg/day), due to increased pig competition and isdependent upon N, FId, maximum feeding rate (FRmax kg/min), and thenumber of minutes in the day, 1440.

FSAcrit = (FId/(1440.FRmax)) N (4.4)

FRmax depends upon aspects of mouth capacity, feed composition andmethod of feed presentation. It can be calculated as:

FRmax = (g3.BW1.0)/(1000.WHC) (4.5)

where WHC (kg/kg) is the water holding capacity of the feed, used as ameasure of feed bulk. It is assumed that g3 is unaffected by genotype.When FSA < FSAcrit, then the constrained feed intake (FIc, kg/pig), iscalculated as:

FIc = (1440.FSA.FRmax)/N (4.6)

If troughs are used FSA is calculated as the number of pigs able to feedsimultaneously so that FSA = trough width/ j.BWk. The values assumed forj and k are 0.064 and 0.33, respectively (Petherick, 1983) and theseestimate the width of the pig at the shoulders.

Mixing

Generally results indicate that mixing is a transient stressor and that, givensufficient time, there are no noticeable effects of mixing on performance inthe longer run (Spoolder et al., 2000; Heetkamp et al., 2002). There ishowever, an initial decline in performance immediately after mixing mostlikely due to the increased frequency of antagonistic encounters (D’Eath,2002) associated with establishing a new stable social structure. Mixingdepresses performance to a greater extent in larger animals due to theincreased ferocity of their fighting (Spoolder et al., 2000) before returningto normal values. The mixing effect is described as:


Group size (N)

1

RN

Fig. 4.2. Effect of increasing group size (N) on relative daily gain (RN) in relation to that of asingly housed counterpart.

RMix = b3 – ((g4.BW) – ((g5.BW).ln(t))) (4.7)

RMix is the performance relative to that of a non-mixed pig. The value ofthe constant b3 is set to 100. The values of the parameters g4 and g5 arelikely to change with genotype (see below); t is the time in days aftermixing occurs. At some value of t, RMix will be estimated to be 100. Fromthen on performance is normal and no longer affected by the past mixing(Fig. 4.3). Values were chosen (Table 4.2) so that mixing decreasedperformance by an average of approximately 25% in a 70 kg pig in the firstweek after mixing and had an effect that lasted for 2 to 3 weeks (Tan et al.,1991; Stookey and Gonyou, 1994).

Mixing also increases the energy expenditure of pigs due to increasedlevels of aggression, especially in the first few days after mixing (Heetkampet al., 1995). This increase in energy expenditure due to mixing, EmixMJ/day, which decreases over time as activity levels return to normal, isadded to the daily energy requirements.

Emix = (x2 – (x3.ln(t))).Emaint (4.8)

The values of the scalars x2 and x3 were chosen to represent an increase inEmaint by a maximum of 15%, following EN, and to have an effect that lastsfor 2 to 3 weeks. These values are expected to change with genotype.

Genetic differences

It is envisaged that there is genetic variation between breeds in their ability tocope with social stressors (Beilharz and Cox, 1967; Grandin, 1994; Schinckelet al., 2003). These differences are accounted for by introducing a parameter,AB, to describe the pigs ‘ability to cope’ when exposed to social stressors. Thisadjusts both the intensity of a stressor at which the animal becomes stressed,e.g. SPAcrit, and the extent to which stress reduces performance (see Fig. 4.4)and increases energy expenditure (activity) at a given stressor intensity. It isassumed in the model that these two factors are correlated.


Time (days)

AD

G (

kg/d

ay)

Non-mixMix

tmix

ADGdep

Fig. 4.3. Effect of mixing on average daily gain (ADG). The extent of depression in ADG(ADGdep) and the time taken (tmix) to return to non-stressed levels of ADG is determined byboth body weight and genotype.

Increasing AB from 1 to 10 represents an increasing ability to cope andmodifies the effect of each stressor by multiplying the estimated parametersshown in Table 4.2 by appropriate scaling factors (Table 4.3). Because thereis currently no established genetic variation in pig’s ability to cope withstressors, values for the scaling factors were estimated to representdeviations of approximately 1% from the mean, AB = 5, per unit change inAB. For example, AB values of 1 and 10 predict an approximate departurefrom the mean of �5 and +5%, respectively, at a given stressor intensity.SPAcrit falls from 0.042 to 0.031 m2/BW0.67 as AB decreases from 10 to 1. Itis expected that modern, ‘leaner’, genotypes will have lower values of ABthan traditional, ‘fatter’, genotypes (Grandin, 1994; Schinckel et al., 2003).

Incorporating Effects of Social Stressors into a More General PigGrowth Model

Information required

The model framework used as the starting point is that described andtested by Wellock et al. (2003a,b). Information is needed about the pig, itsdiet and the social and physical environments in which it is kept. Noadditional inputs are required to describe either the thermal or dietaryenvironment. In addition to the three genetic parameters used to predictpotential growth [protein weight at maturity (Pm, kg), the lipid to proteinratio at maturity (Lm/Pm, kg/kg) and a growth rate parameter (B, d�1)], theparameter, AB, discussed above, is required to describe the pig’s ability tocope with social stressors. Additional inputs to describe the socialenvironment are pen area, the number of pigs per pen (N), the number ofindividual feeders or the trough length, and the occurrence or not ofmixing. Up to two mixing events are allowed during a run and the weightat which each mixing occurs is required. The model can be run either to afinal BW (BWf, kg) or for a given period (t, days).


Area (m2/pig)0.2 0.4 0.6 0.8 1.0

RS

PA

70

75

80

85

90

95

100

105

AB = 10AB = 5AB = 1

SPAcrit

Fig. 4.4. The effect of genotypic differences in ability to cope with social stressors (AB) onrelative daily gain (RSPA) at differing space allowances. SPAcrit represents the points at whichspace becomes limiting.

Integrating the mechanism and social stressor equations

It has been shown in studies with pigs (Hyun et al., 1998a,b) that the effectsof stressors, at intensities expected under commercial conditions, are likelyto be additive rather than multiplicative, antagonistic or synergistic. It istherefore assumed that, within the bounds of the model, the effects ofmultiple stressors on maximum relative daily gain of the stressed animal,Rs, are additive and are predicted by summing the effects of the individualstressors.

Rs = Rp.((100 – ((100 – RSPA) + (100 – RN) + (100 – Rmix))) / 100) (4.9)

Here Rp = ADGp / BW and is the pig’s potential relative daily gain. ADGp isdependent upon the genotype and the current state of the pig. It isassumed in the model that social stressors lead to a down-regulation inlean tissue growth, i.e. a decrease in the animal’s ability to attain itspotential. This is equivalent to lowering the growth rate parameter, B,which in turn leads to a decrease in the ADGp that the pig is able toachieve. Consequently, Rs is calculated on a daily basis and used tocalculate the modified growth rate parameter, Bs = Rs � B, from whichthe maximum daily gain of the stressed animal is predicted, ADGs,replacing ADGp in the model.

As it is assumed that animals eat to attain their potential, a decrease inADGp necessarily leads to a decrease in FId. Consequently, the desired feedintake of the stressed animal is predicted directly from the animal’sdepressed growth potential. Predictions of FId, actual intake and gain arethen made taking account of any changes in energy requirements due toincreases in activity, EN and Emix, and possible constraints on intake due tolimiting FSA, feed composition and the climatic environment.

Introducing Between-animal Variation into the Model

One of the problems and perhaps main limitations of using a model thatrepresents a single average pig, is the assumption that all pigs within apopulation are the same. In reality of course this is not true. Aconsequence of between-animal variation is that there may be differences


Table 4.3. Scaling factors (z) for the appropriate parameters to account for variation in abilityto copea (AB) with social stressors (adapted from Wellock et al., 2003c).

Space allowance Group size Mixing

zb1 = 1.2 – 0.04AB zg2 = 1.5 – 0.1AB zg4 = 1.2 – 0.04ABzg1 = 1.5 – 0.1AB zx1 = 1.1 – 0.02AB zg5 = 0.977 + 0.066AB

zx2 = 1.025 – 0.005ABzx3 = 0.9 + 0.02AB

a An AB value of 5 represents the mean and therefore all parameters are multipliedby a scaling factor of 1 when AB = 5. Values were chosen to represent deviations ofapproximately 1% from the mean performance per unit change in AB.

between the response of the average individual and the mean response ofthe population, which is an average of all individuals (Fisher et al., 1973;Emmans and Fisher, 1986). These differences may prove important whenpredicting nutrient requirements (Fisher et al., 1973; Curnow, 1986),optimizing pig production systems (Pomar et al., 2003) and devising animalbreeding strategies (Knap, 1995).

In order to account for differences between individuals in a group,between-animal variation was introduced into the model. In addition toaccounting for differences in growth potential, as in the stochastic piggrowth models of Knap (2000) and Pomar et al. (2003), variation in initialstate as described by initial BW (BW0) and ability to cope when exposed tostressors were also included. Variation in growth potential was generatedby creating variation around the population means of each of the geneticparameters describing growth, Pm, Lm/Pm and B (Ferguson et al., 1997).Individual variation in BW0 is generated from the assigned genotypemean, (mBW0, kg) and standard deviation (sBW0, kg) using the simulatedgenetic parameters of the individual to correlate BW0 with potentialgrowth. By this means individuals in the group with the greatest potentialwill tend to have the highest BW0 as would be expected from non-limitinggrowth. For further details see Wellock et al. (2004).

It is expected that within a population or group the socialenvironment (i.e. position within the social hierarchy) affects anindividual’s ability to cope (Muir and Schinckel, 2002) and that pigsclassified as dominant tend to outperform their subordinates (e.g. Hessinget al., 1994; D’Eath, 2002). There is also evidence that social dominance ispositively correlated to BW in pigs (Drickamer et al., 1999; D’Eath, 2002).Taken together these results suggest that the larger pigs within a grouptend to be dominant and better able to cope when conditions are sub-optimal, i.e. when pigs are exposed to social stressors. Consequently, it isassumed in the model that there is a positive correlation between BW0 andAB. Individual values for AB (ABi) are generated around the assignedgenotype mean (mAB) and standard deviation (sAB) of AB, whilst beingpositively correlated to BW0.

ABi = mAB + b4.((BW0i / mBW0).(sAB.(mBW0 / sBW0))) ± residuali (4.10)

The parameter b4 determines the degree of correlation between BW0 andAB and is set equal to one. The residuali is drawn at random takingaccount of sAB. Within a population, AB is not directly correlated toleanness. However, leaner animals will tend to have lower AB values due tothe positive correlations between Lm/Pm and BW0 and BW0 and AB.

Model Simulations: Practical Implications of AB in Relation toProduction, Welfare and Genetic Selection

Effect of growth potential and ability to cope on pig performance

The effects of differing abilities to cope when exposed to social stressorswere explored, using the model, for pigs with two levels of potential


performance, ‘good’ and ‘poor’. Simulations for pigs grown from 80 to 100kg and either mixed or not on day 1 are shown in Table 4.4. As expected,mixing led to a decrease in performance, with pigs having the poorestability to cope (AB = 1) displaying the largest decrease. For example, goodgenotype pigs with AB values of 10, 5 and 1 were predicted to show adecrease in ADG of 9, 20 and 35%, respectively, compared to the non-mixed counterparts. Interestingly, poor genotype pigs with high (AB = 10)and average (AB = 5) abilities to cope were both predicted to outperformthe good genotype pigs with a low ability to cope (AB = 1), reaching 100kg 6 and 3 days earlier, respectively. This implies that pigs with the highestpotential for growth do not always outperform others and that an animal’sresponse to stressors, i.e. its ability to cope, may be as important as itsgrowth potential, particularly when raised under commercial conditions.

Average individual versus mean population response

Ferguson et al. (1997) stated that ‘there is a marked difference in theresponse of the average individual in the population and the mean of thepopulation’. Pomar et al. (2003) demonstrated clear differences betweenthe average individual and the mean population response for the rate ofprotein retention in response to increasing dietary protein intake.However, from the model simulations shown in Fig. 4.5 it is clear thatdifferences between the average pig and the mean population responsesshould not always be expected and will depend partly upon the stressors towhich the pigs are exposed. Where all individuals become adverselyaffected at the same stressor intensity, e.g. being housed in a group asopposed to individually or being mixed or not, then no differencesbetween the average individual and mean population response is predicted(Fig. 4.5a). This is because all individuals are either affected or not,although this may be to varying extents. If however the intensity at which


Table 4.4. The effects of pig potential (ADGp) and ability to cope (AB) when exposed tostressors on the time taken (t) to reach 100 kg, average daily gain (ADG), average daily feedintake (ADFI) and feed conversion ratio (FCR) from a starting weight of 80 kg. The effect ofmixing pigs on day 1 of the simulation is also shown for the AB = 10 genotype.

ADGp AB Mix t (days) ADG (kg/day) ADFI (kg/day) FCR (kg/kg)

Gooda 10 No 22 0.93 2.51 1.5810 Yes 24 0.84 2.37 2.825 Yes 28 0.74 2.22 3.001 Yes 34 0.60 2.01 3.35

Poorb 10 No 26 0.80 2.66 3.3310 Yes 28 0.74 2.52 3.415 Yes 31 0.65 2.34 3.601 Yes 38 0.53 2.09 3.94

a Genetic growth parameters: B = 0.016 day�1, Pm = 32 kg, Lm/Pm = 1.2 kg/kg.b Genetic growth parameters: B = 0.011 day�1, Pm = 30 kg, Lm/Pm = 2.0 kg/kg.

the stressor becomes limiting is able to differ between individuals, e.g.critical SPA (SPAcrit, m2/BW0.67) and upper critical temperature, differencesbetween the average individual and mean population response areexpected (Fig. 4.5b).

The linear-plateau response of the average individual to decreasing SPAis a direct outcome of the assumption used in the model. The curvilinear-plateau response of the population however can be explained by individualdifferences in SPAcrit, generated from between-animal variation in BW andAB. The plateau is predicted to occur when SPA > SPAcrit for all pigs in thepopulation and the curvilinear transition phase occurs when only aproportion of the population is constrained, i.e. SPA < SPAcrit for only someindividuals. As the intensity of the stressor increases, the proportion of thepopulation that is constrained also increases until all individuals areaffected. At a fixed SPA the proportion of pigs limited will increase withincreasing population variance and this will result in a greater degree ofcurvature. This was demonstrated by Pomar et al. (2003) for average dailyrate of protein retention in response to increasing protein intake.

Variation in initial state and ability to cope with social stressors

The model predicts that variation in the growth response of a populationis determined to a greater extent by variation in AB and BW0 than byvariation in growth potential, when pigs were exposed to social stressors.This is demonstrated in Table 4.5 and Fig. 4.6.

Table 4.5 shows the effect of variation in growth potential, BW0 andAB on the performance of 500 pigs raised from 60 kg to a given BWf of100 kg when raised under typical commercial conditions. Fig. 4.6 is fromthe same simulations and shows how the distribution in the time taken to


Group size

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AD

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ay)

2.40

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2.44

2.46

2.48

2.50(b)

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Fig. 4.5. Predicted effect of environmental stressors on the average daily feed intake (ADFI)response of the average individual and population mean; (a) the effect of increasing groupsize on the ADFI of pigs from 20 (± 2 kg) to 50 kg; (b) the effect of decreasing spaceallowance on the ADFI of 100 kg (± 10 kg) pigs over a simulation period of one day.


Table 4.5. Effect of variation in initial BW (sBW0, kg) and ability to cope (sAB) on thevariation in the time taken (t, days) to reach 100 kg from a mean BW0 of 60 kg. P and L arethe protein and lipid content, respectively. Mixing occurred at 75 kg and pigs were given aspace allowance of 0.7 m2/pig throughout (adapted from Wellock et al., 2004).

sBW0a sAB t (days) ADG (kg/day) ADFI (kg/day) P (kg) L (kg)

0.00 0.00 50.7 (3.93)b 0.801 (0.060)b 2.17 (0.104)b 17.78 (0.352)b 15.59 (1.534)b

2.07 0.00 50.8 (5.48) 0.804 (0.057) 2.17 (0.107) 17.78 (0.333) 15.59 (1.445)4.19 0.00 51.5 (7.64) 0.802 (0.056) 2.17 (0.119) 17.78 (0.357) 15.59 (1.592)5.74 0.00 51.5 (9.42) 0.801 (0.052) 2.16 (0.121) 17.78 (0.358) 15.58 (1.544)7.87 0.00 52.2 (11.59) 0.801 (0.053) 2.16 (0.131) 17.77 (0.346) 15.63 (1.500)

10.04 0.00 52.2 (14.23) 0.795 (0.054) 2.15 (0.132) 17.78 (0.338) 15.60 (1.506)12.32 0.00 54.1 (17.42) 0.792 (0.054) 2.14 (0.148) 17.78 (0.352) 15368 (1.548)0.00 0.47 50.8 (4.06) 0.799 (0.061) 2.17 (0.105) 17.76 (0.350) 15.70 (1.548)0.00 0.94 50.8 (4.16) 0.798 (0.063) 2.17 (0.108) 17.79 (0.359) 15.54 (1.580)0.00 1.45 50.8 (4.71) 0.799 (0.072) 2.17 (0.117) 17.79 (0.342) 15.61 (1.495)0.00 1.93 50.8 (5.14) 0.799 (0.079) 2.17 (0.128) 17.77 (0.349) 15.64 (1.579)0.00 2.53 50.8 (5.52) 0.802 (0.087) 2.17 (0.140) 17.79 (0.354) 15.53 (1.576)5.77 1.40 52.1 (11.48) 0.801 (0.071) 2.17 (0.161) 17.77 (0.331) 15.63 (1.435)

12.18 2.42 54.2 (21.05) 0.799 (0.080) 2.15 (0.222) 17.79 (0.338) 15.46 (1.479)

a Simulated values. b Result of variation in growth potential only.

reach BWf changes as variation in BW0 and AB increases. Consequently, itis suggested that the pig’s potential for growth might be less importantthan the pig’s response to stressors when pigs are reared in commercialenvironments. This is because improving the ability of pigs to cope wouldallow a greater proportion of their potential to be attained and may be abetter way of improving pig performance and enterprise profitability thanincreasing potential per se. Schinckel et al. (2003) also noted that ‘the pig’sgenetic potential for protein accretion and feed intake are less importantthan the pig’s response to encountered stressors’ and for these reasonssuggested that ‘farm � genetic population specific growth and feed intakeparameters are required’.

If, as suggested, AB and lean growth rate are adversely correlated(Grandin, 1994; Torrey et al., 2001; Schinckel et al., 2003), then there maybe negative implications regarding the welfare of pigs selected for leangrowth. This is because selection for improved lean growth rate wouldindirectly lead to selection for poorer ability to cope in the population. Fig.4.7 shows the correlation between Lm/Pm and AB simulated by the modelfor a population of 500 pigs with population mean (± SD) values of 1.2(0.18) and 5 (1) for Lm/Pm and AB, respectively. Since AB depends in partupon the structure of the group, then group selection may be necessary inorder to improve the ability of animals to cope when exposed to socialstressors. Griffing (1966) found that individual selection could result in anegative response of the population mean. The experiments of Muir and

Schinckel (2002) with quail and Muir (1996) and Muir and Craig (1998)with poultry also demonstrated that selection for desirable associate effectswithin a group may be a means to select animals which are better adaptedto their rearing environment. Any genetic correlation between AB and thegrowth parameters that can be evaluated could be included in the model byincorporating the co-variation between the identified parameters and AB.

Quantifying the variation in AB may improve the rate of breeding fora better ability to cope, as the amount of heritable variation determines thedegree of selection pressure able to be applied. If a parameter such as ABwas included in a selection index then individual pigs with both thegreatest growth potential and best ability to cope could be selected for. Forexample, animal ‘a’ shown in Fig. 4.7 may be a better breeding prospectthan animal ‘b’ as it has the desirable properties of having a low Lm/Pmvalue and high AB unlike animal ‘b’, which has a high Lm/Pm and low AB.This would result in benefits for both welfare and production. If increasedgrowth rate and ability to cope are antagonistic, then trying to increase pigperformance achieved under excellent conditions, i.e. improving potential


(a)

Fre

quen

cy

120

100

80

60

40

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020 30 40 50 60 70 80 90 100

Time (days)

(b)

Fre

quen

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120

100

80

60

40

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020 30 40 50 60 70 80 90 100

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(c)

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Time (days)

(d)

Fre

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100

80

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40

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020 30 40 50 60 70 80 90 100

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Fig. 4.6. The effect of variation in initial BW (sBW0) and ability to cope with social stressors(sAB) on the time taken to reach 100 kg from an initial mean BW of 60 kg (N = 500); (a) sAB= 0, sBW0 = 0, i.e. variation in growth potential only; (b) sAB = 1.5, sBW0 = 0; (c) sAB = 0,sBW0 = 6 kg, and (d) sAB = 6, sBW0 = 1.5 kg. Mixing occurred at 75 kg and pigs were givena space allowance of 0.7 m2/pig throughout.

alone, may not prove to be the best selection strategy. It is likely thatimprovements in the growth potential of the animals and in theenvironment, particularly better biosecurity and vaccination, are requiredin addition to improving pigs’ ability to cope.

Future Model Developments

Estimation of model parameter values with particular reference to AB

Currently there are no means of assigning estimates to the AB parameterintroduced into the model developed here to describe the ability of pigs tocope when exposed to social stressors. However, assuming that there is ameasurable phenotypic difference between types of pigs and individualswithin a population, it is thought that genetic characterization is possible.The work of de Greef et al. (2003) and Kanis et al. (2002) supports this.They described and evaluated a conceptual framework for breeding forimproved welfare in pigs and showed that it is possible to select for abilitiesto cope with stressors such as environmental temperature.


Lm/Pm (kg/kg)

0.0 0.5 1.0 1.5 2.0 2.5

AB

1

2

3

4

5

6

7

8

a

b

Fig. 4.7. The simulated correlation between leanness, as represented by the lipid to proteinratio at maturity (Lm/Pm), and ability to cope when exposed to environmental stressors (AB).Five hundred individuals were simulated with a population mean (± SD) of 5 (1) for AB and 1.2(0.18) Lm/Pm. Animal ‘a’ may be a better breeding prospect than animal ‘b’ as it has thedesirable properties of having a low Lm/Pm value and high AB, unlike animal ‘b’ which has ahigh Lm/Pm and low AB.

To satisfactorily test whether the introduction of AB is useful and toquantify it by experimentation is likely to require an elaborate experimentwith a large number of pigs of different breeds, strains and sexes exposedto a large number of treatments. This is unlikely to be carried out.Nevertheless, it is thought that more modest, small scale, experiments mayallow first tentative estimates of both the genotype mean and between-animal variation in AB to be made. Animal scientists have long beendesigning experiments exposing pigs of different breeds and sexes to anumber of differing social stressors. These have included studiesmanipulating group size (e.g. Wolter et al., 2001), space allowance (e.g.Hyun et al., 1998a), feeder space allowance (e.g. Nielsen et al., 1995) andmixing (e.g. Stookey and Gonyou, 1994). However, it has been scientistsinterested mainly in the behaviour of pigs that have usually conductedthese experiments. As a consequence performance measures have oftenbeen neglected or not suitably reported. For instance, no experimentscould be found in the literature where individual performance of mixedpigs had been presented. The few ‘mixing’ experiments which reportedany performance information (e.g. Hessing et al., 1994; D’Eath, 2002) didso only for the group. Simply including measures of performance inconjunction with the usual behavioural measures would allow progress tobe made. For example, recording individual pig feed intake and gain on adaily basis for the duration of a ‘normal’ mixing experiment would give anindication of the effect the stresses of mixing have on individualperformance. Linking the expected decreases in intake and gain due tomixing with the BW and position of the individual within the dominancehierarchy would also allow an initial test of the assumption used in themodel: that bigger pigs within the population are the ones that cope bestwhen socially stressed.

Comparing the variation in performance observed in experimentaldata with the variation predicted by the model will also allow an initialestimate of the variation in AB to be made. This inverted modellingtechnique was the method used by Ferguson et al. (1997) when predictingthe variation in B*, Lm/Pm and Pm. However in order for this to be donesuccessfully a measure of the heritability of AB is also required. It is alsoimportant to know if any correlations exist between AB and any of theother genetic parameters, particularly leanness described by Lm/Pm. If so,this will affect the nature and description of the variation of the correlatedparameters (Ferguson et al., 1997) and would need to be accounted for inthe model. This of course relies on the simplistic assumption thatindividuals react in the same way to all types of social stressors. However ifthis is incorrect, the introduction of further parameters, in addition to AB,will be required for a sufficient description of ability to cope when exposedto social stressors.


Modelling the effects of infectious stressors

It was assumed in the model that all animals were in good health and freefrom exposure to infectious stressors throughout. Any response toinfectious stressors, such as an increase in resource requirements to copewith the consequences of infection, acquire and express an immuneresponse, a change in the efficiency of energy utilization or a voluntaryreduction in feed intake (anorexia), all of which would result in a decreasein performance, were ignored. In reality of course, pigs are continuouslyexposed to many different kinds and intensities of infectious stressors.These include pathogens and other harmful environmental componentsthat may trigger tissue injury or further infection, such as bites andscratches from other individuals in the same pen.

The incorporation of infectious stressors into simulation models is animportant next step in the attempt to predict commercial pig performanceaccurately. To include the effects of infectious stressors into a model in asystematic way it is necessary first to do a number of things. The metabolicload imposed by infectious stressors, i.e. increased nutrient requirements,and the extent to which performance is decreased need to be quantified.How animals allocate resources when exposed to infectious stressors, e.g.cope with a pathogen challenge, needs investigating and the biologicalmechanism responsible for the decrease in performance needs elucidating.Two possible mechanisms may lead to the decrease in pig performanceobserved when pigs are exposed to disease. These are either a decrease inthe pigs’ ability to attain their potential, as suggested by Schinckel et al.(2003), or a direct decrease in appetite as suggested by Kyriazakis (2003).There is also likely to be between-animal variation in immune responseand resilience, i.e. differences in the ability of individual pigs to cope andperform during exposure to pathogens (see Kyriazakis and Sandberg,Chapter 7, this volume). This should be accounted for in any futuremodelling attempt, along with any potential interactions between stressand disease susceptibility when such information becomes available.

Conclusion

Despite their importance, few attempts have been made to quantify theeffects of social stressors on pig performance and incorporate these effectsinto a pig growth simulation model. Here we describe how the effects ofthe major social stressors, i.e. group size, space allowance, mixing andfeeder space allowance, can be described by conceptual equations based onthe biology of the animal, quantified and incorporated into a more generalpig growth model. The adapted model allows the performance of bothindividuals and populations of growing pigs differing in initial state,growth potential and ability to cope with social stress when raised undergiven dietary, physical and social environmental conditions to be exploredand, at least in principle, predicted.


Among the main outcomes of the model simulations are the following:(i) allowance for population variance is crucial in making decisions as theremay be differences between the response of the population and theaverage individual; (ii) improving management to minimize stressors anddecrease variation in initial state is an important factor in decreasing theheterogeneity of a group, particularly in commercial production systemswhere payment is based upon uniformity; and (iii) if growth rate andability to cope when exposed to social stressors are antagonistic, trying toimprove pig performance by increasing growth potential alone may not bethe best selection strategy.

Acknowledgements

This work was supported by the Biotechnology and Biological SciencesResearch Council of the United Kingdom and the Scottish Executive,Environment and Rural Affairs Department.

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5 Modelling Populations forPurposes of Optimization

R.M. GOUS AND E.T. BERHE

Animal and Poultry Science, School of Agricultural Sciences andAgribusiness, University of KwaZulu-Natal, Private Bag X01,Scottsville 3209, South Africa. [email protected]

Introduction

Broiler and pig growth models have improved considerably sinceWhittemore and Fawcett (1976) developed the Edinburgh Model Pig, yetin most cases such models still work at the level of the individual ratherthan at that of a population. In so doing, the genetic variation inherent ina population, the variation that exists from one end, or side, of aproduction unit (e.g. a broiler house) to the other, and variation in thecomposition of the feed offered to broilers or pigs is ignored, theassumption being that the response of the average individual, housed in anaverage environment and fed an average feed, will be sufficiently similar tothat of the average response of the population from which it comes.Although this is a naïve approach, there is great merit in ensuring that thesimulation of food intake and growth of the individual is sensible andaccurate before expanding the simulation to that of a population. If thesimulation of the growth of an individual meets the above criteria, and hasbeen modelled mechanistically, then it is not an insurmountable problemto expand this to a population model. Models of individuals may beadequate for an understanding of the theory of growth and food intake, aswell as for ‘what-if ’ scenario planning. However, for purposes ofoptimization, it is imperative to account for the variation inherent in thesystem if a realistic assessment of the population response is to besimulated.

According to Knap (1995) stochastic simulation can be defined asproducing simulation outputs that reflect not only the expected populationmeans of the traits of interest but also their expected dispersion, as a resultof deliberately introducing variation in a number of basic parameters ofthe simulation model. He outlined the reasons for considering variationbetween animals in growth models when simulating different systems.


1. The profitability of the systems may be affected to a large extent by theamount of variation in the production traits.2. The change from one system to another may have small effects onaverage levels but large effects on variation.3. Differences between systems can be discovered more readily whenvariation is made visible.4. In order to study the relationships between traits, covariance should becreated, which requires variation (Emmans and Fisher, 1986).

This chapter deals with the sources of variation that should be consideredwhen modelling the growth of a population of broilers for purposes ofoptimization, and presents some comparisons of simulation andoptimization outputs when these were conducted at the individual and thepopulation levels.

Optimizing the Feeding Programme for Broilers

The optimum feeding programme for a broiler producer is that whichresults in the highest profit for the enterprise, e.g. maximum margin/m2

per annum or margin over feeding cost. Determining the optimumnutrient density in the feeds used, the optimum concentrations of aminoacids relative to energy in each feed, and the optimum length of time thateach feed should be fed, are therefore both nutritional and economicdecisions.

The information required for optimization consists of feed costs atdifferent levels of nutrient provision, a description of all the relevantanimal responses, both fixed and variable costs affecting the productionsystem and details of revenue. The complexity of the information requiredwould depend on the level of organization at which the optimization is tobe made. If profit of the broiler grower is to be maximized at the farmgate, then responses in liveability, growth and feed conversion ratio willprobably suffice. However, and more realistically, a wider view will often berequired, and the effect of broiler nutrition on slaughterhouse variables(eviscerated yield, rejects, etc.) and further processing (carcasscomposition) will need to be defined. Mack et al. (2000) emphasized theimportance of broiler companies considering all aspects of the productioncycle when making nutritional decisions.

Feed costs for any nutritional specification are readily calculated bylinear programming. This will take account of feed ingredient availability,analysis and costs. Processing and transport costs may be added. Broilerproduction costs are complex but will usually be specified by eachcompany.

So the only persistent problem in optimization lies, as ever, in thedefinition of animal response. Consider some of the procedures that wouldbe needed when optimizing a feeding programme. It would be necessaryto determine the potential growth rate and potential fatness of the birds to

Modelling Populations for Purposes of Optimization 77

be fed; the distribution of potential growth rates (greater when mixedsexes are used); the environmental conditions provided, and the cost ofaltering the prevailing conditions; the costs of a range of feeds differing innutrient density at each energy-to-protein ratio; and the cost of mixing andthen transporting these feeds to the production site (which would place anupper limit on the number of feeds that could be considered in anyproduction cycle). Consider then that the birds can adjust their intake of agiven food to an extent, this being limited by the environmentalconditions; that the effect of feeding a relatively low quality food initiallycan be compensated for at a later stage if the conditions are such that thebird can either consume more food later, or draw on lipid reserves,thereby exhibiting an improved feed conversion efficiency. Consider, too,that the amount of lipid in the gain is of importance to some producers,but not to others; and that the length of the production cycle can bealtered considerably by the use of different feeding programmes. Itbecomes clear that it is naive to imagine that any one, or even any series, ofexperiments could begin to address the question of defining the optimumfeeding programme. Only with the use of an accurate simulation modelcould such an optimization be contemplated.

An optimization tool for broiler production would need to combinethree types of computer program, namely, a feed formulation program, agrowth model and an optimization procedure. The flow of informationfor such a procedure, shown in Fig. 5.1, bears similarities to thecontinuous quality improvement model of Deming (1986), which consistsof four repetitive steps (Plan, Do, Check, Act), this continuous feedbackloop being designed to assist managers to identify and then reduce oreliminate sources of variation that cause products to deviate fromcustomer requirements. The process in this case is straightforward: theoptimizer defines nutritional constraints for practical broiler feeds, whichare passed to the feed formulation program where the least-cost feed thatmeets these constraints is determined. The characteristics of thisformulated feed are then passed, as input, to the broiler growth model.The performance expected from this feed when given to a defined flockof broilers in a given environment is predicted by the model, and thispredicted performance is then passed to the optimizer to complete thecycle. The next cycle starts with the optimizer modifying the feedspecifications, moving, according to some in-built rules, to an optimumpoint. The objective function to be maximized or minimized can bedefined in terms of any output from the broiler growth model, butrealistically would be an economic index of some sort. Examples aremargin over feeding cost, margin per m2 per year, or maximum breastmeat yield at an age or weight.

The system used in the EFG broiler nutrition optimiser (EFG SoftwareNatal, 1995), (which optimizes three aspects of a commercial broiler feedingprogramme, namely, the amino acid contents in each feed, given a feedingschedule, the nutrient density of each feed in the schedule and the optimumfeeding schedule given feeds of a fixed composition) considers all of the

78 R.M. Gous and E.T. Berhe

criteria mentioned above. The broiler growth model allows for multipleharvesting from one flock and calculates revenues from any mixture ofwhole-bird sales or processing. Typical economic variables are included,although these may be readily customized to fit with individual enterprises.

Growth models developed in different laboratories may be included inoptimization schemes of the sort described above. The key to this approachclearly lies in the ability of the broiler growth model to reflect accuratelythe performance expected under commercial conditions. However, theperformance of the average individual in the flock, subjected to averageconditions in the broiler house and being fed the average food formulatedby the nutritionist, without considering the variation inherent in genotype,environment and food, cannot accurately reflect the variation that wouldresult in commercial conditions. For this, a stochastic model of growth andfood intake is required.

Individuals versus Populations

Because most nutrition experiments in research and all experiments incommercial poultry production are conducted on groups of birds, modelsof the response of individuals are not entirely appropriate for applicationin the poultry industry. For this reason some models have been developedat the level of the group, but a problem with this approach is that therelationships between inputs and outputs for groups are curves, whereas ifone assumes that marginal efficiencies for nutrient utilization are constant,then such relationships are not curves (Emmans and Fisher, 1986). TheReading Model (Fisher et al., 1973) demonstrated convincingly that theresponse of an individual (laying hen) differs markedly from that of thepopulation from which the individual is drawn. Whereas the response ofeach hen to an increasing supply of an amino acid can be assumed to belinear, up to a point where a plateau of output (the genetic potential) isreached, the population response is a continuous, asymptotic curve withno abrupt threshold. This curve results from determining the meanresponse of a group of individuals at a time. In a population of growingbroilers, as with laying hens, there exist differences in the potential output


Feedformulator

Feedcomposition

Broilermodel

Optimizer

Feedspecification

Predictedperformance

Broiler Nutrition Optimizer

Fig. 5.1. Flow of information in optimizing the feeding programme of a broiler chicken.

(growth rate) of each animal at a time, but because each bird is growingand food intake is increasing, variation in growth rate is also introducedwithin each animal over time (Gous and Morris, 1985), making the needfor a population model of broiler growth even more important (or critical)than in the case of laying hens, which are in a relatively steady state. Apopulation model should be built by simulating the responses of manyindividuals, and not directly as a group, so that the accepted assumptionsabout marginal efficiencies are not compromised.

But it is not only the variation between individuals in their response toa given feed or environment that controls the variation in the response of apopulation of birds to a feeding programme in a given environment.Variation also exists in the environmental conditions to which the birds aresubjected, as well as the composition of the feed used. Each of thesesources of variation will be addressed in the following review, but emphasiswill be placed on the effect of variation at the level of the genotype on theresponse, as this aspect has been used in numerous exercises by theauthors to illustrate the difference in response between an individual and apopulation of broilers.

Sources of Variation in a Population of Broilers

Variation in the genotype

When modelling the growth and food intake of a growing broiler it issensible to have some idea of the potential growth rate of the bird, the ideabeing that the bird has a purpose, namely, to grow at its potential(Emmans, 1987). Given this goal, the model can then calculate the desiredamount of the given food the bird needs to consume each day to grow atits potential, and will predict the consequences for food intake, growth andcarcass composition if this intake is constrained by feed bulk or anenvironment that is too hot to allow the bird to lose sufficient heat to thatenvironment.

Describing an individual

Potential feather-free body protein growth may be adequately described bythe three parameters of the Gompertz growth curve, namely, the startingbody protein weight (BP0), the rate of maturing (B) and the matureprotein weight (BPm) (Emmans, 1987). The lipid content of the maturebody is used to define the gross chemical composition of the body at anyintermediate weight. Well-defined allometric relationships betweenprotein, lipid, ash and water enable the growth of the physical componentsof the body to be simulated. However, recent developments in broilergenotypes in which, for example, breast meat yield has been increasedmarkedly by selection, mean that these allometric relationships are unlikely


to be universally applicable to all genotypes, and therefore should beredefined for genotypes whose physical composition has been modified byselection.

The rate of feather growth must also be defined, and a Gompertzgrowth curve may also be used for this purpose. The rate of maturing offeathers differs from that of body protein growth, but may be seen as amultiple of the latter. Feather growth differs markedly between genotypesand sexes, especially in feather-sexable strains. Feathering rate multipliers(FR) are used in the EFG Broiler Growth Model to calculate the rates offeathering of male and female broilers, these differing for feather-sexableand non-feather-sexable strains.

In order to recreate the different responses to dietary protein that areseen between some commercial strains a further genetic parameter isdefined, which controls the maximum lipid in the gain ratio (MLG) in theshort run. In essence, this parameter reflects the ability of the genotype tofatten when presented with a feed in which one or more amino acids orother nutrients are marginally limiting, which causes the bird tooverconsume energy in an attempt to obtain sufficient of the limitingnutrient. Birds with a low propensity to fatten would be disadvantaged insuch a case, as they would be unable to store the excess energy as bodylipid, the resultant food intake therefore being lower than desired, andweight gain being below the potential.

The parameters described above are seen as genetic characteristics ofindividuals in the flock, many of which have been measured in commercialstrains of broiler (Hancock et al., 1995; Gous et al., 1996, 1999). Realisticresponses of individuals, whose genotypes have been described by allocatingappropriate values to these parameters, may then be predicted using asimulation model such as that described by Emmans (1987). Such a modelhas been developed (EFG Software Natal), which simulates the growth of asingle bird, taking account of genetic parameters, diet composition andfeeding programme, the environment, stocking density and other factorsthat may affect the outcome of production decisions in practice. Bodyprotein content is used to define the current state or condition of theanimal, which is then used to quantify the remaining body constituents andtheir respective growth rates (Taylor, 1980). Body protein is the drivingvariable in the model, the assumed goal of the broiler being to grow at itspotential body protein growth rate whenever possible (Emmans, 1981).Food intake, growth, body composition and yield, and a variety ofproduction indices are calculated in each simulation. The model also carriesout basic economic calculations to guide commercial decisions. This modelwas used to perform the simulations that have been used in this chapter.

Describing a population

The parameters describing the genotype of an individual would beexpected to vary normally between individuals in a population. It is this


variation that is used by geneticists to select the more favoured individualswithin a population, thereby moving the mean performance of the strainin a desirable direction. The extent to which each parameter varies and iscorrelated with other parameters, how these values may be predicted, andthe consequences of such variation on the mean performance of thepopulation will be dealt with below.

Variation in the environment within a broiler house

Controlling the physical microenvironment in a broiler house is animportant element in optimizing the production process (Reece and Lott,1982; Mitchell, 1985; Parmar et al., 1992; Aerts et al., 2000). However,depending on the system used for such control, variation in theenvironment within a poultry building may be considerable, impactingsignificantly on the performance of broilers housed in different areas ofthe house. Many factors contribute to this variation such as unadjustedinlet openings, unsealed cracks, dirty fan shutters, loose curtains, theamount of time the fans run, the total length of the timer cycle and theposition of thermo-sensors (Al Homidan et al., 1997, 1998). The behaviourof the broilers themselves will also cause variations in temperature alongthe length of the house, as a result of mass migrations and clustering insome areas (Wathes and Clark, 1981), which will affect thermoregulation.Such variation in the environment is likely to be positively correlated withthe variation in the weight of the end product of the production process,raising the question whether the optimum feeds or feeding programmeshould be adjusted to take account of this variation.

The vertical temperature profile in a poultry house is affected by manyfactors, including heat generated by heaters, the flock and solar radiation,microbial fermentation in the litter, heat fluxes between poultry house airand the soil, walls and roofs, due to temperature gradients, moisture lossfrom the litter and natural convection around broilers (Van Beek andBeeking, 1995; Boshouwers et al., 1996). However, of greater importancein a tunnel-ventilated house is the variation that exists in the horizontaltemperature profile at bird level. Winter and summer conditions alter thisprofile, with differences in temperature along the length of the housebeing considerably greater in winter than in summer. In winter, chicksoften migrate towards the air inlets, thereby increasing the stocking densityin that area, and the temperature differential in the early stages of growthcan be as high as 7–9°C (Xin et al., 1994) and remains at least 3.5°C coolerat the far end, with 7% higher relative humidity, by the end of theproduction cycle. In summer, because of the higher ventilation rates used,Xin et al. (1994) found little difference in temperature at either end of thehouse. Many factors interact to influence this gradient, so it would beexpected that the temperature and humidity gradient would differmarkedly between houses and between seasons.

Poor air quality, due to environmental contaminants such as carbon


monoxide, carbon dioxide, ammonia and dust, reduces performance,increases the potential for respiratory disease and may increase mortality(Weaver and Meijerhof, 1991). Conditions at the exhaust end of a tunnel-ventilated broiler house may be far more hostile than at the inlet end,especially in winter, resulting in considerable variation in the performanceof the flock.

The effects of variation in temperature, humidity and air quality in thebroiler house on the range of body weights present in the house at the endof the production cycle cannot be estimated empirically because of theexpected interactions between these environmental factors and potentialbody protein growth rate, feathering rate and the chemical and physicalcomposition of the feed, all of which are expected to vary also. Theseinteractions can only be assessed with the aid of mechanistic models.

Variation in the nutrient content of the feed

Variation in the nutrient content of feeds offered to broilers in acommercial operation is brought about through three main sources:variation in ingredient composition, mixer inefficiency (including weighingerrors) and separation after mixing and during transportation.

Sources of variation in the physical and chemical characteristics ofgrains used in poultry feeds include variety, seasonal effects, growth sites(Metayer et al., 1993), crop treatment and grain fumigants, post-harveststorage conditions and period of storage and processing (Dale, 1996;Hughes and Choct, 1999), rainfall and environmental temperaturepatterns during the period of grain maturation, genetic effects, level offertilizer usage (Metayer et al., 1993; Hughes and Choct, 1999) andinclusion rate (Senkoylu and Dale, 1999). This type of variation may bedealt with in the formulation process through non-linear stochasticprogramming (Roush et al., 1996), but the consequences of variationintroduced in this way, and through mixer inefficiency, must be modelleddifferently from the variation brought about through separation, which isintuitively less random than the first two types of variation.

Performance is adversely affected when variation in nutrient content infeeds is increased (Duncan, 1988; McCoy et al., 1994). Some of the moresophisticated feed formulation programmes used in the feed industry,which attempt to account for variation in nutrient content in theingredients used in the feed, generally favour the use of ingredients thatexhibit the least amount of variation, thereby potentially reducing thevariation in performance of the broilers being fed such feeds. However,whereas natural variation in the composition of a feed has zero cost, aconsiderable cost is incurred when attempting to reduce variation, as thesenon-linear programmes demonstrate, so there is an economic limit to theextent to which variation in nutrient content should be reduced.

Fawcett et al. (1992) attempted to determine this limit by predicting theresponse of broilers, in margin/m2, to a range of dietary lysine and ME


contents with the use of the ‘Poultry Growth Model’ of Emmans (1981),and then integrating the bivariate probability distribution for differentdegrees of variation in nutrient content over the response surface todetermine the value of reducing the variance in the feed. This approach,although interesting, does not simulate the day-to-day variation in feednutrient content to which broilers are subjected in practice, where nutrientcomposition varies continuously throughout the rearing period. A moreuseful technique would be to predict the response of each bird in thepopulation to random variations in feed quality on each day of thegrowing period, thereby obtaining a more realistic assessment of the effectof variation in feed quality. This would require a stochastic approach to thedefinition of the composition of the feed offered to the broilers, as well asto the broilers themselves.

Such an approach is a useful tool for determining the upper limit tothe value of variance reduction, but does not address the issue of furthersystematic variation in nutrient content brought about by separationduring road, rail, auger, blower or chain transportation. Such variationtends to separate the fine from the coarse particles, particularly when thefeed is conveyed in a mash form, or when the quality of pellets is poor,resulting in a high proportion of fines. This problem does not appear to beaddressed in the literature, so the variation introduced in this way isunknown, but could be considerable. This variation is likely to besystematic, in that separation would take place along the length of thefeeder lines, with fines being left behind as the coarser particles move tothe end of the line. If the fines consisted predominantly of major andminor minerals and vitamins, bone development could be seen to worsenat the far end of a broiler house compared with the end at which the feedis introduced. The effect of such nutrient separation could be modelled inthe same way as are the systematic changes that take place in theenvironment within a broiler house, the birds along the length of thehouse being subjected to changes in temperature, humidity and air quality.But it is not only the chemical separation of the food that takes place thatinfluences performance along the length of a broiler house; the physicalnature of the feed may also be affected.

Pelleted feeds are known to improve feed conversion efficiency whencompared with mash feeds (Jensen et al., 1962), this being due to theshorter period of time spent by the broilers consuming pellets, resulting inlower energy expenditure. The physical nature of the feed therefore hasan effect on performance and, because of the abrasive nature of somefeeding equipment used in broiler houses, the amount of time spenteating, and hence the energy expended in eating, may well increase as thedistance of the feed trough from the hopper increases.

If the performance of broilers subjected to variation in the chemicaland physical nature of the feed offered to them could be accuratelysimulated, a cost benefit analysis could be conducted to determine to whatextent the reduction in such variability is worth pursuing. Only with theaid of stochastic programming is such an analysis possible.


Generating a Population of Broilers

As argued above, when predicting the outcome of an experiment in apopulation of broilers it is more constructive and sound to simulate theperformance of each individual in the population and average theseresponses, rather than attempting to predict the response of thepopulation as a whole. For this approach to work, some theory of thestructure of a population must be developed. The values allocated to eachof the genetic parameters that describe each individual in the populationmust be seen as being stochastic, i.e. they are assumed to be normallydistributed in the population, and thus can be described by allocating amean and standard deviation to each parameter. The population is thendescribed by correlated distributions. Correlations between parameters areeasily dealt with when generating a population, but the values assigned tosuch correlations are not well researched. Of the six genetic characteristicsused to describe the potential growth rate of a broiler, the correlationsbetween B (a parameter defining the decline in logarithmic growth rate)and Pm (the weight of protein in the animal at maturity), and between Band feathering rate, are potentially the most important to be considered.

The negative correlation between B and Pm (Brody, 1945) may be dealtwith by the use of a scaled rate parameter, B*= B Pm 0.27 that is uncorrelatedwith Pm (Taylor, 1980; Emmans and Fisher, 1986). The variation in B andPm may be appreciable within a population, with suggested coefficients ofvariation (CV) of between 0.06 and 0.10, whereas that of B* may be muchlower, at between 0.02 and 0.04 (Emmans and Fisher, 1986). The CV of theparameter LPRm (the lipid:protein ratio in the body at maturity) has beenpredicted to be around 0.04 (Emmans and Oldham, 1988).

The genetic correlation of total feather score with body weight measuredby Singh and Trehan (2002) ranged between 0.179 and 0.444, while thatbetween the increase in feather density score from 4 to 6 weeks of age andbody weight was negative, varying from �0.189 to �0.323. Whereas thesegenetic correlations are relatively high, the negative phenotypic correlationis considerably greater than this, as can be demonstrated by simulation. Theheritability (h2) estimates of rate of feathering of broilers measured by Singhand Trehan (2002) at 10 days varied between 0.231 and 0.580, and the h2 offeather density scores was even higher (0.279–0.925), implying thatgeneticists have the potential to alter these characteristics relatively easily.This may prove to be a relatively simple method of overcoming the effects ofheat stress as broiler genotypes are selected for ever-faster growth rates, assuggested by Cahaner et al. (2003), given that feeding programmes areineffective in overcoming this stress.

Methods of Generating the Individuals Making Up the Population

The individuals making up a simulated population need to be generated insuch a way that the mean of each of the parameters generated is close to


the required mean, and the distribution of values about the mean reflectsthe required standard deviation. The parameter values for each individualmay be generated by means of random numbers. A random number is anumber chosen as if by chance from some specified distribution such thatthe selection of a large set of these numbers reproduces that distribution.The subject of random number generation and testing is reviewedextensively by Knuth (1997) and Hellekalek (2004). Many non-uniformrandom number generators are available, even in such accessibleprogrammes as Excel and Minitab, whilst the source code for generatingthese numbers in C++ is available free on the Internet. Theseprogrammes generate random data from a normal distribution, given themean and standard deviation of the variate. It is also possiblesimultaneously to generate values of correlated variates.

How Many Birds are Needed to Obtain a Realistic Result?

The length of time taken to simulate the performance of the population, inorder to calculate the population mean, is dependent on the number ofpopulation samples simulated, the complexity of the programme and thespeed of the computer. Clearly, the more samples that are simulated, themore representative the sample will be of the population, and therefore themore accurate the population mean estimate will be. Also, the larger thenumber of stochastic variables that will be varied in the simulation, the largerthe sample needs to be for an accurate estimate of the population mean. Sothe number of individuals may need to be large, and the computational timelong, if up to six parameters are made stochastic. For this reason, a weightedsampling method may be more practical. In this method, instead of choosingindividuals randomly selected from the multivariate normal distribution ofpopulation parameters, a sampling ‘design’ is created, in which a fixednumber of individuals with fixed parameter settings are chosen to besimulated. The number of individuals included for each parameter setting ischosen so that they approximate the frequencies of these parameter settingsin a normal distribution. The advantage of such a method is that even withrelatively small numbers of individuals the resultant population will beapproximately normally distributed.

Here is an example of such a design. Suppose m is the mean and d thestandard deviation (SD) of one genetic parameter in the population. Three‘points’ in the population are selected to simulate: those with parameters m,(m�1.5d), and (m+1.5d). That is, the mean, 1.5 SDs below the mean, and 1.5SDs above the mean. In the normal distribution, individuals at 1.5 times theSD from the mean occur with a frequency approximately 2/5ths of those thatoccur at the mean. So we can approximate a normal distribution bysimulating nine individuals: five at m, and two each at (m�1.5d), and(m+1.5d). Of course, the simulation need only be run three times, not nine,since the results for two individuals at the same point in the populationdistribution are always the same.


To extend this idea to two parameters, say x and y, nine populationpoints may be used instead of three: one for each combination of m,(m�1.5d), and (m+1.5d) for each of the two parameters. The number ofindividuals to be simulated at each point is just the product of the numbersused in the single parameter case as shown in Table 5.1.

There are a total of 81 individuals in this population, but only ninesimulations are needed: one for each of the parameter combinations in thetable.

The two methods were compared in an exercise in which the means ofincreasing numbers of individuals, generated with the use of randomnumbers, were compared with the mean individual in the population fromwhich the samples were drawn, and with the mean of the samplepopulation generated with the use of weighted sampling. Because theweighted sampling method produces a fixed population, the CV ofresponse variables does not differ unless the weightings are altered. Also,although the number of simulations is low for a relatively large population(nine simulations for 81 individuals, as described above), the number ofsimulations required rapidly increases as the number of geneticparameters is increased. For example, if six genetic parameters are varied,and three weightings are used, e.g. m, (m�1.5d) and (m+1.5d), the numberof simulations is increased to 36 = 729; and to 15625 where five weightingsare used. Clearly, this would not be a time-saving method, and the randomsampling method would be favoured under such circumstances.

Analysing the Sensitivity of the Genetic Parameters

As a first step in determining whether it should be necessary to simulatethe response of a population rather than that of the average individual, theeffect of variation in each of the genetic parameters describing theindividuals in a population should be simulated. If, by varying the


Table 5.1. An example of the use of the weighted samplingmethod in which a population is made up of 81 individualsusing fixed parameter settings (the mean (m), and + or � 1.5standard deviations (d) from m) for two independentgenotypic parameters. The number of individuals includedfor each parameter setting is chosen so that theyapproximate the frequencies of these settings in a normaldistribution.

Parameter x

Parameter y (m�1.5d) m (m+1.5d)

(m�1.5d) 4 10 4m 10 25 10(m +1.5d) 4 10 4

magnitude of each of the parameters about the mean, a linear response isobtained in the production variables of concern, then it would beunnecessary to simulate the response of more than the average individualin the population, as a sufficiently accurate assessment of the populationresponse could be obtained by applying some variation on either side ofthe resultant mean. It is tempting to use such a technique to generate apopulation response because of the saving in computation time, and forthis reason such a technique has been used in some models. However, ifthe response is not linear, or if interactions occur between parameters,then this method is invalid.

The sensitivity analysis technique proposed by Morris (1991), ofvarying one factor at a time, was used (Berhe, 2003) to determine to whatextent variation in each of the six parameters that describe the genotypewould influence the performance of the broiler. After simulating theresponse of the mean individual in a population, further simulations wereconducted in which each of the six genetic parameters was reduced, inturn, by 0.05, 0.10, 0.15 and 0.20, and then increased by the sameproportions. The exercise was conducted separately on male and femalebroilers, over two periods of growth (starter, 8–21 days, and finisher,22–35 days) using two feeds limiting in lysine (9 or 16 g lysine/kg in thestarter period, and 7 or 11 g/kg in the finisher period, the lysine:proteinratio being the same in both feeds within each period). The objective inusing two sexes, two periods of growth and two lysine contents was todetermine whether the responses to systematic changes in each geneticparameter remained constant under all these conditions.

The genetic parameters that were varied were Pm, B and LPRm(defined above), W0 (initial weight), MLG (maximum lipid in the gain) andFR (a feathering rate multiplier). Some of the results of this exercise areshown in Fig. 5.2, where the effect of variation in the six geneticparameters on food intake in males and females of a feather-sexable strain,in the starter and finisher periods, are illustrated. In both periods foodintake increased almost linearly with B, W0, MLG and Pm, the latter only atthe high lysine content in the starter, but at both lysine levels in the finisherperiod. This would indicate that, if only these four parameters were beingused to describe a population of broilers, there would be no greatadvantage in increasing computation time to simulate the population.

However, the effect of FR was non-linear in all cases, and morepronounced in females than in males, especially in the starter period. Foodintake dropped more substantially with FR among males fed a low lysinefeed in the starter period than those fed the high lysine feed. The effectswere more pronounced and more uniform in the finisher than in thestarter period. The theory of food intake regulation of Emmans (1987)predicts that food intake would decline with a higher rate of feathergrowth, given that the processes of food intake and growth generate heatthat must be lost to the environment if the bird is to remain in thermalneutrality and hence grow at its potential; if the bird cannot lose this heatto the environment, food intake will be constrained. This would occur at


high environmental temperatures and particularly in a bird with anextensive feather cover. The amount of variation introduced by varying FRwas often as great as that resulting from the same degree of variation in B,except that food intake was affected only when FR was above the mean;but the important distinction is between the linear effects of B and thenon-linear effects of FR.

As the CV of FR increases, an increasing proportion of thepopulation (those with the greatest feather cover) will have their foodintake constrained by their inability to lose heat to the environment. Thisis illustrated in Fig. 5.3 by means of frequency distributions of the finalbody weights of broilers given feeds sufficient to allow them to grow attheir potential; as FR is increased, the range of final body weights isincreased, but the distribution is negatively skewed resulting in a lowermean body weight for the population. As the genotype, the feed and theenvironment influence food intake and growth rate, it would be expectedthat the effect of variation in FR would differ depending on the foodcomposition and the prevailing environmental conditions. These will bereferred to below.


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FE

G H

Parameter value (deviation from mean %)

Foo

d in

take

– F

emal

e (%

)F

ood

inta

ke –

Mal

e (%

)

Fig. 5.2. The relative effect on food intake in male and female broilers fed a lysine-limitingfeed containing 9 (A, C) or 16 g lysine/kg (B, D) from 7 to 21 days (left) or 7 (E, G) or 11 glysine/kg (F, H) from 22 to 35 days (right) when the means of each of six genetic parameterswere increased or decreased by 0.05, 0.1, 0.15 or 0.20 whilst holding the five remaininggenetic parameters constant (B = .-�.-; Fr = ..-�..-; LPRm = ..�..; MLG = --�--; Pm = —�—;and Wo = —�—).

Effect of variation in FR on the response to dietary lysine at threeenvironmental temperatures

The simulated effects of increased variation in FR on food intake andconsequent protein gain of female broilers in the period 22 to 35 d of ageare illustrated in Fig. 5.4. Six lysine-limiting feeds (from 4 to 14 g lysine/kgfeed) were offered at three environmental temperatures. Many points ofinterest arise from these simulations. At 29°C, food intake is severelydepressed on all feed treatments, yet food intake increases as the lysinecontent of the feed is reduced, the ability of the birds to compensate forthe deficiency being constrained by, among others, the greater feathercover. As the prevailing temperature declines so the overall food intake isincreased, but the differential between the highest and lowest intakes,especially on the lowest lysine feeds, widens, i.e. the effect of the heavierfeather coat is relatively more severe in constraining intake as theenvironmental temperature is decreased. The characteristic decline in food


2600240022002000180016001400

40

30

20

10

0

CV = 0.0

Body weight (g)2600240022002000180016001400

40

30

20

10

0

CV = 0.05

Body weight (g)

2600240022002000180016001400

40

30

20

10

0

CV = 0.10

Body weight (g)2600240022002000180016001400

40

30

20

10

0

CV = 0.15

Body weight (g)

Fre

quen

cy

Fre

quen

cy

Fre

quen

cy

Fre

quen

cy

Fig. 5.3. Effect of increasing the coefficient of variation (CV) of feathering rate on thefrequency distribution of body weights at 35 d of age in a simulated group of male broilersgiven feeds designed to enable them to achieve their potential growth rate.

intake on feeds with the lowest lysine contents (Gous and Morris, 1985;Burnham et al., 1992) is evident only at the lower environmentaltemperatures. The efficiency of utilization of lysine for body proteingrowth remains the same at all temperatures on the marginally deficientfeeds, so protein gain is the same for a given lysine intake; it is only onfeeds with the highest lysine contents, and at the higher environmentaltemperatures, that protein growth rate is curtailed due to the rapidfeathering rate, resulting in a separation of the maximum protein growthrates at high dietary lysine contents.

Effect of variation in FR on the optimum dietary amino acid contents

Because of the non-linear effect of variation in FR on the performance ofbroilers, it might be expected that the optimum amino acid contents offeeds would differ for the mean individual in the population and for thepopulation itself, and that this difference would increase with variation inFR. However, in spite of a considerable reduction in populationperformance resulting from an increase in the CV of feathering rate (Table5.2), the optimum amino acid contents of the three feeds used in thefeeding programme remained relatively similar for the individual and forthe five populations of broiler females. In the initial series of optimizationsa fixed feeding programme was used, namely, 600 g/bird starter, 1200


100

120

140

16080

100

120

60

80

100

4 6 8 10 12 14 16Lysine content (g/kg)

A

B

C

3

6

9

12

3

6

9

Foo

d in

take

(g/

d)

2

4

6

400 600 800 10001200140016001800Lysine intake (mg/bird day)

A

B

C

Pro

tein

gai

n (g

/d)

Fig. 5.4. The effect of variation in feathering rate (FR) on food intake (g/day) and bodyprotein gain (g/day) of female broilers from 22 to 35 days of age, fed lysine-limiting feeds atenvironmental temperatures of 29°C (A), 25°C (B) and 21°C (C). Coefficients of variationused were 0.0 (�—�), 0.05 (---), 0.10 (�-..-�) and 0.15 (*-.-*).

g/bird grower and the remainder finisher. The CVs of five of the genotypicparameters were held constant (W0 = 0.1, Pm = 0.1, B* = 0.06, LPRm =0.06 and MLG = 0.1) whilst FR was varied. A population of 100individuals was generated afresh for each optimization.

Only one obvious trend emerged from this exercise, namely that theoptimum lysine content in the grower feed increased with variation in FR.Interestingly, this happened also when a fixed number of days on eachfeed was used in place of the fixed amount of each food (Table 5.2). Theinconsistent variation in optimum lysine contents (less when using a fixednumber of days in the feeding programme) probably reflects the variationin the responses to different populations that were simulated for eachoptimization. Generally, though, optimum lysine contents were the same inthe starter feeds, higher in the grower feeds, and lower in the finisherfeeds for populations than for the mean individual in the population.

The relatively small differences in amino acid contents of the threefeeds required to optimize performance of the mean individual and that ofthe population are of more than passing interest, considering that themean performance of the population is much reduced when variation inFR is high. Two precedents can be found to substantiate this observation.The first is in Wethli and Morris (1978), where it was demonstrated thatthe daily tryptophan required by a flock of laying hens does not decrease


Table 5.2. Optimum 35-day performance, and optimum lysine contents in feeds, of anindividual and a population of broiler females, where margin/m2 annum was maximized at fivecoefficients of variation (CV) of feathering rate, whilst the CVs of W0, Pm, LPRm and MLGremained the same, as given in the text. Two feeding programmes were used: fixed amountsof each feed, or a fixed number of days on each feed. Populations of 100 birds weregenerated afresh for each optimization.

CV of feathering rate

Indiv. 0.00 0.05 0.10 0.15 0.25

Liveweight, g/bird 1968 1969 1966 1885 1775 1630Food intake, g/bird 2844 2852 2883 2728 2565 2344Breast meat, g 344 345 343 329 307 279Abdominal fat, g 47 46 49 41 37 31Cost of feeding, relative 100 101 101 97 91 84Margin over feeding cost 100 100 98 95 90 82

Optimum lysine content, g/kg feedFixed amount of feed:Starter (600 g/bird) 12.95 13.11 13.11 13.11 12.95 12.47Grower (1200 g/bird) 8.72 8.94 9.17 9.17 9.17 9.40Finisher (remainder) 8.11 7.89 7.16 7.89 7.89 8.08

Fixed number of days:Starter (14 days) 13.14 13.11 13.11 13.11 12.64 13.11Grower (10 days) 9.16 9.39 9.61 9.61 9.66 9.77Finisher (remainder) 8.12 8.11 8.11 8.11 7.81 7.99

during the first laying year, despite a decrease in mean rate of egg output.The second is that when pigs are housed at high stocking rates, causingreduced feed intakes and growth rates, efficiency of lysine utilization isunaffected by the stress, and optimum biological performance is obtainedon feeds with lysine contents the same as those which optimize theperformance of individually housed pigs growing close to their potential(B.A. Theeruth and R.M. Gous, 2005, unpublished results). It is notunusual, therefore, for the optimum feeds to be unaffected by the reducedmean performance of the animals in the population.

Effect of variation in FR on the optimum feeding programme

The non-linear effect of FR on the performance of a population was againdemonstrated where the feeding programme of broiler males and femaleswas optimized, with margin over feeding cost being maximized, first when only five of the genetic parameters were varied (using the same CVsas in the previous exercise, and the CV of FR = 0), and secondly, with theCV of FR = 0.2. The results of the optimization process for an individualand for the two CVs of FR are given in Table 5.3. Whereas theperformance at the optimum was the same for individuals and for apopulation in which the CV of FR was 0.0, the performance of thepopulation with a higher CV of FR was markedly lower, this being theresult of the difficulty that broilers with a high FR experience in losingheat to the environment, which results in a constrained growth rate. Theoptimum amounts of each of the three feeds in the feeding programmealso reflect these differences in performance: with no variation infeathering rate the optimum feeding programme for the population isalmost the same as for an individual, whereas with a large variation infeathering in the population, approximately twice the amount of starterfeed is required by the population and, in males, approximately twice theamount of grower feed is also required in order to maximize margin overfeeding cost.

Conclusions

Two conclusions may be reached from these exercises, both of which relateto the non-linear effect of variation in FR, which both increases thevariation in response within a population and decreases its meanperformance. The first is that, where a fixed feeding programme is beingused, the optimum amino acid content in the feeds used in the programmediffers only marginally for a population and for the mean individual in thepopulation; whereas, if proprietary feeds of fixed composition are beingused, almost twice as much of the starter and grower feeds is needed tooptimize the performance of a population of broilers compared with thatrequired for the mean individual in the population. The second conclusion


is that, because the effect of FR is non-linear, whereas that of the othergenetic parameters is linear, if a population model is to be used whenoptimizing the feeding programme of broilers, the population meanshould be generated by simulating the responses of individual animalswhose genotypes reflect the diversity found in a given population. It is notpossible to generate a population of broilers successfully without using thistechnique.

References

Aerts, J.M., Berckmans, D., Saevels, P., Decuypere, E. and Buyse, J. (2000)Modelling the static and dynamic responses of total heat production of broilerchickens to step changes in air temperature and light intensity. British PoultryScience 41, 651–659.

Al Homidan, A., Robertson, J.F. and Petchey, A.M. (1997) Effect of temperature,litter and light intensity on ammonia and dust production and broilerperformance. British Poultry Science 38, S5–S6.

Al Homidan, A., Robertson, J.F. and Petchey, A.M. (1998) Effect of environmentalfactors on ammonia and dust production and broiler performance. BritishPoultry Science 39, S9–S10.

Berhe, E.T. (2003) Introducing stochasticity into a model of food intake and growthof broilers. MScAgric thesis. University of KwaZulu-Natal, Pietermaritzburg,South Africa.

Brody, S. (1945) Bioenergetics and Growth. Reinhold, New York. Boshouwers, F.M.G., Develaar, F.G., Landman, W.J.M., Nicaise, E and Van Den

Bos, J. (1996) Vertical temperature profiles at bird level in broiler houses.British Poultry Science 37, 55–62.

Burnham, D., Emmans, G.C. and Gous, R.M. (1992) Isoleucine responses in broilerchickens. Interactions with leucine and valine. British Poultry Science 33, 71–87.


Table 5.3. Simulated 35-day comparative performance of an individual and of a population ofmale and female broilers at, and amounts of each feed needed to achieve, maximum marginover feeding cost, when the coefficient of variation (CV) of feathering rate is increased from0.0 to 0.2 with the CV of all other genotype parameters remaining the same in bothpopulation simulations.

Male broilers Female broilers

Individual Population Individual Population

CV = 0.0 CV = 0.2 CV = 0.0 CV = 0.2

Body weight, g 2359 2336 2080 1920 1911 1679Food intake, g 3762 3735 3335 3230 3230 2924Breast meat, g 404 400 351 336 334 289Margina 100 99 62 100 99 61Starter, g/bird 225 300 465 143 185 340Grower, g/bird 524 585 1160 428 408 470Finisher, g/bird 3013 2850 1710 2659 2637 2114

aMargin over feeding cost, relative to individual.

Cahaner, A., Druyan, S. and Deeb, N. (2003) Improving broiler meat production,especially in hot climates, by genes that reduce or eliminate feather coverage.British Poultry Science 44, S22–S23.

Dale, N. (1996) Variation in feed ingredient quality: oilseed meals. Animal FeedScience Technology 59, 129–135.

Deming, W.E. (1986) Out of the Crisis. MIT Center for Advanced Engineering Study,Cambridge, Massachusetts.

Duncan, M.S. (1988) Problems of dealing with raw ingredient variability. In:Haresign, W. and Cole, D.J.A. (eds) Recent Advances in Animal Nutrition.Butterworths, Boston, Massachusetts, pp. 3–11.

EFG Software Natal (1995) Advanced Computer Software for the Animal Industry.http://www.efgsoftware.com/ (accessed February 2005).

Emmans, G.C. (1981) A model of the growth and feed intake of ad libitum fedanimals, particularly poultry. In: Hillyer, G.M., Whittemore, C.T. and Gunn,R.G. (eds) Computers in Animal Production. Occasional Publication No.5. BritishSociety of Animal Production, Edinburgh, UK, pp. 103–110.

Emmans, G.C. (1987) Growth, body composition, and feed intake. World’s PoultryScience Journal 43, 208–227.

Emmans, G.C. and Fisher, C. (1986) Problems of nutritional theory. In: Fisher, C.and Boorman, K.N. (eds) Nutritional Requirements and Nutritional Theory.Butterworths, London, pp. 9–39.

Emmans, G.C. and Oldham, J.D. (1988) Modelling of growth and nutrition indifferent species. In: Karver, S. and Van Arendonk, J.A.M. (eds) Modelling ofLivestock Production Systems. Kluwer Academic, Dordrecht, Netherlands,pp. 13–21.

Fawcett, R.H., Webster, M., Thornton, P.K., Roan, S.W. and Morgan, C.A. (1992)Predicting the response to variation in diet composition. In: Recent Advances inAnimal Nutrition. Butterworths, Boston, Massachusetts, pp. 137–158.

Fisher, C., Morris, T.R. and Jennings, R.C. (1973) A model for the description andprediction of the response of laying hens to amino acid intake. British PoultryScience 14, 469–484.

Gous, R.M. and Morris, T.R. (1985) Evaluation of a diet dilution technique formeasuring the response of broiler chickens to increasing concentrations oflysine. British Poultry Science 26, 147–161.

Gous, R.M., Pym, R.A.E., Mannion, P. and Wu, J.X. (1996) An evaluation of theparameters of the Gompertz growth equation that describe the growth of eightstrains of broiler. In: Balnave, D. (ed.) Australian Poultry Science Symposium, Vol.8. University of Sydney, Sydney, New South Wales, pp. 174–177.

Gous, R.M., Moran, E.T. Jr, Stilborn, H.R., Bradford, G.D. and Emmans, G.C.(1999) Evaluation of the parameters needed to describe the overall growth, thechemical growth and the growth of feathers and breast muscles of broilers.Poultry Science 78, 812–821.

Hancock, C.E., Bradford, G.D., Emmans, G.C. and Gous, R.M. (1995) Theevaluation of the growth parameters of six strains of commercial broilerchickens. British Poultry Science 36, 247–264.

Hellekalek, P. (2004) PLab. Theory and Practice of Random Number Generation.http://random.mat.sbg.ac.at/ (accessed February 2005).

Hughes, R.J. and Choct, M. (1999) Chemical and physical characteristics of grainsrelated to variability in energy and amino acid availability in poultry. AustralianJournal of Agricultural Research 50, 689–701.

Jensen, L.S., Merrill, L.H., Reddy, C.V. and McGinnis, J. (1962) Observations on


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eating patterns and rate of food passage of birds fed pelleted and unpelleteddiets. Poultry Science 41, 1414–1419.

Knap, P.W. (1995) Aspects of stochasticity: variation between animals. In: Moughan,P.J., Verstegen, M.W.A. and Visser-Reyneveld, M.I. (eds) Modelling Growth in thePig. EAAP publication no 78, Wageningen Agricultural University,Wageningen, Netherlands, pp.165–172.

Knuth, D.E. (1997) The Art of Computer Programming: Seminumerical Algorithms, Vol.2, 3rd edn. Addison-Wesley, Reading, Massachusetts, USA.

Mack, S., Hohler, D. and Pack, M. (2000) Evaluation of dose-response data andimplications for commercial formulation of broiler diets. In: Balnave, D. (ed.)Australian Poultry Science Symposium, Vol. 12. University of Sydney, Sydney, NewSouth Wales, pp. 82–87.

McCoy, R.A., Behnke, K.C., Hancock, J.D. and McEllhiney, R.R. (1994) Effect ofmixing uniformity on broiler chick performance. Poultry Science 73, 443–451.

Metayer, J.P., Grosjean, F. and Casting, J. (1993) Study of variability in Frenchcereals. Animal Feed Science and Technology 43, 87–108.

Mitchell, M.A. (1985) Effects of air velocity on convective and radiant heat transferfrom domestic fowls at environmental temperatures 20°C and 30°C. BritishPoultry Science 26, 413–423.

Morris, M.D. (1991) Factorial sampling plans for preliminary computationalexperiments. Technometrics 33, 161–174.

Parmar, R.S., Diehl, K.C., Collins, E.R. and Hulet, R.M. (1992) Simulation of aturkey house environment. Agricultural Systems 38, 425–445.

Reece, F.N. and Lott, B.D. (1982) The effect of environmental temperature onsensible and latent heat production of broiler chickens. Poultry Science 61,1590–1593.

Roush, W.B., Cravener, T.L. and Zhang, F. (1996) Computer formulationobservations and caveats. Journal of Applied Poultry Research 5, 116–125.

Senkoylu, N. and Dale, N. (1999) Sunflower meal in poultry diets: a review. WorldPoultry Science Journal 55, 153–174.

Singh, P. and Trehan, P.K. (2002) Inheritance of rate of feathering and featherdensity score and its relationship with body weight in broiler chicken. SARASJournal of Livestock and Poultry Production 18, 41–47.

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Van Beek G. and Beeking, F.F.E. (1995) A simple steady state model of thedistribution of vertical temperature in broiler houses without internal aircirculation. British Poultry Science 36, 341–356.

Wathes, C.M. and Clark, J.A. (1981) Sensible heat transfer from the fowl: radiativeand convective heat losses from a flock of broiler chickens. British Poultry Science22, 185–196.

Weaver, W.D., Jr and Meijerhof, R. (1991) The effect of different levels of relativehumidity and air movement on litter conditions, ammonia levels, growth andcarcass quality for broiler chickens. Poultry Science 70, 746–755.

Wethli, E. and Morris, T.R. (1978) Effects of age on the tryptophan requirement oflaying hens. British Poultry Science 19, 559–565.


Xin, H., Berry, I.L., Tabler, G.T. and Barton, T.L. (1994) Temperature andhumidity profiles of broiler houses with experimental, conventional andtunnel ventilation systems. Applied Engineering in Agriculture 10, 535–542.


6 Advancements in EmpiricalModels for Prediction andPrescription

W.B. ROUSH

USDA-ARS Poultry Research Unit, Mississippi State, MS 39762, [email protected]

From the beginning of efforts to model systems – long before the computer era – linearity has dominated computation. This is not because anyonebelieved that the systems of interest were truly linear, but simply for reasons ofcomputational tractability.

(Simon, 1990)

Nothing in Nature is random … A thing appears random only through theincompleteness of our knowledge.

(Spinoza; quoted by Peitgen et al., 1992a, p. 319)

Introduction

The objective of this chapter is to present some thoughts on developmentsin empirical prediction and prescription modelling. Each topic hasinteresting implications for biological modelling. It is beyond the scope ofthis chapter to go into detail. It is hoped that this brief introduction to thedevelopments in empirical models will serve as a catalyst in promoting andconsidering their inclusion in the development of animal models.

Some Modelling Concepts

Modelling animal responses for prediction and prescription applications isbiologically complex. The ideal animal model for biological and economicdecisions has been identified as being composed of mechanistic, stochasticand dynamic elements (Fisher, 1989; Theodorou and France, 2000).


Mechanistic and empirical models

Brown and Rothery (1994) define mechanistic models as concerned with the‘nuts and bolts’ of biological processes and the way in which thecomponent parts fit together. They attempt to describe the observations interms of fundamental postulates about the biological processes. Theodorouand France (2000) have noted that mechanistic models are constructed bylooking at the structure of the whole system, dividing it into its keycomponents and analysing the behaviour of the whole system in terms ofits individual components and their interactions with one another.

In contrast, empirical models provide quantitative descriptions ofpatterns in the observations without attempting to describe the underlyingprocesses or mechanisms involved. In a sense, all models are empirical,differing only in the degree of resolution and level of complexity.Nevertheless, the broad distinction between mechanistic and empiricalmodels is a useful one (Brown and Rothery, 1994).

Theodorou and France (2000) have noted that the accuracy ofprediction of animal response using mechanistic models currently may belower than that achieved by the empirical methods used in practicalapplication. However, these research models are very useful in evaluatingthe adequacy of current knowledge and data, identifying those areaswhere research should be focused.

Empirical models are commonly referred to as black boxes. That is,their mathematical workings are not transparent. Mechanistic models, atthe other extreme, are white boxes (or at least off-white boxes). The goal isto have mechanistic models in which the workings are transparent. Artificialneural networks (to be discussed later) are the ultimate empirical black box.

Recent research has suggested a merger between empirical andmechanistic models. The merging of the two methods of modelling resultsin a grey-box model. The grey-box model is intended to blend the better of twoworlds: knowledge-based modelling and black-box modelling (Oussar andDreyfus, 2001).

Stochastic and fuzzy logic models

Two of the tenets of classical science are order and precision. Howevernature is not always orderly and precise. There is much variability andimprecision. Casti (1994) comments:

… one of the great challenges to both science and philosophy is to provide arational, coherent account of the perceived uncertainty surrounding the eventsof daily life. Classical probability theory offers one such approach but is riddledwith many well-known epistemological flaws and paradoxes. The theories offuzzy sets, satisfying and possibilities represent recent attempts to rectify someof the deficiencies in the classical methods. Each of these newer schemes has atits heart the basic fact that randomness is only one face of the mask ofuncertainty.

98 W.B. Roush

The stochastic and fuzzy concepts change the picture of the accurateand precise answer of a deterministic model to a model that producesanswers that are based on probability and possibility. This presents achallenge to the researcher in classical modelling and decision making. AsZimmerman (1992) points out:

… until the 1960s, uncertainty, vagueness, and inexactness were features withrather negative meanings. Nobody wanted to be called a ‘vague decisionmaker’; a scientist that could not make precise and definite statements was notregarded as a ‘true’ scientist, and uncertainty was considered to be somethingdisturbing that should, if at all possible, be avoided in models, theories, andstatements. The only theory that dealt with uncertainty was probability theory,and this – predominately in its frequentative interpretation – was restricted tosituations in which the law of large numbers was valid and uncertainty couldbe attributed to randomness.

Recent discoveries in nonlinear dynamics (chaos theory) furthercomplicate the matter of uncertainty by calling into question the nature ofrandomness (Peitgen et al., 1992a).

Probability versus precision

Precision and accuracy in meeting nutrient levels and animal requirementshave been important goals; however, the inherent biological variance ofnutrients and requirements cannot be overlooked. Deming (2000) in hisstudies on quality control has shown the futility of trying to get rid ofvariability.

Precision and accuracy relate to average values. The variability ofnature makes the decisions associated with biology into risk problems(Roush, 2001a). That is, in the case of nutrients, with what probability canan animal’s requirement be met? Consideration of chance-constrainedprogramming, as an alternative to linear programming, to accomplish thisprobabilistic approach to feed formulation is discussed below under theheading Prescription Models.

Fuzzy set logic: dealing with imprecision

Fuzzy logic was introduced by Dr Lotfi Zadeh (1965) as a means ofdefining the uncertainty of natural language to a computer. Forexample, how does one define the concepts of hot and cold in acomputer program? To a human these words have meaning, though nota precise meaning. The fuzzy set concept is related to set theory. Intraditional set theory an object is a member of a set of like objects. Forexample, in comparing a baseball with a book, it is obvious that thebaseball would belong to a set of round objects and a book would belongto a set of square objects. In the case of the colour spectrum, thequestion becomes where does red become yellow and yellow become

Advancements in Empirical Models for Prediction and Prescription 99

red? From the fuzzy logic point of view the nanometres of lightrepresenting red would be full membership in a red set and thenanometres of light representing yellow would be full membership inthe yellow set. Nanometres representing colours between red and yellowwould have partial memberships in the red and yellow sets. Half waybetween the red and yellow are the nanometres representing orangewhich would have 0.5 membership in the red set and 0.5 membership inthe yellow set. Other imprecise concepts such as hot and cold, light andheavy, short and tall, etc. can be represented by fuzzy logic in a similarmanner. Roush et al. (1989) and Roush and Cravener (1990) used fuzzylogic to describe the imprecise concept of stress in a caged layingsituation. Fuzzy sets have been applied to the imprecision of humannutrition and nutritional requirements by Wirsam and Uthus (1996),Wirsam et al. (1997) and Gedrich et al. (1999).

There have been interesting fuzzy logic extensions to modelling ofcontrol systems (Kosko, 1992) and simulations of social interaction of fish,using fuzzy cognitive maps (Dickerson and Kosko, 1997).

Nonlinear dynamics: developmental history

Aristotle (c. 330 BC) pointed out that the ‘whole is greater than the sum ofits parts’. This is very evident in agricultural systems in which the responseof the organism results from the interaction of numerous inputs. Biologicaland environmental inputs and the resulting outputs are not necessarilyadditive or linear.

Sir Isaac Newton, early in his education, was a student of Aristotle’sphilosophy. However, Newton’s views of the world changed as he was laterinfluenced by the works of René Descartes and other mechanicalphilosophers. The mechanical philosophers, in contrast to Aristotle, viewedthe world as composed entirely of particles of matter in motion and heldthat all phenomena of nature result from their mechanical interaction(Encyclopædia Britannica, 15th edn).

As a result, Newton and Descartes were advocates of a universe thatoperates like clockwork, where everything is very orderly and mechanical.The assumption was that if enough is known about a system (universe),there is nothing that cannot be predicted for that system (universe). Underthis philosophy, the universe was a gigantic complicated clockworkmechanism. The logic makes perfect sense that, if we understand each andevery part of the machine, then we can predict how the machine will actand react. By taking apart the clock and studying each gear, anunderstanding of the workings of the clock can be developed. Hence thedevelopment of a reductionist approach to science.

Modern biology has inherited the reductionist approach. The livingorganism is viewed as a complex biochemical machine. Examination ismade of the organs, tissues, cells and even the molecules in an effort todefine the mechanisms of life. Although the mechanistic view is desirable, it

100 W.B. Roush

has been recognized that the ideal model involves, in addition to definingmechanisms, the inclusion of stochastic and dynamic concepts. Modelsneed to contain all three elements. The current focus has been mainly onmechanistic models. There is a caveat that the exclusion of the dynamicand stochastic elements in modelling promotes an illusion of precision inattaining answers.

Mathematics of chaos theory

The firm concept of mathematical predictability, derived from experiencewith linear equations, changed in 1963 when a weather researcher, EdwardLorenz, discovered that small changes in the initial conditions (e.g.1.00000 to 1.00001) of his mathematical model would result inunpredictable changes in response over time. He developed a very simplecomputer model of motion in which the air is heated from below andcooled on top. Hot air rises and cold air falls. The air moves in rotatingcylinders that bring the hot air up and the cold air down on the other side.The motion of the air mixes the hot and cold air, reducing the temperaturedifference which is driving the motion of the air. Meanwhile the air is stillbeing heated from below and cooled at the top. After the cylinders of airslow to a complete stop, they begin to rotate again and sometimes theyrotate in the opposite direction. That is, if the rotation was originallyclockwise, a switch is made to a counter clockwise direction. The rotation ofthe cylinder speeds, slows and the rotation changes.

The Lorenz system consisted of three coupled differential equations(Gleick, 1987):

dx/dt = 10 (y – x)dy/dt = – xz +28x – ydz/dt = xy – (8/3 z).

If a simple three equation model like that of Lorenz can exhibit surprisingdynamics, what does this infer about the dynamics involved in thenumerous differential equations involved in making a mathematical modelof a broiler, pig or cow?

The dynamics of the new science of chaos (Gleick, 1987) can beillustrated with the following difference equation:

Xt+1= a Xt(1–Xt).

This (logistic) equation looks very predictable. However when iterated overtime as a difference equation the dynamics can be quite dramatic withchanges in the coefficient ‘a’.

May (1976) comments:

The fact that a simple deterministic equation can possess dynamical trajectorieswhich look like some sort of random noise has disturbing practical implications.It means, for example that apparently erratic fluctuations … need notnecessarily betoken either the vagaries of an unpredictable environment or


sampling errors: they may simply derive from a rigidly deterministic …equation such as (the logistic difference equation).

His sobering point is that the dramatic responses are not an influenceof the environment or of measurement error. The dramatic responses area phenomenon of nonlinear mathematics.

The reader is encouraged to examine the phenomenon with thefollowing BASIC program:

10 INPUT a20 x = 0.5432130 FOR n = 1 to 15040 x = a*x*(1-x)50 PRINT x60 NEXT n70 STOP

It is suggested to start ‘a’ at 2.0. Then increase the value of ‘a’ until itequals 4.0. There will be a change in the output from periodic responses toaperiodic (chaos) responses.

It seems as though there are different levels of the nonlinear dynamics.Difference equations capture the moment-to-moment oscillation, whiledifferential equations capture the overall effect of interacting variables. Itseems that a three-dimensional system of first-order ordinary differentialequations is required for the manifestation of chaotic behaviour (May,1976).

It is interesting that

Xt+1= a Xt (1–Xt)

is the difference equation form of the differential equation

which is the rate (velocity) form of the logistic equation of Robertson(1908) (see Parks, 1982, p. 14). The equation is commonly used to modelgrowth in population studies. Derivation of the difference equation todescribe logistic growth from the Verhulst differential equation is outlinedin Solé and Goodwin (2000).

Because animal growth is often described as a logistic equation, thenext question is whether, in real life, growth shows the same moment-to-moment dynamics as the difference equation form of the logistic equation.

Several studies have shown the day-to-day growth rate (velocity) ofbroilers to be oscillatory (Roush et al., 1994; Roush and Wideman, 2000). Theoscillation has exhibited evidence of the new mathematics of chaos. Biologicalsystems, including heart rate dynamics and other physiological systems, havealso shown evidence of chaos (Degn et al., 1986; Glass and Mackey, 1988).

How does one deal with the nonlinear dynamics of chaos? A similarproblem in dealing with uncertainty and lack of precision occurs inquantum theory. The suggested solution is to take a probabilistic point of

dXdt

aX (1 X )t t= −

102 W.B. Roush

view. Mathematical chaos, along with randomness and imprecision, thenbecomes a component of the variability inherent in the system.

For further information on nonlinear dynamics (chaos) and its relatedtopic, fractals, the following are suggested: Peitgen et al. (1992a,b); Moon(1992); and Williams (1997).

Operations Research: the Science of Decision Making

Operations (Operational) Research (OR) is the formal discipline thatencompasses the development of the concepts, methods and tools fordecision modelling. It has a successful history for making efficient andeffective management decisions (Hillier and Lieberman, 2005). Roush(2001b) has discussed OR from a poultry science point of view.

Much of the fundamental research for empirical prediction andprescription decisions involves the discipline of OR. The development ofOR decision tools encompasses the disciplines of mathematics, statistics,decision sciences, computer science and artificial intelligence. The wellknown linear program was developed within the OR discipline.

Prediction models

Predictive models are designed to generate knowledge and come to thetruth without making any value judgments (Casti, 1989). Predictive modelsare made for growth, feed intake, etc.

Traditionally, the tools for prediction have been algebraic andregression equations, differential and difference equations. These are validand useful. However, research in artificial intelligence has added someadditional approaches including artificial neural networks, fuzzy logic andgenetic algorithms for modelling and prediction. In addition, the KalmanFilter, a self-adjusting regression associated algorithm, has been suggestedfor short term predictions (Roush et al., 1992).

Statistical analysis for biological research is sometimes taught as anembellishment for a research project and it is often applied to the data asan afterthought. In reality, the statistical design is an important tool forobtaining a perspective of what is going on with the data and for efficientand effective analysis. Traditionally, the student was taught to hold allvariables constant except for the variable of interest. This principle iswidely followed but, with the aid of modern statistical techniques it is nowpossible to test many variables at the same time. It is interesting to notethat Beveridge (1957) gave this advice in 1957.

Regression analysis: response surface methodology

Factorial statistical models are known by most students who have taken agraduate course in statistics. Usually the factorial model is analysed


qualitatively as an analysis of variance. However when factorial modelsinvolve quantitative values such as levels of nutrients, an effective design isto use response surface methods (RSM).

Response surface methods allow the simultaneous variation of two ormore variables to find the quantitative level that will give the mostdesirable response. Box and Wilson (1951) were the first to report on thistopic. Recommended texts on response surface methodology are Cochranand Cox (1957), Box and Draper (1987), Khuri and Cornell (1996) andMyers and Montgomery (2002).

Yoshida et al. (1962, 1968, 1969) have used RSM to optimize thegrowth and feed efficiency of chicks by varying protein and energy levels ofthe ration. Mraz (1961a,b) used RSM to study the influence of calcium,phosphorus and vitamin D3 on the uptake of several minerals. Waddel andSell (1964) used RSM designs to study the effects of calcium andphosphorus on the utilization of iron by the chick. The studies by Mrazand Waddel and Sell appear to have used RSM for their efficiency ratherthan for their optimization capabilities.

Roush et al. (1979) used RSM to investigate the protein and energyrequirements of Japanese quail. The study showed an advantage of RSMto identify optimal conditions outside the exploratory region covered in aninitial trial. A second experiment was run using the first trial predictedoptimum to pinpoint the optimal protein and energy levels for bodyweight gain and feed conversion. Roush (1983) used RSM to examine theprotein levels in broiler starter and finisher diets and the optimal time ofration change. Roush et al. (1986) investigated optimal calcium andavailable phosphorus requirements for laying hens using RSM.

The response surface model allows the researcher to examine optimalconditions such as the optimal levels of protein and energy to produce aresponse. This is much more powerful and informative than justexamining differences between treatments.

The following is an example of a nonlinear quadratic equation to befitted by regression analysis:

This model would probably give a useful approximation to the trueresponse surface. Three dimensional and two dimensional contour plotscan be drawn to define visually the optimum combination of variables andthe value at the optimum. These optimum values can also be found bytaking the first derivative of the equation for each variable and setting theequations equal to zero.

Mixture models: making a cake

Mixture designs are a type of response surface design that have applicationto problems in the animal sciences. In the general mixture problem, the

y = b +b x +b x +b x +b x +b x x0 1 1 2 2 11 12

22 22

12 1 2

104 W.B. Roush

measured response is assumed to depend only on the proportions of theingredients present in the mixture and not on the amount of the mixture(Snee, 1971; Cornell, 2002). However there are mixture designs where theamount is also considered (Piepel and Cornell, 1985). Types of mixtureproblems include cake formulations, content of construction concrete,making flares, fruit punches, photographic film and gas blends. The modeladds to unity and does not have an intercept.

Gous and Swatson (2000) have used mixture experiments to study theability of the broiler to choose from three protein sources the combinationof ingredients that would maximize biological performance. Roush et al.(2004) suggested that the optimal time to feed broilers the starter, growerand finisher feeds could be viewed as a mixture problem with the objectiveof finding the optimal proportion of time to feed each diet.

Artificial neural networks – the ultimate black box

Neural networks are an alternative to regression analysis. The neuralnetwork was inspired by the structure and function of biological neurons.Neural networks are trained through iteration of example patterns. Theneuron receives one or more inputs and transforms the sums of thoseinputs to an output value which in turn is transferred to other neurons.The artificial neural network is a set of processing units that simulatebiological neurons and are interconnected by a set of weights that allowsboth serial and parallel processing through the network. The artificialneuron works like a switch; when there is sufficient neurotransmitteraccumulated in the cell body, an action potential is activated. In theartificial neuron, a weighted sum is made of the signals coming into a nodefrom other nodes. A comparison is then made to a threshold value. If thethreshold is exceeded, the node fires a signal that becomes the input foranother node or an output value. The key attribute of a neural network isnot the complexity of the neurons: power comes from the density andcomplexity of the interconnections (Cross et al., 1995).

One of the challenges for neural networks is the over-training of themodel to the point that the model is not useful beyond the data on which itwas trained or developed. This is also true of regression polynomials. Theregression polynomial can be over developed by adding more variables tothe model. The neural network overcomes this problem in two ways. Thefirst method is to include a test set which represents a randomly chosen setof data from the training data set (for example 20% of the training dataset) that is set aside. During the training procedure the model iscontinually evaluated against the test data set and the error between theinput and output is determined. As the training proceeds, it is expectedthat the error between predictions and actual values of the test set will

y = b x + b x +b x +b x x +b x x +b x x1 1 2 2 3 3 12 1 2 13 1 3 23 2 3


decrease. There will be a point at which the errors will start to increasewhich is the point at which over-training has started to occur. That is thepoint at which the neural network is saved. At this point, validation is madeof the new neural network on data that are independent of the trainingand testing data sets. The second procedure for reducing over-training isto use statistical Jack-Knife and bootstrap procedures, where theexperimental data are re-sampled in the process of development of theneural network. In this way there is not a need for the test set.

The development of neural networks can incorporate training, testing(to avoid over-training) and validation to make robust models. Forexample Roush et al. (1996b) developed an artificial neural network topredict the presence or absence of ascites in broilers. The neural networkwas a three layer back propagation neural network with an input of 15physiological variables. After developing the neural network with trainingand test sets, the neural network predictive ability was validated with twodata sets that were not involved in the training. The neural networkaccurately identified two false positives and one false positive in the firstand second evaluation data sets, respectively. The birds identified as falsepositives were actually determined to be in the developmental stages ofascites.

There are many different types of neural networks. These differenttypes can be generally classified as supervised and unsupervised networks.In supervised learning, the neural network learns from an example. Withunsupervised learning, the neural network examines the data to defineclusters of information. The neural network is used to associate data,classify data, transform data into a different representation and to modeldata (Zupan and Gasteiger, 1993). The commercial neural networkpackage NeuralShell 2 (Ward Systems Group, 1996) contains 16 differenttypes of neural network, which include the following:

1. Backpropagation neural networks. This neural network is the standard.Usually three layers are sufficient. The layers are the input, hidden andoutput layers. Each layer is linked only to the previous layer.2. Jump connection neural network. This type of backpropagationnetwork has every layer connected to every previous layer.3. Recurrent network. This is a type of backpropagation neural network.There is feedback to previous layers. These networks are often used fortime series data. Regular feed forward neural networks respond to a giveninput with the same output each time. A recurrent network may respondto the same input pattern differently from time to time, depending uponthe input patterns previously presented to it. The recurrent networkbuilds a long term memory based on the patterns presented. 4. Kohonen architecture. This is an unsupervised neural network. It isable to learn without being shown correct output patterns. The use of thistype of network is for clustering problems. The network is able to separatedata into a specified number of groups or categories.5. Probabalistic neural network (PNN). This is a powerful neural network

106 W.B. Roush

for classification problems. It is able to train on a sparse data set. PNNseparates data into a specified number of categories. 6. General regression neural networks (GRNN). GRNN are powerfulneural networks that have been shown to outperform backpropagationmethods. They train quickly on sparse data sets and are particularly usefulfor continuous function approximation as in the case of examining therelation between body weight and time. The GRNN is a three-layer neuralnetwork with the number of hidden neurons equal to the number oftraining patterns. 7. Group method of data handling (GMDH). This network derives amathematical formula which is a nonlinear polynomial expression relatingthe values of the most important inputs to predict outputs. The networkworks very much like the genetic algorithm in that the mathematicalexpression is based on variables that survive.

For more information on neural networks (and fuzzy logic) see Tsoukalasand Uhrig (1997).

Genetic algorithms

Genetic algorithms are search procedures that use the principles of naturalselection and genetics. The genetic algorithm was first developed by JohnH. Holland in the 1960s. The search procedure is usually looking for anoptimum condition. The model to be optimized can be a formula or even aneural network in which the maximum, minimum or a particular value isrequired. The genetic algorithm works particularly well with problems thatare ‘not well behaved’. That is, situations where it may be difficult to findthe global optimum.

Commercial neural networks and genetic algorithms are available thatcan be incorporated into a spreadsheet. The setup for the geneticalgorithm is based on an objective equation and constraints similar to thesetup of a linear program.

Kalman filter: tracking targets

The Kalman filter is a recursive algorithm for making short termpredictions. Biological monitoring is complicated by variation (noise) inresponses that may mask abrupt changes in responses. The monitoring ofchanges in responses containing variation is a common problem in manydisciplines. An algorithm was developed by Kalman (1960) for applicationto such problems. The algorithm has been used for navigation, missileguidance, and satellite tracking. This type of problem requires short-termprediction and adjustments. The Kalman filter has been applied tobiological problems such as monitoring renal transplants (Smith and Cook,1980; Smith and West, 1983; Trimble et al, 1983), heart rates (Heath, 1984)


and poultry production responses (Garnaoui, 1987; Roush et al., 1992).The Kalman Filter has predicted animal breeding values (Hudson, 1984),estimated lactation curves (Goodall and Sprevak, 1985) and feed intakeand growth of beef cattle (Oltjen and Owens, 1987).

Prescription Models

Prescription models are designed to define values in making decisions.Linear programming for feed formulation is one of the most commonlyused prescriptive models.

Linear programming

Since its inception in 1947, linear programming has been the workhorse ofdecision-making algorithms. Numerous texts and applications have beenwritten about its use. Linear programs have been used for blending (e.g.petroleum products), mixes (e.g. investments and budgeting), scheduling(e.g. production to satisfy customer demand, production capacity, andstorage limitations), assignment (e.g. workers to tasks) andtransportation/dispatching (e.g. routing of pick up and deliveries). In theanimal sciences, the term ‘linear programming’ is considered by many assynonymous with the mixing problem of feed formulation. The Sadiacompany, the largest broiler producer in Brazil, used linear programmingand other operations research methods effectively to improve decisionmaking about production and product distribution in their business(Taube-Netto, 1996).

The linear program consists of an objective equation and constraintequations. For example in a feed formulation problem the objective is tominimize the cost of ingredients subject to meeting the nutritionalconstraints. The following is an example:

Objective equation:Minimize cost: 0.08 Maize + 0.20 Soybean

Constraint equations:87 Maize + 488 Soybean ≥ 230 (protein constraint)Maize + Soybean = 1 (amount constraint)

where 0.08 and 0.20 represent the price ($/kg) of maize and soybean and87 and 488 represent the protein contents (g/kg) of these ingredients. Theobjective is to minimize the cost of the diet, subject to the constraints thatthe protein supplied by the maize and soybean together must be ≥ 230g/kg diet (the requirement of the animal) and the fractional amounts ofmaize and soybean must total to 1.

Mathematically there are certain assumptions made about linearprogramming (Render and Stair, 1982; Roush et al., 1996a):

108 W.B. Roush

1. Conditions of certainty exist; that is, the numerical values in theobjective and constraint equations are known with certainty and do notchange during the period being studied. It is assumed there is novariability in the numerical values.2. Proportionality exists in the objective and constraints. This means thatthe units are consistent for each of the equations. 3. Additivity is assumed: that is, the total of the activities equals the sum ofeach individual activity.4. Divisibility is assumed: that is, the solutions need not be whole numbers.Instead, they are divisible and may take a fractional value.5. The answers or variables are non-negative.

Early in the advent of computer formulation with linear programming, itwas recognized that biological variability, particularly nutrient variability,was a problem in meeting the nutrient requirements of animals. A linearprogram solution based on an ingredient matrix of average nutrient valueshas a 50% probability of not meeting the nutrient requirements of a groupof animals. In order to avoid this risk, some nutritionists incorporate amargin of safety in the ingredient matrix. Nott and Combs (1967)suggested an adjustment of the nutrient means by subtracting (or adding)a fraction (they suggested 0.5) of the standard deviation from (or to) thenutrient mean which would provide a probability of 69% or greater inmeeting the nutrient requirement. The adding or subtracting depends onwhether the constraint is for a maximum or minimum value.

Generally there is not a problem in meeting assumptions (2)–(5) forfeed formulation. However, the basic assumption of certainty (1) is violatedby the inherent nutrient variability of feed ingredients. A consequence ofthis violation brings unexpected results. Usually there is an over-formulation of the requested probability and requirements in the feedformulation.

Chance constrained programming

A more appropriate approach is to use chance-constrained programming(sometimes referred to as stochastic programming). Using the exampleabove the protein constraint becomes:

This method more accurately calculates the nonlinear nutrient variation.An intuitive analogy is to compare the following two, similar looking, butunequal equations:

9 + 16 =7 (6.1) and

9+16 =5 (6.2)

87 Maize+ 488 Soybean – 0.5 (8 Maize) +(4 Soybean) 2302 2 ≥


The linear program with a margin of safety corrects the nutrients byadjusting the individual square root values as in Eqn 6.1 and the chanceconstrained program adjustment is accomplished by a square root of thesummation (Eqn 6.2). The consequence is that Eqn 1 has a larger numberthan Eqn 6.2. From a feed formulation point of view there would be anover-correction using the Eqn 6.1 approach. The overcorrection results ina higher cost ration and overshoots the requested probability for nutrientlevel. Roush et al. (1996a) discuss examples of the difference between linearprogramming with a margin of safety formulation and a chance-constrained program formulation.

Goal programming: more than one objective

The goal program is a multiple objective approach to solving mathematicalprogramming problems. Ignizio and Cavalier (1994) point out that the goalprogram may more accurately define real world problems than a rigid singleobjective linear program. A single objective linear program sometimes resultsin solutions that are infeasible. In contrast, the philosophy of a goal programis of satisficing and not that of optimization. The concept of satisficing is anattempt to seek an acceptable solution, that is, one that satisfies desired goals(Ignizio and Cavalier, 1994). The approach is to make the goals intoconstraints. Examples and illustrations of the methodology can be found inHillier and Lieberman (2005), Oberstone (1990) and other operationsresearch and management science texts.

Several animal science papers have been based on goal programmingincluding Rehman and Romero (1984, 1987), Lara and Romero (1992,1994) and Zhang and Roush (2002).

It should be noted that a fuzzy linear program is a special case of agoal program. Examples of such a program are given in Zimmermann(1996).

Quadratic programming

Miller et al. (1986) and Pesti et al. (1986) combined broiler growthequations obtained using response surface methodology with quadraticprogramming. The result was that they were able to demonstrate that aquadratic programming model would provide a method of rationformulation that would take into account the productivity of the broiler.They did this by defining a quadratic objective as the growth response tointake of protein and energy. Live weight, transformed to feed input space,was maximized subject to a given cost per bird and other commonconstraints in linear programming of a feed mix. Linear programming(LP) and quadratic programming (QP) results were compared. Pesti et al.(1986) reported the energy concentrations of the diets were similar by bothmethods of formulation (LP = 13.62 and QP = 13.232 MJ/kg). However,

110 W.B. Roush

the protein content was much higher when the QP method was used (LP= 217 and QP = 244 g/kg). Miller et al. (1986) reported that analysis usingQP indicated that a leading broiler firm could have improved economicefficiency by increasing protein density and (slightly) reducing energydensity of broiler finisher feed. Further if this was applied industry wide,the savings would be US$120 million per year.

Decision analysis

Decision analysis is a technique for providing solutions to problems bydetermining proper courses of action. The decision method isaccomplished by listing all available courses of action, expressing subjectivevariables quantitatively, and determining possible returns based on eachaction. Decision analysis is a framework upon which mathematical modelscan be evaluated under different scenarios.

Roush (1986) showed how conventional decision analysis using a profitpotential equation based on different price situations for eggs and feedcould be used to examine the number of hens to place in laying hen cages.In two subsequent papers, Roush et al. (1989) and Roush and Cravener(1990) used fuzzy decision analysis to evaluate crowding of caged layinghens based on cage space (in the first paper) and cage space and colonysize (in the second paper). Multicriteria decision analysis was applied byRoush and Cravener (1992) to demonstrate how the choice of acommercial laying hens strain could be made when the information usedin the comparison has incommensurate units.

Conclusion

This chapter has been an attempt to present some of the developments inempirical models that may help in defining and making decisions withanimal models.

Casti (1989) lamented:

Should you have the misfortune to pick up a typical current textbookpurporting to address the arcane arts of mathematical modelling, the chancesare overwhelmingly high that the author will transport you back into the 1950swith an account of how to model an oscillating pendulum, freeway traffic, ordog food using the static, equilibrium-centered, linear techniques ofmathematical programming, regression analysis or, perhaps, elementaryfunctional analysis. My feeling is that the time is long overdue to bring themathematics of the 1980s into contact with the students of the 1980s and offercourses on modelling that stress dynamics rather than statics, nonlinearityrather than linearity and possibility rather than optimality.

Though there is still room for improvement, several modelling bookshave modernized their mathematical approaches (e.g. Griffiths andOldknow, 1993; Brown and Rothery, 1994).


In the experience of the author, some of the mathematical resultsappear to some researchers and practitioners to be ‘tricks with smoke andmirrors’. One can be assured that the results of a concept like chance-constrained programming are real. There are measurable differences inthe nutrients formulated with a margin of safety and with a chance-constrained approach. There are mathematical reasons for this.

The nonlinear dynamics of chaos are also real. May (1976) suggested

… that people [should] be introduced to X(t+1)=aXt(1�Xt) [i.e., the LogisticEquation] early in their mathematical education. This equation can be studiedphenomenologically by iterating it on a calculator, or even by hand. Its studydoes not involve as much conceptual sophistication as does elementarycalculus. Such study would greatly enrich the student’s intuition aboutnonlinear systems.

The study of chaos, its implications and how it occurs, is a hot topic inmathematics and physics. The dynamic results are not tricks.

Developments in empirical modelling are constantly expanding.Nonlinear mathematics, Artificial Intelligence and a relatively new field,Artificial Life (Levy, 1992), are areas where, in the opinion of the author,there will be important melding of empirical and mechanistic modelling.

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116 W.B. Roush

7 The Problem of Predicting thePartitioning of Scarce Resourcesduring Sickness and Health in Pigs

I. KYRIAZAKIS AND F.B. SANDBERG

Animal Nutrition and Health Department, Scottish Agricultural CollegeWest Mains Road, Edinburgh, EH9 3JG, [email protected]

Introduction

Pigs are often faced with the problem of partitioning one or more scarcefood resources. This situation may arise when they are offeredintentionally restricted amounts of food, but also when they are offered adlibitum access to a food. In the latter case intake of scarce resources mayarise when pigs are given access to a poor quality food (e.g. bulky food,Whittemore et al., 2001) or when environmental stressors unintentionallyconstrain food intake (e.g. high environmental temperature, Wellock et al.,2003a). The voluntary reduction of food intake that accompaniessubclinical infection (anorexia, Kyriazakis et al., 1998) is a special case thatmay lead to intake of scarce resources.

We are interested in the problem of predicting the partitioning ofabsorbed scarce protein (and energy) to protein (PR) and lipid (LR)retention in healthy and ‘diseased’ growing pigs. Quantitative solutions tothis problem in healthy pigs have been evolving for over 30 years. For thisreason, we will start with a historical approach to resolving the issue. Wewill then discuss the current solutions to it offered in the literature and aimto reach a solution that appears able to predict satisfactorily protein andlipid retention in healthy growing pigs. The preferred solution will formthe basis of a framework that will be developed to account for thepartitioning of absorbed scarce resources in pigs challenged by pathogens.This part of the framework will mainly have a heuristic value, as it will bepointing towards issues that need to be resolved in order to be able topredict adequately protein and lipid retention in pigs challenged bypathogens.


Inherent in the above is the definition of scarce food resources. We takethese to be resources that limit the pig from achieving its capacities, forexample for maximum protein retention (PRmax), as these are defined by itsgenotype. For a description of these capacities and the resultant nutrientrequirements, the reader is referred to Emmans and Kyriazakis (2001).

A Historical Perspective to the Partitioning of Scarce Protein andEnergy in Healthy Pigs

The current solutions to the problem of partitioning scarce protein andenergy in pigs are summarized in Table 7.1. The solutions have beengrouped according to the ‘school of thought’ they have evolved from; thisis the key characteristic they invoke to resolve the problem.

Some of these solutions have now only historical value and theirproposers have replaced them with more recent ones, e.g. Whittemore andFawcett (1974, 1976) have been replaced by Green and Whittemore (2003).Others represent a purely statistical, best-fit approach to a particular dataset (van Milgen and Noblet, 1999) and hence lack general applicability.These solutions will not be considered any further here.

Three of the remaining proposed solutions may be rejected onqualitative grounds alone. Whittemore (1995) and Green and Whittemore(2003) propose the ratio of lipid to protein in the body as a possibleconstraint to PR. Operating within a certain range, this solution does notallow lipid to be lost whilst there is a gain in protein, despite the strongevidence that this can occur (Stamataris et al., 1991; Kyriazakis andEmmans, 1992a,b). The rule of Fuller and Crofts (1977) recognizes thatthe efficiency of using protein above maintenance might be a function of

118 I. Kyriazakis and F.B. Sandberg

Table 7.1. The current solutions to the problem of predicting the partitioning of scarceresources. The solutions have been grouped together according to the key characteristic theyinvoke to resolve the problem.

Solutions Key characteristic

Whittemore and Fawcett (1974, 1976)Whittemore (1995)

A minimum ratio of lipid to protein in gainde Lange (1995)Green and Whittemore (2003)

Fuller and Crofts (1977) Efficiency of using protein

Black et al. (1986)de Greef and Verstegen (1995)NRC (1998) Marginal responses in protein retention to van Milgen and Noblet (1999) energy intakevan Milgen et al. (2000)

Kyriazakis and Emmans (1992a,b) Marginal responses in protein retention to Sandberg et al. (2005a,b) ideal protein intake

⎫⎩⎧⎭

⎫⎪⎬⎪⎭

}

the energy to protein ratio of the food. It calls for the values of fourparameters in order to solve the problem; each of these values are stated tobe affected by genotype, state, liveweight and nutritional history. Thepractical consequence of the solution is that each experiment needs to becarried out across all of these factors, possibly in all combinations, in orderfor the rule to apply in any given case. An enormous amount ofinformation is called for, and for this reason this rule will not be discussedany further. The same criticism applies to the rule proposed by van Milgenet al. (2000), as they estimate that 21 parameters are required in order topredict protein and lipid retention. The information required by this rulefor any particular genotype, existing in the future, is unlikely ever to beavailable. Sandberg et al. (2005a,b) have provided recently a more detailedcriticism on the deficiencies of the three rules and why they cannot have ageneral application to the prediction of PR and LR.

The three solutions that survive qualitative testing againstexperimental evidence (i.e. Black et al., 1986 (and its derivative by NRC,1998); Kyriazakis and Emmans, 1992a,b and de Greef and Verstegen,1995) identify the marginal response in protein retention to protein andenergy intakes as the key variable to solving the problem. Black et al. (1986)proposed that:

PR = b . (MEI – (c . MEm)) g/day (7.1)

where MEI is metabolizable energy intake, c is a constant and MEm is themetabolizable energy requirement for maintenance. On the other hand,Kyriazakis and Emmans (1992a,b) propose that:

PR = ep. (IP – IPm) g/day (7.2)

where IP is the ideal protein intake and IPm the ideal protein requirementsfor maintenance. The solution offered by de Greef and Verstegen (1995)has been shown by Emmans and Kyriazakis (1997) to be algebraicallyequivalent to that offered by Kyriazakis and Emmans (1992b) and has arelatively high information requirement. For these reasons, their solutionwill not be considered further here. The question then is whether either ofthe above two key parameters, the marginal response in PR to energysupply (b) and the marginal response in PR to protein supply (ep) areaffected by the pig, the environment in which it is kept and the compositionof the food it is offered. These factors will be considered in turn below.

The Marginal Response in Protein Retention to Energy Supply

The solution of Black et al. (1986) was developed for energy limiting foods,i.e. when MEI is less than required for PRmax. An implicit assumption wasthat for such foods the value of b would be independent of food composition,i.e. it would attain its maximum value. Below we review the effects ofliveweight, genotype including sex, and environmental temperature on themarginal response in protein retention to energy supply on such foods.

Partitioning of Scarce Resources during Sickness and Health 119

The effect of liveweight

The experiment of Quiniou et al. (1995) where pigs of different liveweight(range 45 to 94 kg) were given access to four levels of feeding, all of whichprovided a constant high supply of protein, is shown in Fig. 7.1.

A model that fitted a common slope of PR against MEI (i.e. b) was notstatistically different from a model that allowed for different slopes atdifferent liveweights. In addition, the different slopes did not support asystematic change in the value of b with increasing liveweight. This findingis consistent with subsequent experiments performed by Quiniou et al.(1996) and Mohn et al. (2000), who concluded that stage of growth had nosignificant effect on b.

The contradictory evidence comes from the experiment of Dunkin andBlack (1985) who estimated values of b, for pigs of a range of liveweight (30to 90 kg) fed eight levels of an energy limiting food. The values of b were8.25, 6.44, 5.75 and 6.75, respectively and therefore they too do notsupport a systematic effect of liveweight on the value of b. The latter wouldbe the necessary quality of a rule that aims to have a general applicability.The evidence, taken as a whole therefore, is more consistent with the viewthat the marginal response in protein retention on energy limiting foodsdoes not vary with pig liveweight.


5 7 9 11 13 15 17 19 21

ME intake (MJ/day)

210

190

170

150

130

110

90

70

Pro

tein

ret

entio

n, P

R (

g/da

y)

Fig. 7.1. The response in protein retention (PR) to metabolizable energy intake (MEI) abovemaintenance of pigs of four different live weights (Quiniou et al., 1995): these were 45 kg(–�–), 65 kg (- -�- -), 80 kg (–�–) and 94 kg (- -�- -). The four levels of MEI were achieved byfour levels of feeding, all of which provided a constant high supply of protein. A commonslope has been fitted for the relationship between PR and MEI.

The effect of genotype, including sex

Two experiments have addressed the effect of genotype on the marginalresponse in PR to energy supply. Kyriazakis et al. (1995) used two verydifferent breeds of pig, Chinese Meishan and F1 Large White � Landrace,and gave them access to a high protein basal food that was diluted withstarch to different extents. The authors concluded that the values of b werevery similar between the two breeds (9.65 (SE 0.16) and 9.93 (SE 0.55)),respectively. The experiment of Quiniou et al. (1996) is morecomprehensive as three genotypes, boars and castrates of a Large White �Pietrain breed and castrates of a Large White breed were used. Theresponses in PR to four levels of energy intake at a constant high proteinintake were considered at four different liveweights. The authorsconcluded that the response in PR to increasing supplies of ME wasindependent of liveweight, but differed between genotypes, when theintercept of the response was fixed. The highest marginal response wasobserved in the Large White � Pietrain boars. Recently, Sandberg et al.(2005b) reanalysed the data of this experiment by assuming that both theintercept and slope of the response were allowed to vary. A model with acommon slope was not statistically different from the model where theslopes were different between genotypes. Based on the above, the evidenceon the effect of genotype on b is inconclusive.

The effect of environmental temperature

In their proposals for the nutrient requirements for swine, NRC (1998)suggested that the marginal response to energy intake, on protein-adequate foods, falls as the temperature increases. The argument followsfrom the experiment of Close et al. (1978), whose data are plotted in Fig.7.2.

Although it is difficult to be certain that the foods used in theexperiment were limiting in energy, the data are far from persuasive thatthe response varied with temperature. This is consistent with the view ofBlack et al. (1986) and Wellock et al. (2003a), who propose thatenvironmental temperature has no effect on the marginal response in PRto energy intake on protein adequate foods.

The Marginal Response in Protein Retention to Protein Supply

Unlike the previous solution, the rule proposed by Kyriazakis and Emmans(1992a,b) is intended to apply across protein- and energy-limiting foods.According to this rule, such foods are defined according to their ratio ofthe metabolizable energy content (MEC, MJ/kg) to the digestible crude


protein content (DCPC, kg/kg) of the food, R (MJ ME/kg DCP). Foods witha value of R > 72.55 are defined as being protein limiting and themarginal response in PR to protein supply on such foods, ep, is assumed toattain its maximum value (ep)max. Foods that are defined as energy limitinghave an ep that varies according to R:

ep = µ.R (7.3)

The above rule makes the distinction between the protein and energydependent phases of the marginal response in PR to protein supply. Themarginal response in PR when both the energy and the protein allowancesoffered to pigs are varied is shown in Fig. 7.3.

Thus, liveweight, genotype and environmental temperature have thepotential to affect both (ep)max in protein limiting foods and ep in energylimiting foods.

The effect of liveweight

Experiments that address the effect of liveweight on the marginal responsein PR to protein supply have usually employed protein-limiting foods.Most of these experiments (e.g. Black and Griffiths, 1975; Campbell et al.,


0 500 1000 1500 2000 2500

MEI (kJ/kg0.75.day)

300

250

200

150

100

50

PR

(kJ

/kg0

.75 )

0

Fig. 7.2. The response in protein retention (PR kJ/kg0.75.day) to metabolizable energy intake(MEI kJ/kg0.75.day) for pigs given different allowances of the same food at five differenttemperatures from Close et al. (1978); 10°C (�), 15°C (�), 20°C (�), 25°C (�), and 30°C (�).The regression line for all the data is PR = 0.147 (0.0062).MEI – 44.07 (7.58).

1985a; Mohn et al., 2000; and de Lange et al., 2001) conclude that themaximum ep, around 0.75, is not affected by liveweight. The onlyexperiment where a liveweight effect has been reported is that of Campbelland Dunkin (1983) who found a high response in N retention to N intakefor pigs between 1.8 and 6.5 kg liveweight. Their value of (ep)max is closer to0.90 and it is perhaps a reflection of the difficulty in measuring N balancein very small pigs. Emmans and Kyriazakis (1996) have measured the ep forsmall (12 kg) and large (72 kg) pigs given access to both protein- andenergy-limiting foods. The mean values of ep are not different between thetwo different liveweights on any of the foods used.

The effect of genotype, including sex

Kyriazakis et al. (1994) used entire male Large White � Landrace and purebred Chinese Meishan pigs to investigate the effect of genotype on therelationship between food composition and ep in foods of varyingenergy:protein ratios, R. The value of ep was found to be directly proportionalup to a maximum value of R. The overall constant of proportionality, µ, was0.0108 and did not differ significantly between the two breeds. Themaximum value of ep was also similar between the two breeds.

Other experiments by de Greef et al. (1992) and Fuller et al. (1995) alsoconclude that the maximum ep does not differ between different genotypes.There is also evidence that different sexes of pigs use a limiting proteinsupply with similar efficiency, ep. Campbell et al. (1984, 1985b) found nodifference in maximum ep between entire males and females. The data ofBatterham et al. (1990) shown in Fig. 7.4 lend strong support to thisconclusion.

It would, therefore, appear safe to conclude from the aboveexperiments that the marginal response in PR to protein supply does notdiffer between different genotypes, including sexes.


Pro

tein

ret

entio

n (g

/day

)

Protein intake (g/day)

PRmaxE3

E2

ep

E1

Fig. 7.3. The predicted rates of protein retention of a pig given access to feeds of differentprotein contents at different levels of feed (and hence energy intake). Feeding levels E1 andE2 constrain protein retention by being energy limiting, whereas level E3 is protein limitingand hence allows the animal to reach its maximum rate of protein retention, PRmax.

The effect of environmental temperature

The data of the experiment by Ferguson and Gous (1997), who grew pigsfed ad libitum from 13 to 30 kg on food with 93–230 g crude protein/kg at18, 22, 26 and 30°C, are reproduced in Fig. 7.5.

The data clearly show that the marginal response in protein retentionwas not affected by environmental temperature. They are consistent withthe findings of Berschauer et al. (1983) and Campbell and Taverner (1988)who conclude that temperature does not affect ep.

Predicting Protein and Lipid Retention of Healthy Pigs

The implication of the above is that, irrespective of whether PR is madeeither a function of energy or a function of protein intake, the informationrequired to predict the rates of protein and lipid retention are low. Themarginal response in protein retention would be unaffected by pigliveweight and genotype, and even by the environmental temperature.Given this, the application of either framework would predict that pigsselected, for example, for different levels of fatness when they have beengiven access to a non-limiting food, would perform identically when theyare given access to the same amount of food above maintenance, which is


Lysi

ne r

eten

tion

(g/d

ay)

10

8

6

4

2

00 2 4 6 8 10 12 14 16 18

Ileal digestible lysine intake (g/day)

Fig. 7.4. Response in lysine retention (Rlys g/day) to ileal digestible lysine intake (Ilys g/day):the regression line is Rlys = 0.763.(Ilys – 1.245) for the combined data of male (�) and female(�) Large White (20–45 kg) pigs used by Batterham et al. (1990). Separate plateaux formales and females are shown.

limiting for both genotypes. The same would apply for male and femalepigs, despite the fact that females have the propensity to be fatter thanmales of the same protein weight when fed ad libitum. Here, it would beimportant to emphasize that we need to account for potential differencesbetween the genotypes (or sexes) in their maintenance requirements. Thishas not always been taken into account in the interpretation ofexperiments that have measured PR responses to different levels ofprotein and/or energy intake (e.g. Quiniou et al., 1996, see above).

A second implication is that both frameworks are capable of makingpredictions across a wide range of conditions. These include conditionswhere the pig is depositing protein at the expense of lipid retention. Suchconditions may arise in weaned pigs consuming small amounts of arelatively high protein content food (Kyriazakis and Emmans, 1992a,b).Many current solutions in the literature are still unable to predict this (e.g.de Lange, 1995; Whittemore, 1995; Green and Whittemore, 2003).

The framework that predicts PR as a function of protein intake does soon the basis of ideal protein. It is, therefore, an implicit assumption in thisframework that the marginal response in PR will be the same for all aminoacids, when they are first limiting. This assumption has recently beenchallenged by Heger et al. (2002, 2003), but there is considerableuncertainty over their estimates of maximum efficiency of amino acidretention (with values ranging from 1.17 to 0.66 for different amino acids).


Pro

tein

ret

entio

n (g

/day

)140

120

100

80

60

2050 100 150 200 250 300 350 400

Crude protein intake (g/day)

40

Fig. 7.5. The response in protein retention to crude protein intake for pigs fed ad libitumfoods that were limiting in protein at four different temperatures: 18°C (�), 22°C (�),26°C (�), and 30°C (�) as found by Ferguson and Gous (1997). The solid line is describedby PR = 0.525 (CPI – 4.92) until the plateau of 117.4 g/day is reached.

For the time being it may be safe to assume a single overall efficiency for allamino acids, whichever is the first limiting (Sandberg et al., 2005b).

Whilst the position that the marginal response in protein retentionmay only be affected by food composition may be attractive from anutritional modelling point of view, it can be viewed as having unattractiveperspectives (Luiting and Knap, 2005). Animal breeders, interested ingenetic variation between individuals, have criticized it on the basis that itdoes not ‘accommodate a genotype-specific drive towards body fatness aswell as a drive towards protein deposition’. The task is always to keep theframework variables to the necessary minimum in order to lead totractable solutions and make predictions for populations of pigs. Thisbecomes more important when the framework is broadened to account, forexample, for the partitioning of nutrients during disease.

The Partitioning of Scarce Protein in Pigs Challenged byPathogens

When a pig that has not been previously exposed to a pathogen, i.e. animmunologically naive pig, encounters the pathogen for the first time, itmay require nutrients for functions that will enable it to cope with thechallenge. Such functions may include the innate immune response, whichis one of the first lines of defence to pathogens, and the repair andreplenishment of damaged or lost tissue, such as blood plasma or cells.Eventually, the pig will be expected to develop an acquired immuneresponse towards the pathogen, and nutrient resources will need to bedirected towards the maintenance of this function. When the pig is re-exposed to the same kind of pathogen, the main additional resourcerequirement would be due to the function of acquired immunity, asinvestment towards this function would minimize the potential pathogen-associated damage to the host.

When nutrient resources are scarce, the challenged pig can be seen ashaving the problem of allocating these resources between its variousfunctions. These arise from the exposure to the pathogen, but they alsoinclude the ‘normal’ functions of a healthy pig, such as maintenance andgrowth. In this chapter, we concentrate upon the problem of allocatingscarce protein during exposure to pathogens. This is because: (i) currentevidence suggests that protein is often the first limiting resource inchallenged pigs; (ii) many components of the immune response are highlyproteinaceous (Houdijk et al., 2001); and (iii) as a consequence, mostevidence in the literature is in relation to the partitioning of protein oramino acids during challenge. There is some limited evidence that energymay become a limiting resource during pathogen challenge, as aconsequence of the increased energy requirements due to fever and therequirements of the immune response. It is generally accepted, however,that these requirements are relatively small for growing animals (chickens,Klasing et al., 1987; mice, Demas et al., 1997; pigs, van Heugten et al., 1996).


The partitioning of scarce protein during pathogen exposure in naive pigs

Exposure to pathogens is usually accompanied by a voluntary reduction infood intake in naive hosts, Fig. 7.6. The extent of anorexia is dependenton pathogen dose, i.e. the number of pathogens that enter the host. Thereis, however, a wide range of doses over which animals show a reduction inthe order of 15–20% of their normal voluntary food intake: this range ofdose is often that associated with sub-clinical disease. Higher pathogendoses may lead to clinical disease and catastrophic reductions in voluntaryfood intake. Currently there are at least two proposed mechanisms thatmay lead to this pathogen-induced anorexia: (i) food intake is reducedbecause the potential for growth (protein retention) of the challengedanimal is reduced (Wellock et al., 2003b); and (ii) the reduction in foodintake is a direct consequence of the exposure to the pathogen (Kyriazakiset al., 1998). Mechanism (ii) implies that the animal will always be in a stateof nutrient (protein) scarcity during exposure to pathogens.

As stated previously, a naive pig exposed to a pathogen would beexpected to divert resources towards the functions of innate immunity andrepair; some resources will also have to be diverted towards the acquisitionof immunity. These increased requirements appear only as increases inmaintenance requirements, in experiments where naive pigs have beenexposed to a variety of antigenic challenges, including pathogens (Webel etal., 1998a,b). In addition, the marginal responses in protein retention toeither protein or energy supply do not seem to be affected by exposure topathogens in naive pigs (Van Dam et al., 1998; Webel et al., 1998a,b). Thisimplies that the function of innate immunity, at least, is prioritized over thefunction of growth in terms of nutrient allocation. The above further implythat the framework developed to predict protein retention for healthy pigsneeds to be modified only slightly for naive pigs challenged by pathogens


Pathogen dose or level

Clinical

0

0

Foodintake(g/day)

Sub-clinical

Fig. 7.6. A proposed schematic description of the effect of dose or level of parasites on thedaily rate of food intake by the host, reproduced from Kyriazakis et al. (1998). Food intake isreduced once a threshold pathogen dose (or level) is reached which leads to sub-clinicaldisease. Reductions in food intake become very severe at higher pathogen doses or levelsthat lead to clinical disease.

(Eqn 7.2). The modification would be due to an increase in IPm in order toaccount for the requirements of the innate immune response. Thissuggestion assumes that the composition of the ideal protein required bythe innate immune response is similar to that required for maintenance.Given current evidence that the requirements for the innate immuneresponse may be relatively small (Reeds et al., 1994), this position is atenable one.

However, both requirements for the functions of innate immunity andrepair are expected to be a function of pathogen challenge. This includesthe pathogen kind and level, which may be described as either pathogendose or load. The latter is the number of pathogens that establish, replicatewithin the host and affect its function and metabolism. Although mostinvestigations usually refer to pathogen dose, there are now good modelsthat translate this into pathogen load for both pathogens that replicatewithin the host (i.e. bacteria (Wilson and McElwain, 2004) and viruses(Bocharov, 1998; Nowak et al., 1996)) or not (i.e. macroparasites, Louie etal., 2005). Although relevant experiments that have investigated therelationship between pathogen load and requirements for innate immunityand repair have not been reported in the literature for pigs, evidence fromother species (Taylor-Robinson, 2000) suggests that they can berepresented as follows:

PIIm = ai. (PL – PL0) g/day (7.4)

where PIIm is the requirement for the innate immune response, PL (n) ispathogen load and PL0 (n) is the minimal PL required to activate theinnate immune system. The PIIm is the requirement to reduce PL to PL0.In cases where PL ≤ PL0 the animal would not be expected to require anyresources for the innate immune response, perhaps because the smallpathogen load does not warrant the effort. It is also expected that agenetically determined maximum (PIIm)max exists, which denotes themaximum capacity for response (rather than the maximum requirement)and, therefore, may be genotype and size dependent. The above simplelinear relationship, which represents the response of a single pig, will leadto a sigmoidal relationship for the response of a population of pigs (Fisheret al., 1973; Pomar et al., 2003). The values of ai and PLo are expected to beboth pathogen and genotype specific.

A widely accepted relationship between PL and damage caused is thatproposed by Behnke et al. (1992):

Ploss = Prep = ek.PL – 1 g/day (7.5)

where Ploss is the amount of protein lost or damaged due to pathogenexposure, and is equivalent to the amount of protein required for repair(Prep). This protein loss may be actual tissue damage, such asgastrointestinal tract (Yu et al., 2000) or blood constituent loss, includingplasma (Yakoob et al., 1983; Le Jambre, 1995). The expectation is thatgiven the available resources the pig will attempt to repair the ‘damage’caused by the pathogen as fast as possible and return to a ‘healthy’ state.


Parameter k would be pathogen specific and may also reflect the virulenceof the pathogen. The exponential form of the relationship is consistentwith the view that small pathogen loads have little effect on hosts and thatan already weakened system would suffer more damage from increases inits challenge (i.e. further exposure to pathogens). It should be emphasizedthat there would be a (Ploss)max value equivalent to the amount of damagethat may lead to death.

The prediction of partitioning of scarce protein in naive pigs duringexposure to pathogens appears to be straightforward. Scarce proteinwould be expected to be prioritized towards the functions of maintenanceand innate immune response; any protein above this should be used forgrowth, after the protein needs for repair have been accounted for. Theparameterization of Eqns (7.4) and (7.5) should be relativelystraightforward to estimate for specific pathogens, providing that duringthe course of the measurement the animal does not develop an acquiredimmune response to the pathogen. As the development of the acquiredimmune response may be very rapid, current information presented in theliterature where PR is measured over a number of days usually includesboth the phase of innate and acquired immune responses. This makesinterpretation of current experiments difficult (see below).

The partitioning of scarce protein during pathogen exposure in immune pigs

Information on the effect of pathogen (re-)challenge on the food intake ofalready immune animals is significantly scarcer than for naive animals. Thevery few experiments that have investigated the phenomenon (Takhar andFarrell, 1979; Greer et al., 2005) suggest that re-exposure to pathogensdoes not seem to be accompanied by anorexia. This raises the possibility,yet untested, that re-exposed, immune animals may increase food intake inorder to meet their increased requirements due to exposure to apathogen. However, as maintenance of immunity is a dynamicphenomenon (Anderson, 1994) and may be lost if hosts do not continue tobe exposed to a pathogen, it is possible that anorexia may reappear inhosts that have lost their acquired immunity.

In parallel to the argument presented above for the requirements ofthe innate immune response, the requirements for adaptive immunity canbe expressed as:

PAIm = aa. (PL – PL0) g/day (7.6)

where PAIm is the requirement for the acquired immune response, whichis also expected to attain a genetically determined maximum (PAIm)max ata certain value of PL, when PL � PL0. PAIm is the requirement to reducePL to PL0. However, an increase in the requirements for acquiredimmunity does not manifest as an increase in the maintenancerequirements of immune pigs when they are re-exposed to a pathogen andgiven access to scarce protein intake. There are now several experiments in


the literature to suggest that acquired immunity responds to increases inprotein intake, whilst at the same time animals increase protein retention(pigs, Zijlstra et al., 1997; sheep, van Houtert et al., 1995; chickens,Bhargava et al., 1971). This implies that a degree of competition for scarceprotein above maintenance exists between acquired immunity and proteinretention (growth). From an evolutionary point of view this is an attractiveproposition, since it would be consistent with the position that the animaltries to grow as fast as it can, whilst it maintains some degree of acquiredimmunity, which allows it to exert a degree of control over its pathogensand their consequences (Coop and Kyriazakis, 1999). This is equivalent tooptimizing nutrient partitioning between long term (attainment ofreproductively mature size) and short term objectives (survival).

The above also implies that the simplicity of the framework developedto account for the partitioning of protein in naive pigs, cannot bemaintained for immune pigs. Instead, one should be considering how torepresent the partitioning of scarce protein above maintenance betweenthe two competing functions of protein growth and acquired immunity.Here, it is proposed that this partitioning may be represented by apartitioning ratio, p, which is the amount directed towards the function ofacquired immunity and is expected to be a function of pathogen load. Itmay attain a value of 0 < p < 0.5. This is because growth seems to have ahigher relative priority than the immune response, and hence is penalizedto a lesser extent during protein scarcity. The value of p is expected toincrease linearly as pathogen dose and/or virulence increase:

p = d. (PL – PLo) (7.7)

Any amount of protein invested in acquired immunity is expected to leadto a reduction in pathogen load in the manner:

PL1 = PL – (PL. (PAAIm/PAIm)) n (7.8)

where PL1 and PL are pathogen loads post- and pre-immunity effects.PAAIm is protein actually invested in immunity and may be less than or equal to PAIm (as defined in Eqn (7.6)). In the latter case, when PAAIm = PAIm, then PL1 = 0. If, on the other hand, PAAIm = 0 thenpathogen load would be unaffected, i.e. PL1 = PL. The new pathogen load,PL1, can be used to calculate the actual damage achieved by a pathogen in apig that expresses acquired immunity (Eqn 7.5). Equation (7.8) can besubstituted into Eqn (7.5) to represent the relationship between damagecaused by a given pathogen load and the relative investment in acquiredimmunity (PAAIm/PAIm), as shown in Fig. 7.7, given that:

Prep = ek.PL1 – 1 = ek. (PL – (PL. (PAAIm/PAIm))) – 1 g/day (7.9)

The resulting negative exponential relationship between damage and hostresponse is in agreement with the relationships proposed to hold forcommon microbial pathogens (Casadevall and Pirofski, 1999).

If it is assumed that the efficiency of ideal protein use for acquiredimmunity is the same as that for PR (i.e. ep), then the above framework can


be brought together to predict the PR of an animal exposed to a certainpathogen dose (and hence PL) whilst given different amounts of protein,Fig. 7.8.

The predictions are made over one particular time step (day). As idealprotein intake increases, the amount of protein actually invested inacquired immunity (PAAIm) is described by:

PAAIm = ep.p. (IPI – IPm) g/day (7.10)


Maximumdamage

Actualdamage

Level of investment in immunity

Fig. 7.7. The proposed relationship between the actual damage caused by a pathogen loadto a host in relation to the level of investment in immunity (see Eqn 7.9 in text). The maximumdamage caused by the pathogen load is achieved when there is no investment in immunity.

Ideal protein intake (g/day)

Pro

tein

ret

entio

n (g

/day

)

200

180

160

140

120

100

80

60

40

20

00 50 100 150 200 250

PRmax

Fig. 7.8. Predictions of protein retention in relation to different intakes of ideal protein for anuninfected (solid line) and an immune pig challenged by a pathogen (dotted line). The increasein the intercept for the challenged pig is a reflection of the costs associated with the pathogen,when there is no investment of protein intake in immunity. Both healthy and challenged pigsare expected to attain their genetically defined maximum protein retention, PRmax.

The increase in investment up to a maximum PAIm, predicts that the rateof PR is brought closer to that of a healthy pig, due to the associated gains(i.e. reduction) in the amount needed to be invested for repair. Furtherinvestment in immunity is not associated with significant gains, and this isreflected in the decline in the rate of PR. Finally, it is assumed that themaximum capacity for protein retention (PRmax) is the same betweenhealthy and immune pigs challenged by a pathogen. As discussedpreviously, the above predictions cannot be compared directly to actualexperiments, mainly because what is reported in the literature usuallyaggregates data on both the naive and immune status in the same animal,as well as the transition between the two phases.

Towards the Prediction of Protein and Lipid Retention in PigsChallenged by Pathogens

The use of the concept of ideal protein

The above framework was developed on the basis of ideal protein intake.This assumes that the composition of the protein retained as either theimmune response or growth is similar. In Table 7.2 the amino acidcomposition of some proteinaceous components of the immune response iscompared to the composition of pig body protein, which forms the basis ofthe ideal protein system (ARC, 1981). The difference in amino acidcomposition between these two body components is striking. Suchdifferences will be expected to have a significant effect on the prediction ofprotein retention, if the contribution of the immune response to theoverall protein retention is relatively high (Wang and Fuller, 1989). In thiscase, the framework will need to be modified to make predictions on thebasis of individual amino acid responses. Protein retention would then bereconstituted on the basis of individual amino acid retention. This solutionwill have exceedingly high information requirements and, therefore,parameterization of the framework will be exceedingly difficult. An addedcomplication would also arise from the fact that stimulation by differentpathogens invokes different effector mechanisms of the immune response(Dong and Flavell, 2001). These different effector mechanisms may havedifferent amino acid compositions (Table 7.2), which in turn may beutilized by different efficiencies.

An alternative, but indirect solution to the problem that arises fromthe above would be to retain the ideal protein system, but assume thatthe efficiency with which protein is utilized for the purposes of theimmune response is modified. This would be in order to account for thedifferent ‘ideal’ protein composition of the two body components. Thisseems to be a less onerous task than the above and experiments that canbe designed to contribute towards the parameterization of this solutioncan be envisaged.


The genetic ability to cope with pathogens

In the previous sections, several of the parameters identified in theframework were proposed to be genotype dependent. These were theminimum pathogen load that activates the immune system (Lo), the rates ofincrease in the requirements for the innate (ai) and acquired (aa) immuneresponses, and the maximum capacities for these responses (PIIm andPAIm, respectively). Pig genotypes that may be defined as resistant orsusceptible in terms of how they cope with a pathogen challenge (Knapand Bishop, 2000), would be expected to differ in the values of theseparameters. It is likely that a degree of correlation exists between suchparameters. For example, a resistant pig genotype may have a lowerthreshold for its immune system activation (PLo), whereas its maximumcapacity to cope with a pathogen may be reached at a higher pathogenload. Thus, the additional parameter requirements for describing the hostgenotype would be reduced if the correlation between parameter values asaffected by host resistance is known.

The idea of the lower PLo threshold for resistant genotypes may beextended to the relationship between the partitioning ratio, p, and PL (Fig.7.9). The consequence then would be that, with other things being equal,resistant genotypes would be directing more nutrients towards theacquired immune response than susceptible genotypes at a given pathogenload (Kreukniet and van der Zijpp, 1989).

If the rate of increase in the value of p is also higher for the resistantgenotypes, then even more nutrients would be expected to be directed


Table 7.2. A summary of the amino acid composition of different effector proteins associatedwith the immune response, in relation to the reference pig body protein that is normally usedfor calculating the biological value of a food (ideal protein).

Amino acid composition (g/kg protein)a

Average of Pig protein 7 APPs IgA IgE MCP Mucin

Phe 36.7 71.8 26 30 29 15Tyr 25.6 57.3 24 43 29 13Trp 9.1 32.5 26 20 8 –Leu 69.5 64.8 120 87 90 31Ile 31.9 43.2 13 39 69 15Val 44.2 55.3 96 80 73 222Lys 64.2 73.3 39 57 53 18Hist 28.0 28.3 11 18 29 –Met 19.6 20.8 6 7 33 –Thr 36.9 57.0 75 103 45 224

a Amino acid compositions for pig protein from average value calculated by Sandberg et al.(2005), acute phase proteins from Reeds et al. (1994) and for IgA, IgE, sheep mast cellproteases (MCP) and mucin were taken from Houdijk and Athanasiadou (2003).

towards the immune response at a given pathogen load. This could, inpart, account for the observed interactions between nutrition and hostgenotype in their ability to cope with pathogens (Stewart et al., 1969; Rao etal., 2003; Haile et al., 2004).

When nutrient (protein) intake is scarce, the pig genotype may bedescribed only according to the above parameters. As stated previously,when protein intake is scarce there is no variation between individuals intheir drive towards body fatness and protein deposition. In thesecircumstances, any differences in performance would be attributed todifferences in the above five parameters. Animal breeders should beencouraged to describe pig genotypes accordingly, if progress is to be madetowards the prediction of the performance of pigs exposed to pathogens.

The continuum between naive and immune states

The above framework predicts the partitioning of scarce resources foreither naive or immune pigs exposed to pathogens at one point in time. Assuch, there is an artificial distinction between these two states; this wasconsidered as the necessary first step for the purposes of the framework.However, in most cases the transition between the two states is not abruptbut continuous (Anderson, 1994), as they are linked by the phase ofacquisition of immunity. Therefore, in order to progress towards dynamicpredictions of protein and lipid retention one would need to account forthis transition over time.

There are currently a number of simulation models that predictadequately the acquisition of immunity and make its onset a function ofpathogen load (for example, Barnes and Dobson (1993) for gastrointestinalparasites, and Bocharov (1998), for viruses). In other words, how quickly


p

PL0

Pathogen load

Fig. 7.9. The proposed relationship between the level of pathogen challenge and thepartitioning ratio of scarce resources (denoted by p) between growth and immune functions,once the level of challenge has exceeded a threshold, PL0, in a susceptible pig (dotted line)and resistant pigs (solid line and dashed lines). The two resistant pigs differ in the rate ofincrease in the value of p for a given change in pathogen load.

the animal starts to acquire immunity depends, within certain limits, uponits pathogen load. This is assumed to be a reflection of the PL required tostimulate the acquired immune response (see above). However, theduration of the phase of acquisition of immunity is assumed to beindependent of pathogen load (Steel et al., 1980; Houdijk et al., 2005), andonly dependent on pathogen type. Duration of this phase can be very shortin certain pathogens, such as bacterial (Turner et al., 2002a,b) and viral(Zijlstra et al., 1997) challenges.

The above models also assume that the duration of the acquisition ofimmunity is independent of host nutrition. Sandberg et al. (2006) reviewedthe literature on this issue and concluded that whilst this variable may beaffected by food composition (food protein content in particular), nogeneral relationship could be proposed between the two. As such, it wassuggested that until experiments that address this issue are performed, theabove simple assumption should be retained. A simulation of howpathogen load changes within the host as a function of time based on theabove assumptions is shown on Fig. 7.10. The change in pathogen load,assuming normal acquisition and expression of immunity, is consistent withexperimental findings for bacterial (e.g. Kelly et al., 1996) and viral (e.g.Bocharov, 1998; McDermott et al., 2004) pathogen challenges.

The effect of nutrition on pathogen load as shown in Fig. 7.10 is theoutcome of the proposed framework.

Future Directions

The problem of predicting partitioning of absorbed scarce resources to PRand LR in healthy pigs has occupied animal scientists for over 30 years. We


Time

Pat

hoge

n lo

ad

Fig. 7.10. A prediction of the change in pathogen load (arbitrary units) over time of animalsgiven access to different levels of protein supply low (dashed line), medium (solid line) andhigh (dotted line). No difference is observed in the early stage of infection whilst the animalacquires immunity; however, once expression of acquired immunity commences, its level ofexpression is proposed to be affected by the level of resource supply.

believe that the current solution offered in this chapter is capable ofpredicting these responses in a variety of conditions and for pigs ofdifferent genotypes. Experiments are warranted to fine-tune the solutionand these have been defined above. These, however, would not diminishthe strength, general applicability and heuristic value of the positionoffered.

The solution offered for healthy pigs formed the basis of a frameworkthat was developed to predict the partitioning of absorbed scarceresources to PR and LR in pigs challenged by pathogens. Unlike theframework developed for healthy pigs, the completion of the frameworkfor ‘diseased’ pigs presents us with significant challenges. The informationrequirements that would enable us to progress towards quantitative,dynamic predictions from this framework have been described above. Inthis chapter we purposely did not specify (describe in quantitative terms)the pathogen challenge under consideration, as our aim was to develop ageneric framework. Parameterization of this framework may then bepossible by focusing on the characterization of specific pathogens andtheir consequences, including disease. We considered this to be a morefruitful approach than the creation of a model to account for theconsequences of exposure to a specific pathogen (e.g. the approach takenby Black et al. (1999) to predict the consequences of pleuropneumonia inpigs).

As reliance on chemoprophylaxis to control pathogens is decreasing,due for example to consumer concerns or legislation (Waller, 1997; Olesenet al., 2000), interest in the understanding of the performance of animals inthe presence of pathogens will increase. A framework that predicts theperformance of pigs during exposure to pathogens may then have a valueas a management tool to develop strategies, including breeding andnutritional strategies, to deal with this challenge.

Acknowledgements

This work was in part funded by the Biotechnology and Biological ScienceResearch Council of the UK and PIC/Sygen. SAC receives support from theScottish Executive, Environment and Rural Affairs Department. We aregrateful to our colleagues Dimitris Vagenas, Andrea Doeschl-Wilson andWill Brindle for comments on earlier versions of the manuscript and toeveryone in the Animal Nutrition and Health Department for their supportin this activity.

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Takhar, B.S. and Farrell, D.J. (1979) Energy and nitrogen metabolism of chickensinfected with either Eimeria acervulina or Eimeria tenella. British Poultry Science20, 197–211.

Taylor-Robinson, A.W. (2000) Increased production of acute-phase proteinscorresponds to the peak parasitemia of primary malaria infection. ParasitologyInternational 48, 297–301.

Turner, J.L., Dritz, S.S., Higgins, J.J., Herkelman, K.L. and Minton, J.E. (2002a)Effect of a Quillaja saponaria extract on growth performance and immunefunction of weanling pigs challenged with Salmonella typhimurium. Journal ofAnimal Science 80, 1939–1946.

Turner, J.L., Dritz, S.S., Higgins, J.J. and Minton, J.E. (2002b) Effects ofAscophyllum nodosum extract on growth performance and immune function onyoung pigs challenged with Salmonella typhimurium. Journal of Animal Science 80,1947–1953.

Van Dam, J.T.P., Schrama, J.W., Vreden, A., Verstegen, M.W.A., Wensing, T., vander Heide, D. and Zwart, A. (1998) The effect of previous growth retardationon energy and nitrogen metabolism of goats infected with Trypanosoma vivax.British Journal of Nutrition 77, 427–441.

van Heugten, E., Coffey, M.T. and Spears, J.W. (1996) Effects of immune challenge,dietary energy density, and source of energy on performance and immunity inweanling pigs. Journal of Animal Science 74, 2431–2440.

van Houtert, M.F.J., Barger, I.A., Steel, J.W., Windon, R.G. and Emery, D.L. (1995)Effects of dietary protein intake on responses of young sheep to infection withTrichostrongylus colubriformis. Veterinary Parasitology 56, 163–180.

van Milgen, J. and Noblet, J. (1999) Energy partitioning in growing pigs: the use ofa multivariate model as an alternative for the factorial analysis. Journal ofAnimal Science 77, 2154–2162.

van Milgen, J., Quiniou, N. and Noblet, J. (2000) Modelling the relation betweenenergy intake and protein and lipid deposition in growing pigs. Animal Science71, 119–1130.

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Wang, T.C. and Fuller, M.F. (1989) The optimum dietary amino acid pattern forgrowing pigs. 1. Experiments by amino acid deletion. British Journal of Nutrition62, 77–89.

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8 Nutrient Flow Models, EnergyTransactions and Energy FeedSystems

J. VAN MILGEN

INRA – UMR SENAH, Domaine de la Prise, 35590 Saint-Gilles, [email protected]

Introduction

Systems of nutrient and energy utilization are widely used in the animal feedindustry. Existing energy systems such as digestible energy (DE),metabolizable energy (ME) and net energy (NE) attribute a single energyvalue to a feed but differ in the way that energy losses are accounted for.Although these systems are simple to use and relatively robust, they havebeen criticized because they cannot account for interactions between the feedand the animal. This has led to the development of more mechanistic modelsthat can be used for feed evaluation or that predict the response of ananimal to a changing nutrient supply. The objective of this chapter is todescribe different aspects of energy loss and energy utilization in animals andto challenge this knowledge with empirical and mechanistic approaches tofeed evaluation. Mechanistic models of animal nutrition undoubtedlyprovide a more solid theoretical basis for feed evaluation. However, theyonly explain part of the efficiency with which nutrients are used for differentproductive purposes. Moreover, although ‘scientific truth’ may be a reason topush for a more mechanistic approach to feed evaluation systems, there arealso reasons to be somewhat conservative. Past history, establishedknowledge and the use of an established reference base can be expected toplay major roles in the acceptance or failure of future energy systems.

Energy Values and Energy Losses

Gross energy

There are different ways to express the energy value of a feed. In one of itsmore basic forms, it can be represented by its gross energy (GE) value,


which can be estimated by combustion in a calorimeter. Alternatively, it canbe estimated from the chemical composition of the feed by multipleregression. Using data from Noblet et al. (1994), the following equationestimates the GE content of a feed (kJ/g):

GE = 22.6•CP + 38.8•EE + 17.5•starch + 16.7•sugars + 18.6•residue

where CP is the proportion of crude protein (g/g), EE the ether extract,and residue is the difference between organic matter and the otheridentified fractions in the equation (essentially fibre). Equations of thisform have the advantage that they attribute an energy value to eachcategory of nutrient, which bears close resemblance to their theoreticalenergy values. For example, the energy value of glucose is 2820 kJ/mol (1mol = 180 g). The theoretical energy value of starch, a polymer of glucose,is then 2820 / (180–18) = 17.4 kJ/g, which corresponds closely to thecoefficient in the equation given above.

Depending on the amino acid composition of protein and the fatty acidcomposition of lipid, their GE content may vary (Boisen and Verstegen,2000; van Milgen, 2002). Moreover, there are other nutrients (e.g. volatilefatty acids or lactic acid in fermented products) that also contribute to theGE content of a feed, although their contribution is not specificallyaccounted for in the equation above. Tran and Sauvant (2002) and Nobletet al. (2003) included correction factors for each group of feed ingredientsto account for these deviations.

Faecal energy losses

In contrast to current practice for amino acids, digestibility of energy is notconsidered at the ileal but at the faecal level. The faecal energy digestibilityin typical pig diets ranges from 70 to 90%. The energy digestibility of feedingredients can be much more variable. Energy digestibility declineslinearly with neutral detergent fibre (NDF) content (Noblet and Perez,1993; Le Goff and Noblet, 2001; Lindberg and Pedersen, 2003). Theextent of this decline is such that NDF contributes little to the energysupply to the animal and mainly acts by diluting the energy content. Forgrowing pigs, a 1% increase in NDF content reduces the energydigestibility by 0.9% (Le Goff and Noblet, 2001). This does not necessarilymean that fibre or NDF is not digested by growing pigs. It is possible thatthe actual digestibility of fibre is offset by increased endogenous secretionsor by a reduction in digestibility of other nutrients, so that the overallcontribution of fibre to the energy supply is close to zero. The fact thatNDF appears to be a good indicator for energy digestibility should not beinterpreted as meaning that all NDF is the same. Le Goff et al. (2002)observed that the NDF digestibility in growing pigs ranged from 38% formaize bran to 71% for sugar beet pulp. The low digestibility of fibre ingrowing pigs seems mainly due to the high rate of passage when feedingfibre-rich diets (Le Goff et al., 2002). Adult sows are much more capable of

144 J. van Milgen

digesting fibre than growing pigs, due to the four-times greater retentiontime of digesta in the gastro-intestinal tract. Similarly, finishing pigstypically digested fibre better than did growing pigs (Le Goff et al., 2002).This means that, in contrast to GE, the DE value of a diet is not acharacteristic of the diet itself but is influenced by the animal.

Urinary and gaseous energy losses

The metabolizable energy (ME) value of a diet accounts for energy lossesthat occur from fermentation gases and in the urine. Energy losses asmethane and hydrogen are relatively small for diets fed to growing pigs(typically less than 0.5% of DE). Noblet et al. (2002) assumed that energylosses in fermentation gases correspond to approximately 0.67 kJ/g offermented dietary fibre. Energy losses in the urine are of the order of 3.5%of DE. Most of this energy is lost as urea (or uric acid in birds), whichoriginates from amino acid catabolism in the liver. Amino acids given inexcess of requirements will be deaminated and result in additional urinaryenergy loss. There is a relatively straightforward relation between thenitrogen and energy contents in the urine. In the INRA tables (Noblet etal., 2002), the following equation is used for pigs:

(energy in urine; kJ/kg DM intake) = 192 + 31 × (nitrogen in urine; g/kgDM intake)

Under the assumption that approximately half of the digestible nitrogen isexcreted in the urine, the equation above can easily be converted into arelation between urinary energy losses and dietary protein content.

Heat production

All metabolizable energy that is not retained by the animal is lost as heat.Heat production can be measured through calorimetry, whereas energyretention can be measured using the serial slaughter technique. Indirectcalorimetry is based on the measurement of gas exchanges between theanimal and its environment. When nutrients are oxidized, animalsconsume oxygen and produce carbon dioxide and methane. These gasexchanges and the nitrogen excretion originating from protein catabolism,combined with the stoichiometry of carbohydrate, protein, and lipidoxidation allow calculation of heat production (Brouwer, 1965).Calorimetry has the advantage over the serial slaughter technique that itcan be used to measure energy balance over successive short periods oftime. We have further refined this technique in order to obtain estimates ofdifferent components of heat production related to fasting, physical activityand the thermic effect of feeding (van Milgen et al., 1997). The energy andnitrogen balance techniques typically give higher retention values than thecomparative slaughter technique (Quiniou et al., 1995) and are thought tooverestimate actual lipid and protein retention.

Flow Models, Energy Transactions and Feed Systems 145

Total heat production is not to be confused with the heat increment (orthermic effect of feeding). As indicated above, total heat production is thedifference between ME intake and retained energy. The heat increment isthe change in heat production associated with a change in ME intake.

Energy Systems

The purpose of an energy system is to attribute an energy value to a feedso that it can be compared with the energy requirement for a specificfunction, which should be expressed on the same scale. Expressing thefeed and requirement value as a single entity has the advantage of beingsimple to use.

Several systems of energy utilization have been proposed. The DEsystem accounts for differences in digestive utilization. The ME system alsoaccounts for energy losses in the urine and as combustible gasses. The NEsystem is calculated as the sum of fasting heat production (FHP) and theretained energy, or as ME minus the heat increment of feeding. Because itis difficult and costly to measure directly the energy value of a diet, severalresearch groups have proposed equations to estimate the energy (DE, MEor NE) values from the chemical composition of the diet. Because therecan be important differences in approaches and methodologies (e.g. withinNE systems), energy values are not necessarily interchangeable betweenlaboratories. The equations below estimate the DE, ME and NE values (inkJ/g) from digestible nutrients (as a proportion of the diet). Theseequations originate from statistical relationships between the measuredenergy value and the (digestible) nutrient composition for 61 differentdiets (see Noblet et al., 1994 for a description of methods):

DE = 23.25•dCP + 38.73•dEE + 17.45•starch + 16.77•sugars +16.68•dresidue

ME = 20.40•dCP + 39.28•dEE + 17.45•starch + 16.47•sugars +15.45•dresidue

NE = 12.08•dCP + 35.01•dEE + 14.32•starch + 11.94•sugars +8.64•dresidue

where dCP is the faecal digestible crude protein, dEE is the digestible etherextract, and dresidue is the digestible residue (i.e. the difference betweendigestible organic matter and the digestible CP, EE, starch and sugarcontents). Starch and sugars are both assumed to be completely digestible atthe faecal level. The coefficients estimated for the nutrients have someinteresting features. First, because the DE value is based on the digestiblenutrient content, the coefficients correspond closely to the GE values foreach nutrient. When the coefficients for the ME equation are comparedwith those of DE, it is clear that the difference between the DE and MEvalues is mainly due to the protein and residue contents. The energy lost inthe urine (from protein) and as combustible gases (from fibre fermentation)is the cause of this. Comparing the coefficients of NE with those of ME

146 J. van Milgen

illustrates the differences in energetic efficiencies between nutrients (see alsothe section ‘Confronting stoichiometry with experimental data’, p.150).Dietary fat is used with the highest efficiency (89.1%), followed by starch(82.0%) and sugar (72.5%), and finally fibre (55.9%) and protein (59.2%).

Excess dietary protein is thus a relatively inefficient source of energy.The consequence of this is that the contribution of protein to the energyvalue of the diet diminishes in the order DE, ME and NE. For example, ina typical European cereal-based diet, soybean meal may contribute 25% tothe GE or DE value (16.2 and 13.5 kJ/g, respectively), 23% to the ME value(13.0 kJ/g) and only 19% to the NE value (9.6 kJ/g). Fat, on the other hand,may contribute 4.8% to GE, 4.9% to DE, 5.2% to ME and 6.2% to the NEvalue of the diet. In other words, the ranking of different feed ingredientsis affected by the system of expressing the energy value. Feed ingredientsrich in protein (or fibre) have relatively lower values in an NE system,whereas those rich in fat will be attributed a higher value.

Apart from establishing energy values for a diet, requirement valueshave to be defined in an energy system. The following two equationsindicate the ME and NE requirements (kJ/d) for growing animals:

ME = MEm + PD/kp + LD/kfNE = FHP + PD + LD

where MEm is ME for maintenance, PD is protein deposition (kJ/d), LD islipid deposition (kJ/d) and kp and kf are the efficiencies of protein and lipiddeposition, respectively. On average, these efficiencies are close to 60 and80%, respectively (Noblet et al., 1999). The ME system does not account forthe fact that these efficiencies may be affected by the diet. The differencebetween both equations also illustrates that in the ME system the heatincrement is accounted for in the requirements (albeit in a very crudeway), whereas in the NE system this is accounted for in the feed value. Theeffective energy system (Emmans, 1994) uses an intermediate approach byattributing part of the heat increment to the effective energy feed valueand another part to the effective energy requirement. Heat increments forurinary nitrogen excretion, faecal organic matter excretion, and methaneproduction are deducted from the ME supply (corrected for zero nitrogenretention), whereas heat increments for protein and lipid deposition areincluded in the effective energy requirement. In addition, on the supplyside a distinction is made between the heat increment of using dietarylipid, as opposed to non-lipid sources, for lipid deposition

Shortcomings of Classical Feed Evaluation Systems

In classical energy systems, energy values and requirements are reduced toa single number. This has the advantage that the system is simple to useand relatively robust. Tabular values of feed values and animalrequirements can be established and the user only has to ensure that thesematch. The disadvantage is that the system is not necessarily consistent


with biological reality and the following examples will illustrate this. Asindicated earlier, dietary protein affects the ME value of a diet becauseamino acids that are not deposited are deaminated, and urea is excreted inthe urine. In other words, it is not the dietary protein itself that willdetermine its ME value, as it will also depend on what fraction of thatprotein the animal retains. A similar example can be given for the NEsystem. The NE requirement is based on a requirement for maintenance(FHP) and energy retention. The maintenance requirement is essentiallyan ATP requirement. If glucose and lipid are compared, it can be shownthat their potential to produce ATP is similar (~ 74 kJ/ATP produced; vanMilgen, 2002). When these nutrients are used for maintenance, glucoseand lipid should therefore be attributed similar energy efficiencies.However, when these nutrients are used for lipid deposition, largedifferences occur. The biochemical efficiency of using glucose for lipiddeposition is close to 81%, whereas the efficiency of using dietary lipid forlipid deposition is around 98%. This indicates that the final utilization willeventually determine the energy value.

The fact that there are interactions between the animal and its dietimplies that classical energy systems are theoretically incorrect. Thisproblem can only be overcome if we acknowledge that there is no suchthing as ‘an energy value of a diet’ expressed in such a way that it can berelated to a requirement. The only energy value that would be an attributeof the diet itself would be its GE value. However, this is of no use whenexpressing a requirement.

Mathematical models are ideally suited to account for interactionsbetween the diet and the animal. In the past and also recently, severalmodels have been published that address this issue. It is beyond the scopeof this paper to compare these models, but Luiting and Knap (Chapter 13,this volume) deal with this in some detail. This chapter will focus only onhow recent models deal with nutrient and energy transactions and to whatextent this mechanistic approach is more useful than classical systems ofnutrient evaluation.

Stoichiometry of Energy Transactions

When developing a more mechanistic approach to energy evaluation,several issues have to be taken into account. These include thestoichiometry of energy transactions, the pathways and organs involved inthe transaction and the energy cost of physiological functions. Thestoichiometry of the quantitatively most important transactions is wellestablished. For the interested reader, I would recommend the work ofSalway (1994), which helps to get an overview of major pathways ofmetabolism including some aspects of regulation. In the past, differentpublications addressed the issue of quantifying the stoichiometry ofnutrient transactions (Armstrong, 1969; Krebs, 1972; Schulz, 1978;Livesey, 1984). We expanded on this by providing a generic framework

148 J. van Milgen

that can be used to construct and quantify the energetics of differentmetabolic pathways (van Milgen, 2002). The model, a simple spreadsheet,is used in this presentation to quantify the energetics of nutrienttransactions; the model is available from the author on request.

Although stoichiometry may seem merely a matter of book keeping,some differences between approaches can occur depending on thepathways involved (especially for catabolism of essential amino acids). Forexample, the different pathways of tryptophan catabolism may lead todifferences in stoichiometric results. Also catabolism of glycine, methionine(methyl-groups) and cysteine has been quantified in different ways (vanMilgen, 2002). In addition, a decision has to be made about whichnutrients will be represented specifically in the model. For example, thecomplete oxidation of glucose in the TCA cycle is a process involving (atleast) 18 intermediate steps involving the carbon chain (glucose, glucose-6-phosphate, fructose-6-phosphate, etc.). It goes without saying that itwould be of little use to include all these steps in whole animal models. Inour framework (van Milgen, 2002), we used six carbon chain ‘pivots’ andeight co-factors (e.g. ATP, NADH) to quantify nutrient transactions. Mostmodels use considerably fewer energy pivots to express these transactionsand acetylCoA and/or ATP are most frequently used (Boisen, 2000; Chudy,2000; Birkett and de Lange, 2001a; Lovatto and Sauvant, 2003; Green andWhittemore, 2003; Halas et al., 2004). AcetylCoA may seem an obviouschoice as a carbon-chain pivot as it plays a central role in the use ofnutrients for oxidation in the Krebs cycle (ATP synthesis) or for fatty acidsynthesis required for lipid deposition. A necessary condition in the choiceof pivots is of course that the energy released (or required) fromtransforming a nutrient to the pivot is accounted for. For example, thetransformation of 1 mol of glucose to acetylCoA requires 2 ATP but alsoreleases 4 ATP and 4 NADH. If the NADH is oxidized in the mitochondria,it can be expressed as an ATP equivalent.

By reducing complete pathways to pivot equivalents, some informationwill be lost. For example, NADH can be produced both in the cytosol andthe mitochondrion. As ATP synthesis from NADH occurs in themitochondrion, and the transfer of NADH from the cytosol to themitochondrion implies a loss of energy (Salway, 1994), one may opt toinclude this energy loss directly in the stoichiometric balance. However,when glucose is used for fatty acid synthesis, the NADH released duringglucolysis can be re-used (in the cytosol) in the pyruvate/malate cycle,thereby avoiding the energy loss. Consequently, cytosolic NADH can beused in different metabolic pathways, having different energeticefficiencies. One option to solve this problem is the inclusion of zero-poolsin the model. These pools are present only for accounting purposes andare programmed so as to maintain a zero size. For example, a zero-pool ofcytosolic NADH may be programmed so to transfer its surplus to a zero-pool of mitochondrial NADH (while accounting for the correspondingenergy loss) which, in turn, transfers its surplus to a zero-pool of ATP.Zero-pools should be programmed so that when positive, they transfer


their content to another nutrient pool, whereas if negative, they pullenergy from a preceding nutrient pool. For example, if insufficientNADPH is available for fatty acid synthesis, the system may pull from aglucose pool to generate NADPH in the pentose-phosphate shunt. The useof zero-pools is a convenient way for bookkeeping without making a prioridecisions on pathways involved in metabolism.

Short-term Energetics of Nutrient Transactions

Metabolism includes several pathways that are designed to cope with theshort-term dynamics of nutrient supply and requirement, or that deal withnutrient transfers between different organs. Apart from the physiologicalcost of using these pathways, there is also a biochemical cost related to thenutrient transformations. Few, if any, of the published mechanistic wholeanimal models include the examples that will be developed here. Theseexamples are not given to criticize these models, but to illustrate thatenergy metabolism in animals is a very complex process, which goes farbeyond the approach employed in most models.

Although it may seem evident not to include glycogen in models thatare based on empirical estimates of efficiency (as the energy loss isincluded, empirically, in the efficiency estimate and glycogen stores varylittle from day to day), this is less so for models that are based onbiochemistry. Depending on the site of glycogen storage and utilization(muscle or liver), ATP synthesis from glucose is stoichiometrically 3 to 6%less efficient if this glucose is stored as glycogen before being oxidized.Type IIb muscle fibres have a high glycogen storage capacity. As theirmitochondrial oxidative capacity is limited these fibres, when solicited,produce ATP mainly through glycolysis and yield lactate as an end-product. Although lactate can be used directly by some tissues (e.g. heartmuscle but also skeletal muscle itself), it can also be used by the liver toregenerate glucose through gluconeogenesis. In the transformation ofglucose to lactate (in muscle) and back to glucose (in the liver), a total offour ATP will be lost, hence an energy loss of more than 10%.

Another example is the temporary storage of energy as lipid (see alsoBaldwin, 1995 for a discussion of this topic). Type I (red) muscle fibres areused to provide sustained muscular work (e.g. for maintaining posture).Although these oxidative fibres can use both lipid and glucose as fuel, mostof the energy storage occurs as lipid. The temporary energy storage ofglucose as lipid is rather inefficient and requires 30% more energy than thedirect utilization of glucose.

Confronting Stoichiometry with Experimental Data

Stoichiometry explains only part of the observed heat increment. Table 8.1shows some results of an experiment in which either starch, maize gluten

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meal (an unbalanced protein source), casein or lipid was added to a basaldiet limiting in lysine supply (van Milgen et al., 2001). Also the coefficientsof the ME and NE equations described above can be used to evaluate thecontribution of stoichiometry to observed energy efficiencies.

The stoichiometric efficiency of using glucose for lipid varies between81 and 84%, depending on whether the ATP synthesis during lipogenesisfrom glucose is accounted for or not (Baldwin, 1995; van Milgen, 2002).For starch, the NE/ME ratio from the equations used above is 0.82,whereas van Milgen et al. (2001) observed a value of 0.84 (Table 8.1). Thissuggests that the heat increment of glucose metabolism not related tostoichiometry (e.g. intake, hydrolysis of starch, absorption, maintainingblood glucose) is relatively small or that this cost is accounted forelsewhere, for example in the maintenance energy expenditure.

Larger differences occur when comparing the stoichiometric andexperimental efficiencies for lipid metabolism. The theoretical efficiency oflipid deposition from dietary lipid is very high. The only energy loss is dueto the re-activation of fatty acids to acyl-CoA during re-esterification.Assuming that dietary lipids are hydrolysed and re-esterified twice, theenergy loss does not exceed 3%. However, the NE/ME ratio of theequations above suggests that more than 10% of the energy in dietary lipidis lost when it is used for lipid deposition. The results in Table 8.1 alsoindicate that the observed efficiency is much lower than the stoichiometricefficiency. The relatively low efficiency of using dietary lipid may be due tothe oxidation of dietary lipids (e.g. for ATP synthesis) combined with de


Table 8.1. Utilization of energy by growing pigs (van Milgen et al., 2001).

Maize gluten Starch meal Casein Lipid

Chemical composition (%)Nitrogen content 0.13 10.89 15.28 n.a.Lysine content n.a. 0.56 8.13 n.a.Fat n.a. 2.5 n.a. n.a.Starch 97.7 17.7 n.a. n.a.

Energy utilizationIleal digestibility 0.988 0.848 0.971 0.900Faecal digestibility 1.001 0.889 0.965 0.859Metabolizability 1.002 0.843 0.884 0.985Fraction of ME used for PD 0.044 0.050 0.420 –0.025Efficiency of lipid deposition 0.842 0.520 0.520 0.883Energy cost of protein deposition(kJ NE/kJ PD) 0.484 0.484 0.484 0.484

Energy values (kJ/g)GE 17.27 24.33 22.86 39.47DE (faecal) 17.29 21.63 22.06 33.90ME 17.32 18.23 19.50 33.40NE – excluding the energy cost of PD14.71 9.92 14.07 29.39NE – including the energy cost of PD 14.34 9.48 10.11 29.80

novo lipid synthesis from other nutrients. The scenario is energeticallymuch more expensive than the use of dietary glucose for ATP synthesisand the use of dietary lipids for lipid deposition. Lizardo et al. (2002)assumed that only 85% of digested lipids were deposited in growing pigsbut recent data from our laboratory suggest an even lower value of 70%(Kloareg et al., 2005).

An even greater difference between stoichiometry and experimentaldata is observed for protein deposition. Synthesis of a peptide bond fromamino acids requires at least 5 ATP and, based on the efficiency of ATPsynthesis, the maximum efficiency of protein deposition ranges between 85and 90%. However, experimental values of the energetic efficiency ofprotein deposition are much lower. We estimated that 0.484 kJ of NE (asATP) was required to support the deposition of 1 kJ of protein (van Milgenet al., 2001). Because the efficiency of using ME for NE (ATP) varies withthe nutrient source, the estimated experimental efficiency of proteindeposition ranges from 0.52 (using amino acids for the support costs) to0.63 (using glucose for the support costs). It is thought that proteinturnover (i.e. the repeated hydrolysis and synthesis of peptide bonds)contributes to a large extent to the low efficiency of protein deposition.Based on the hypothesis that 5 ATP are required to synthesize a peptidebond, 18–22 ATP would be required to explain the observed efficiency ofprotein deposition. This value would correspond to the synthesis of fourpeptide bonds for each peptide deposited. Lobley (2002) estimated thatwhole animal protein synthesis in pigs could reach a value of 600 g/day,which is indeed about four times the protein deposition rate in pigs.

The reasoning above applies to the case of using dietary protein forprotein deposition. However, typically not more 50% of dietary protein willbe deposited, which means that the remainder will be deaminated andused for other purposes. Although the synthesis of urea requires ATP, theenergy cost involved is not sufficient to account for the heat increment ofexcess protein. In our experiment, excess protein was used with anefficiency of 0.52 for lipid deposition and the NE/ME ratio was 0.59 (Table8.1). This may be due to the fact that providing unbalanced dietary proteinstimulates protein turnover. This protein will first induce an ATP cost dueto the synthesis and hydrolysis of peptide bonds and finally induce an ATPcost for urea synthesis. It is interesting to note that the experimentalefficiencies of using dietary protein for protein deposition or for lipiddeposition are almost identical (van Milgen et al., 2001).

The difference between experimental values of energy efficiency andstoichiometry has, to some extent, been accounted for in models of nutrientmetabolism. Green and Whittemore (2003) included a ‘residual efficiency’in their model in order to account for differences between stoichiometricand experimental efficiencies. Nutrient transport was seen as a majorcontributor to the residual efficiency. Birkett and de Lange (2001a,b) alsocalibrated experimental efficiency values to stoichiometric ones. However,in contrast to Green and Whittemore (2003), they chose to relate theunaccounted efficiency to physiological processes such as intake of digestible

152 J. van Milgen

nutrients, excretion of faeces and urine, and costs of protein and lipiddeposition, all expressed on an ATP basis. As such, the model resembles theconcepts used in the effective energy system (Emmans, 1994), although theunits of expression are different. The model of Halas et al. (2004) also relieson the stoichiometry of nutrient transactions. However, rather thanestimating efficiency values for different processes through calibration,energy expenditures were attributed a priori to different physiologicalprocesses. Energy costs for absorption and transport were attributed todifferent nutrients. Protein synthesis was assumed to cost 4 ATP perpeptide, whereas hydrolysis of a peptide bond also required 1 ATP. Becausethe model includes four different protein pools (muscle, skin–backfat,organs and bone), each with their own turnover characteristics, differencesin body protein composition will result in differences in ATP requirementand, hence, energy expenditure. Other costs specifically accounted forinclude urea synthesis and bone mineralization.

Support Costs (Maintenance)

The most difficult part of establishing a system (or a model) of nutrientevaluation is the quantification of the energy cost of physiologicalfunctions. Processes such as muscle contraction, ion transport, peptidesynthesis all require energy, most of which will come directly or indirectlyfrom ATP. The largest contribution to this energy expenditure comes frommaintenance functions. Especially nervous functions, maintainingmembrane potential, and protein resynthesis contribute largely to the basalmetabolic rate (Table 8.2). Many physiological functions are driven by aNa+ gradient. For example, during active transport of glucose Na+ entersthe cell, which will be pumped out of the cell by a Na/K-ATPase at the costof ATP. Consequently, the Na+ gradient by itself represents an energyreserve, which has to be maintained.

It is virtually impossible to specifically include the energy costs of allphysiological functions in a model. Although certain aspects may be


Table 8.2. Energy expenditure of several maintenance functions(Baldwin, 1995).

% of BMR

Service functionsKidney (Na+ transport) 6–7Heart 9–11Nervous tissues 15–20Respiration 6–7

Repair functionsProtein re-synthesis 10–15Lipid re-synthesis 1–2Na+ transport (membrane potential) 20–25

included (e.g. the cost of protein turnover discussed above), we will have torely to a large extent on empirical estimates of maintenance. From abiological and physiological point of view, it is very difficult to define andmeasure maintenance unambiguously. Theoretically, maintenance corre-sponds to a situation in which energy retention equals zero (i.e. energyintake equals heat production) but, for a growing animal, this correspondsto a non-physiological situation. Moreover, zero energy retention maytheoretically be achieved while depositing protein and catabolizing bodylipid and therefore does not correspond to maintaining a constant bodyweight.

The FHP is closely related to the maintenance energy requirement andserves as the maintenance energy requirement in NE systems (Noblet et al.,1994). During fasting, animals mobilize body reserves in order to supplyenergy for vital body functions. Measured values for FHP after a 1-dayfasting period range from 700 to 800 kJ/((kg BW)0.60•d) in growing pigsoffered feed close to ad libitum prior to fasting. Genotype (or leanness)appears to have an important impact on FHP with lower estimates forobese Meishan barrows and higher estimates for lean Piétrain boars (vanMilgen et al., 1998). Part of the difference between genotypes seems to bedue to differences in body composition. In particular, the viscera make animportant contribution to FHP. This is consistent with the observation thatthe previous plane of nutrition, and thus the viscera mass, affects FHP(Koong et al., 1982) and justifies the use of different protein pools toexplain energy expenditure (Halas et al., 2004).

Part of the differences observed in FHP may be due to differences inthe body reserves that are mobilized during fasting. It is likely that duringfasting, the animal first mobilizes glycogen reserves, followed by themobilization of labile protein stores (visceral proteins) and lipids.Consequently, the length of the fasting period may affect FHP. Duringprolonged fasting, the animal is likely to adapt its metabolism so as tominimize energy expenditure. It is for this reason that in our laboratorywe measure FHP after a 1-day fasting period so that metabolism still bearssome resemblance to a producing animal.

The energy cost of physical activity can be an important source ofvariation between animals. Energy expenditure per hour of standingappears at least fourfold greater in pigs than in most other domesticspecies (Noblet et al., 1993). Different techniques exist to measure physicalactivity including measurement of standing duration, motion detection,and force detection. Heat production due to physical activity is estimatedfrom a statistical relation between variation in heat production andvariation in recorded physical activity. Our current estimate (based onforce detection) is approximately 200 kJ/((kg BW)0.60 •d), whichcorresponds to 3 h of standing per day (van Milgen et al., 2001); this valuecorresponds to approximately 20% of the maintenance energyrequirement. Physical activity appears rather variable between animals andmay be affected by feeding level, type of diet, and genotype (Susenbethand Menke, 1991; Schrama et al., 1996). Because of its contribution to heat

154 J. van Milgen

production and thus its effect on energy retention, it is important to obtainreasonable indicators of physical activity.

Energy Status and Energy Scales

In the literature, there are different approaches to evaluating the energystatus of an animal. How does the animal know where it is and how does itknow where it has to go? Although these issues are probably more ofphilosophical than of practical interest, it is nevertheless interesting to seehow different modellers view this issue.

It has been known for a long time that energy supply affects thepartitioning of energy between protein and lipid deposition. In one of thefirst models of pig growth, Whittemore and Fawcett (1976) assumed theexistence of a minimum ratio between lipid and protein retention. In theirview, the animal ‘monitors’ the potential composition of the gain, whichmay result in the catabolism of additional dietary protein to favour lipiddeposition. Moughan et al. (1987) and de Lange (1995) used a similarlogic, but assumed the existence of a minimum lipid to protein mass ratio.Wellock et al. (2003) and Green and Whittemore (2003) assumed thatgrowing animals have a preferred lipid to protein mass ratio that they willtry to achieve or maintain. These models therefore include a control onthe ‘receiving’ side of the equation. The animal (in the modeller’s view)somehow wants to control its body composition and therefore changes thepartitioning of nutrients between protein and lipid deposition.

However, also on the ‘supply side’, the energy status of the animal hasto be quantified. The response curve of protein to energy will be differentwhen the latter is expressed on a DE, ME, NE or ATP scale. In addition, theinterpretation of a given energy scale may change during growth. Does a30-kg pig interpret an additional kJ of DE in the same way as a 100-kg pig?Black et al. (1986) scaled protein deposition as a function of energy intakeand body weight on a linear MJ/day scale whereas van Milgen et al. (2005)expressed the same relation as multiples of maintenance (i.e. related bodyweight raised to the power 0.60). Halas et al. (2004) scaled many equationsto metabolic empty body weight (kg0.75) thereby implying a scaling tomaintenance. The use of metabolic body weight (kg0.75) originates from thecomparison of maintenance between different species of mature animals.When MEm or FHP is compared for animals of different BW within aspecies, the value of ‘b’ is typically lower than 0.75 and, for growing pigs, avalue close to 0.60 is often found. Although this may seem a minor issue, ithas important consequences for the dynamics of heat production duringgrowth. For example, suppose that one has obtained a reliable estimate ofMem at 60 kg of BW. If maintenance is constant per kg0.60, it would resultin an 18% higher maintenance requirement at 20 kg BW compared toassuming a constant maintenance requirement per kg0.75. However, atgreater BW, the ranking is reversed so that at 120 kg of BW, Mem is 10%lower when using the power 0.60 compared to using 0.75.


The choice of an appropriate energy scale is also important whenmodelling or describing voluntary feed intake. Most applied models ofanimal production consider voluntary feed intake as a user input, and it isoften described as an empirical function of body weight. When it isassumed that feed intake is regulated by quantity, feeding an energy-richdiet (e.g. by adding vegetable oil) will thus provide more energy resultingin a higher growth rate. On the other hand, if feed intake is assumed to beregulated on an NE basis, feeding an energy-rich diet will result in similarNE intakes (for different quantities of feed) and similar performance. Theenergy scale for expressing voluntary feed intake (DE, ME, NE) thus hasimportant consequences for model predictions. Using NE as the energyscale to describe voluntary feed intake implies that animals eat for energyretention. The model of Wellock et al. (2003) expands on this byconsidering that animals eat to attain a desired body composition.

A novel approach to representing the energy status of the animal wasproposed by Lovatto and Sauvant (2003). They considered that growth ofan animal is regulated by homeostatic and homeorhetic controls.Homeorhetic regulation ensures the long-term control of growth and isdriven by the current state of the animal. Protein and lipid deposition arerepresented as the difference between catabolism and anabolism:

dS/dt = (A – C) • S

where S is the current state of the animal (i.e. protein or lipid mass) and Aand C are the fractional anabolic and catabolic rates, respectively, whichwere represented by:

A = k1 + k2 • exp (–k3 • time)C = k1 + k4 • exp (–k5 • time).

At maturity, both fractional rates are equal to k1, whereas during growth Ais greater than C due to the fact that k2 > k4. Thus, at maturity bothcatabolism and anabolism continue to operate but at an equal homeorheticrate. The equations used by Lovatto and Sauvant (2003) have twointeresting features. First, the equations for A and C resemble theGompertz function, which is often used to describe growth. However, inthe Gompertz function, the asymptote (k1) equals zero and the function isnot used to describe anabolism and catabolism separately. Secondly, ‘time’is specifically represented in this model (in addition to ‘state’). This meansthat animals cease to grow due to the fact that they age (and lose thepotential to grow), rather than the fact that they approach a mature bodystate. Although there is some debate on whether growth is determined byage or by state (van Milgen et al., 2000; Wellock et al., 2003), Lister andMcCance (1967) concluded that pigs severely undernourished for a year(i.e. 5.5 kg of body weight after 1 year) stopped growing at the samephysiological age as normal pigs and did not attain the same adult size.Nevertheless, growth during the re-feeding phase was virtually identical tothat of normal pigs. This seems to suggest that both age and state play arole in determining the status of the animal.

156 J. van Milgen

The homeostatic control for carcass protein proposed by Lovatto andSauvant (2003) is depicted in Fig. 8.1. At the homeostatic equilibrium (thesolid dots), protein anabolism will be greater than catabolism, resulting in anet positive protein deposition. Increasing the plasma amino acidconcentration above the equilibrium value increases both proteinanabolism and catabolism, although the former increases to a greaterextent. This mechanism allows the animal to respond quickly to achanging nutrient supply. The integration step in the model of Lovattoand Sauvant (2003) was 0.001 days (1.44 min), which is ten times smallerthan that used in the model of Halas et al. (2004). In the latter model, thesupply of acetylCoA may push certain anabolic processes, but it relies on aconstant supply of nutrients. A good challenge for testing metabolite-driven models is to see how they operate under different conditions ofnutrient input (e.g. frequent meal patterns vs continuous nutrient input).Perhaps these different situations will result in completely different modelpredictions. Consequently, when assuming a constant nutrient input, thenumerical values of model parameters (e.g. Vmax in the model of Halas etal., 2004) have a meaning only when applied to long-term (daily)phenomena and most likely have no meaning at the tissue or cellular level.

Where Should We Go from Here with Energy Evaluation?

The shortcomings of current energy evaluation systems are currentlyleading to proposals for new systems or models that are based on thebiochemical utilization of energy sources. It is clear that these systemsprovide a more solid theoretical basis for feed evaluation. However,scientific soundness is not sufficient for adopting a new system. Pasthistory, established knowledge and the use of a reference basis play a majorrole in the acceptance or failure of future energy systems. For example, theconcept of maintenance used in many energy systems has been heavily


equilibriumnutrient concentration

nutr

ient

flow

Fig. 8.1. Homeostatic regulation of amino acid catabolism (solid line) and anabolism (dashedline) of carcass proteins. At equilibrium nutrient concentration (the solid dots), anabolism andcatabolism are regulated by a time-dependent homeorhetic process (Lovatto and Sauvant,2003).

criticized because it does not correspond to a physiological reality forproducing animals. On the other hand, it is sufficiently robust and well-established that a statement like ‘I offered pigs feed at a level of 10 timesMEm’ will be readily qualified as nonsense. On the other hand, how manynutritionists are able to evaluate a statement such as ‘a 60-kg pig requires300 moles of ATP per day’? Expressing requirements and feed values as‘ATP equivalents’ will probably require considerable time before one isaccustomed to this mode of expression. However, one may say that, bydoing so, we separate some of the ‘known’ (stoichiometry) from the‘unknown’ (turnover, ion pumping, etc.) and are thus making progress.However, a quantitatively important part of what we thought was ‘known’is now considered to be highly questionable. The synthesis of ATP in themitochondria from NADH and FADH2 has been considered for a longtime as fixed (i.e. 3 ATP/NADH and 2 FADH2/ATP) and many (older)biochemistry text books still use these values. It is now more common toassume lower ATP yields from NADH and FADH2 and, due to uncouplingof mitochondrial membrane potential from ATP production, it even maybe variable. This means that the ATP yield from most nutrients will bemuch lower (e.g. 31 rather than 38 ATP from glucose). Stated otherwise,we would require more energy from nutrients to provide the same amountof ATP. This means that the ATP by itself is not a stable currency to expressan energy value. For models that use ATP and calibrate the model forunaccounted energy expenditure, this finding would lower the ATPrequirement while increasing the heat increment of ATP synthesis.

Apart from changing the reference base of expressing energy values,there is another, probably more important reason to be conservative inadopting new systems of energy evaluation. As mentioned earlier, theclassical system reduces energy to a single value. Although too simplistic,the user can easily manipulate and work with feed values in hiscalculations. The system is additive and transparent to the end-user. If asystem is adopted based on biological reality, both the diet and the animalwill determine the energy value of the diet. The only way to deal with theinteraction between the diet and the animal is by using modellingtechniques. It will essentially change the type of question from ‘what doesthe animal need?’ to ‘how does the animal respond to a changing nutrientsupply?’. Although there is considerable progress to make by changing tothis type of questioning, it will make the system less transparent to the end-user. Model developers have to be aware that development of the modelstructure is only a very small part of proposing a new system of evaluatinganimal feeds. In order to gain confidence, the model should be astransparent as possible so that end-users can follow the modeller’s logic.This requires a considerable investment in terms of interface developmentand ensuring appropriate user training. Although these new systemsdefinitely have something to offer, it goes without saying that there is still along way to go.

I do not want to leave the reader with the final impression that I feelthere is no use in developing mechanistic models. I do think that there is a

158 J. van Milgen

tremendous future for these models, especially when studying nutrienttransfer and interactions between organs. At the cellular level, andespecially in combination with the enormous amount of informationbecoming available from genomics and proteomics, mechanistic modelsbased on stoichiometry will have a very important role to play instructuring and understanding the data. At the whole animal level,mechanistic models can be very useful for research and educationpurposes. However, in our systems approach, we have to be careful not tobecome reductionists only for the purpose of including the cause. Thepurpose of many operational nutrition models of animal production andfeed evaluation systems is to control: control growth, control fatness,control the weight at slaughter, etc. The following example that Pattee(1997) gives concerning the light in his room may also apply to establishingapplied models of animal nutrition.

The electrical power that provides the light in my room is ultimately caused bynuclear fission in the sun that drives the water cycle and photosynthesis, or bynuclear fusion on earth. Many complex machines and complex powerdistribution systems are also necessary in the causal chain of events lighting myroom. So why do I think that the cause of the light in my room is my turningthe switch on at the wall? Because that is where I have proximal, focal control,and also because switching is a simple act that is easy to model, as contrastedwith the complexities of nuclear reactions and power distribution networks.

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9 Evaluating Animal Genotypesthrough Model Inversion

A.B. DOESCHL-WILSON, P.W. KNAP AND B.P. KINGHORN

Sygen International, Scottish Agricultural College, Bush Estates, Penicuik,Edinburgh, EH26 0PH, UK. [email protected]

Introduction

Specification of the animal’s genetic potential for growth, efficiency androbustness to environmental stressors is the key to successful livestockproduction and breeding. The current practice in breeding is to recordperformance traits on individuals and use regression to disentangle thegenetic from the environmental influence (Fig. 9.1, top). Traits consideredare typically related to growth, feed efficiency and, more recently,robustness to various stressors. This widely used technique has severalshortcomings.

First, as noted by Bourdon (1998), the obtained estimated breedingvalues (EBVs) do not represent the ‘true genetic potential’ (the maximumperformance given optimal conditions), because the data were measuredunder sub-optimal conditions. Second, regression models are designed tofit a specific data set rather than to represent the underlying biologicalprocesses. This usually results in useful statistics (EBVs) appropriate forthe prevailing conditions. However, it provides a narrow scope of use; inparticular, empirical models assume simple linear relationships between(combinations of) individual model components, which can cause problemswhen extrapolating to conditions not covered in the data. In order toavoid unexpected poor performance in environments that differ from thedata conditions, the covariances required for the EBVs need to be re-estimated whenever the production conditions change.

Illustrating the genotype-phenotype relationship is Fig. 9.1, withphenotypic performance at one end of the spectrum and the genotype atthe opposite end; mechanistic animal growth models represent thisrelationship in the reverse direction to the mathematical models currently


used in breeding. Mechanistic models use as inputs descriptions of thegenetic potential for growth and efficiency in optimal conditions, togetherwith descriptions of the environmental and dietary conditions. Genotypicand environmental specifications are assumed mutually independent. Thegrowth model then simulates the (non-linear) interaction betweenenvironmental conditions and genetic potential. Model outputs arephenotypic predictions of the performance traits. By contrast, phenotypicdata serve as inputs for the statistical models normally used in animalbreeding.

The description of the genotype in mechanistic growth models is freefrom environmental influences, which makes it theoretically more closelyassociated with the true genotype than the phenotypic traits. As aconsequence of the explicit description of genotype by environmentinteractions in mechanistic models, these can provide for properextrapolation outside the data. As Black (1995) states, ‘mechanistic piggrowth models have proved great value to research and industry as theycombine the present knowledge about the influencing factors of piggrowth and predict performance where knowledge is limited’.

All this raises the question of why current methods in breeding are stillfocusing on phenotypic performance traits instead of the more adequate

164 A.B. Doeschl-Wilson et al.

Genotypespecification

Estimated geneticcomponents ofphenotypic traits(EBVs)

Multi-variate regression,covariance estimates, BLUP

Recorded phenotypicperformance

Recorded environmentalconditions

Recorded pedigreeinformation

Genetic potentialfor growth,energy efficiencyand robustness

Potentialperformance

environmental,dietary andphysiologicalconditions

Phenotypicperformance×

Simulation model

Mathematical methods Measurable traitsGenes

Traditional method of pig breeders

Mechanistic growth model

Modelinput

Modeloutput

Fig. 9.1. Illustration of the different approaches for specifying genotypes.

‘universal description of the genotype’ (Bourdon, 1998) of mechanisticgrowth models. The main reason is that the underlying physiological traitsrequired for growth model parameterization are difficult to measure.However, accurate estimates for the underlying trait levels are not onlyessential for accurate description of the genotype, but also for accuratemodel predictions, and thus for the appropriate application of growthmodels.

The genotypic model parameters intend to describe the pig’s intrinsicability to grow and cope with stressors. Luiting and Knap (Chapter 14, thisvolume) list the growth descriptors of the main pig growth models incurrent use. Most of these models simulate growth performance in a non-limiting environment with two to five genotypic parameters. Theprediction of performance under the influence of physical, social, climaticor pathological stressors requires additional parameters describing theability to cope with these (see for example Wellock et al., 2003b; Kyriazakiset al., Chapter 7, this volume).

The number of genotypic model parameters depends also on thepurpose of the model. Models that predict the performance of anindividual animal or of a population average describe the genotype by oneparameter for each of the underlying traits. Models that simulate apopulation of distinct individuals require parameters representing themeans of and covariances among the underlying traits (Knap, 2000b;Pomar et al., 2003; Wellock et al., 2004). If various generations areinvolved, such as in problems in pig breeding, heritabilities of theunderlying traits are of additional interest. Thus, every underlying traitrequires several model parameters (mean, covariances and heritability),which can add up to a large number of parameters to be determined.

Methods for Estimating Genotypic Specifications

Knap et al. (2003) proposed two methods for estimating genotypic modelparameters: (i) direct measurements of the underlying traits representedby the model parameters, combined with controlled environmentalconditions; and (ii) serial measurement of performance traits and fittingthe data to the mechanistic growth model itself (Model inversion).

Using direct measurements of traits represented by the genotypic modelparameters

Ferguson and Gous (1993a) described techniques to obtain estimates of theparameters of the Gompertz equation, which they use to model thepotential rate of body protein growth and, from that, potential rates forother components using allometry. These involve serial slaughter trialswith measurement of chemical body composition. The crux of these trialsis to minimize environmental load, maximizing the chance that the growth

Evaluating Animal Genotypes through Model Inversion 165

potential can be achieved. Dietary and environmental conditions must becarefully balanced, so that protein retention can reach its maximumwithout causing lipid retention to exceed the animal’s intrinsic desire.Knap et al. (2003) proposed a controlled experiment that would allow thegenetic potential for protein and lipid retention, and for intrinsicmaintenance energy requirements, to be fully expressed either at differentgrowth stages or in different individuals from the genotype. Such anexperiment would enable direct measurement of traits whose extremes areunlikely to be reached in normal conditions.

Such techniques have provided estimates for population means of modelparameters. Direct estimates for population means of Gompertz curveparameters for protein and lipid deposition and of maintenance energyrequirements in pigs were also obtained by Knap (2000a), who analysedserial slaughter data from the literature for a wide range of genotypes, andby Landgraf et al. (2002), who used deuterium dilution techniques andcomputer tomography in vivo combined with chemical analysis.

The estimation of the within-population variation of these parametersrequires serial measurement of the related traits in several animals over asignificantly wide body weight range, as demonstrated by results fromcomputer tomography and deuterium dilution measurements (Knap et al.,2003). These data indicate a substantial variation between animals in theunderlying traits of the growth model used by these authors (coefficients ofvariation ranged between 8 and 27%), which was interpreted to be ofgenetic nature.

The estimation of heritabilities of underlying traits requires serialmeasurement of the related traits in several animals with a known familystructure. Roehe et al. (2002) exemplified this method by estimatingheritabilities of Gompertz parameters for body weight growth.

The combined results of these studies suggest that it is possible tospecify genotypic model parameters from direct experimental measure-ment, but that it requires complex experimental design and expensive,time consuming measurement techniques.

Fitting phenotypic performance trait measurements to the growth model(model inversion)

The second method proposed by Knap et al. (2003) involves, instead ofcomplex experimental design for direct measurement of underlying traits,readily obtained performance data and the growth model itself. Modelinversion builds upon the idea that phenotypic performance data can beused to estimate those particular values of the genotypic model parametersthat produce model predictions for the performance traits that match theobservations. The model is ‘inverted’ in the sense that the conventionalmodel input traits are treated as model outputs that need to be determinedin the inversion process, and the conventional model output traits aretreated as inputs through substitution of performance data.


Knap et al. (2003) mention two alternative methods of performing theinversion process. The first is an iterative process, first described byBaldwin (1976), which is essentially a trial and error approach, in whichthe model parameters are systematically adjusted so that thecorresponding model predictions approach and eventually give a best fit tothe performance data. We refer to this process as model inversion byoptimization, and will deal with it below.

The second method involves rearrangement of the model equations sothat, upon substitution of observations into the model output variables, theresulting equation system can be solved for the genotypic modelparameters. This we call algebraic model inversion.

Algebraic Model Inversion

Assuming that the growth model is able to reproduce performance data,the possibility arises of substituting these observations for the modelpredictions and solving the system for the genotypic parameter values.Most mechanistic growth models use algebraic equations to relate genotypeand environmental conditions to observable production traits. Theseequations must then be rearranged so that the system of equations can besolved for the unknown parameters.

Compared to numerical optimization routines, methods for calculatingunique, exact solutions are more robust as they do not require subjectivecriteria that determine when an approximate solution is acceptable andwhich solution is classified as optimal. Animal growth models that userelatively simple algebraic expressions to describe the growth mechanismmay lend themselves to this method for determining appropriateparameter values.

However, unique exact solutions of a system of algebraic equationsonly exist if certain assumptions are met. This section presents theconditions for the algebraic invertibility of mechanistic growth models, anddemonstrates how the theory applies to a specific pig growth model. Themodel of de Lange (1995) was originally prepared for educationalpurposes, and was later used as the basis for an attempt to algebraicallyinvert a model to relate pig genotype to nutritional requirements(unpublished results; see www.defra.gov.uk/science/LINK/agriculture forbackground information). The case study below represents furtherdevelopment of that work.

Mathematical Theory for Algebraic Model Inversion

A prerequisite for determining genotypic parameters by algebraicinversion is a one-to-one relationship between model input and modeloutput as expressed by the model equations. If various combinations ofinput parameters produce the same predictions, or if several predictions


www.defra.gov.uk/science/LINK/agriculture

are possible for a given set of input parameters, the inversion processcannot produce unique values for the input parameters. All mechanisticpig growth models fall into this category. Stochastic models, for example,which integrate a random component, cannot be inverted by this method.

Most pig growth models are a composite of several algebraic equationswith an intrinsic hierarchical structure. This prevents a straightforwardreversion of the multiple modelling steps. It is therefore desirable torepresent the entire model by one system of equations with the modelinput parameters as unknowns and the observable model outputs assumedas known. The inversion process then corresponds to solving the system ofequations for the genotypic parameters for given values of predictableperformance traits. Exact solutions of a system of algebraic equationsrequire that the system is exactly determined, i.e. that the number ofvariables to be solved for equals the number of equations.

The Implicit Function Theorem of multivariate calculus

Mechanistic growth models are generally non-linear. The conditions forthe existence of a unique solution of a non-linear system of equations aregiven by the Implicit Function Theorem of multivariate calculus (see forexample Krantz, 1951). A local unique solution of the equations systemexists if the local linear approximation of the system has a unique solution.The theorem provides further information about the solution space bystating that solutions corresponding to similar performance have the sameform, i.e. can be expressed through the same multivariate function. Theterm ‘local’ means that the existence, uniqueness and unique expression ofthe solutions hold only within a limited region in the parameter space, itdoes not guarantee that the specific solution is the only solution in theentire parameter space. The restriction from global to local properties is ageneric characteristic of non-linear problems, which prevails for everymethod of calibrating model parameters.

Representing Pig Growth Models by a System of AlgebraicEquations

Most mechanistic growth models share properties that determine whetherthey can be represented by a system of equations that can be solved for thegenotypic parameters, and which simplifications are necessary to derivesuch a system.

Reduction to few equations

Most pig growth models represent the genotype of the pig by two to fiveparameters. This implies that for model inversion, the model should be


reformulated to a system with two to five equations and the genotypicparameters as the only unknowns. Other model input parameters, forwhich no measurements exist, must be either eliminated from the systemor described empirically.

Recurrence relations and long time spans between observations

Dynamic growth models describe growth through time, but genotypicparameters are generally assumed to be time invariant. Although dynamicsystems are most accurately represented by differential equations (forexample, see Parks, 1982), most growth models approximate the growthchanges by first order difference equations, which describe the change ofmodel variables between two specific points in time (usually 1 day apart) ortwo specific body weight values. The estimation of the time invariantgenotypic parameters through algebraic model inversion then requiresinformation about the animal’s performance at two instances of time (orweight).

Many growth models use a 1-day time step, but daily observations ofperformance traits are rare. Using observations over a longer period thanthe model’s therefore requires either reformulation of the model equations(e.g. cumulative instead of daily feed intake), or an interpolation of theproduction traits for the model’s time interval from longer-termobservations. In either approach, short-term environmental fluctuationscannot be accounted for, which reduces the accuracies of the calculatedparameters.

Often, more than two measurements of performance traits areavailable. The use of repeated measurements of performance traits forderiving genotypic parameters would result in different equation systemsfor different periods, and thus most likely to different values of thegenotypic parameters for different growth phases. These would need to becombined to an individual value to match the model assumptions of time-invariant genotypic parameters.

Hierarchical model structure

Animal growth is the result of various mechanical and biochemicalprocesses, many of which are modelled sequentially. For example, mostgrowth models give priority to the satisfaction of body maintenancerequirements over processes related to growth. Reformulating sequentialprocesses to one system of equations is not straightforward as the processesgenerally depend on conditions specified at intermediate steps in themodel. For example, most models include a process that reduces thepotential rates of protein and lipid retention if the environmental ordietary conditions are found limiting. Other examples of events triggeredunder certain conditions are thermoregulatory processes, which come only


into play when the ambient temperature is outside the pig’s comfort zone(Bruce and Clark, 1979; Black et al., 1986; Knap, 2000b; Wellock et al.,2003a), and abrupt changes in the rates of lipid retention undermalnutrition (Green and Whittemore, 2003; Wellock et al., 2003a).

Since many of these criteria depend on intermediate model results andare therefore not known a priori, the representation of the model by asystem of equations suited for algebraic model inversion can becomeproblematic. Model inversion may thus require prior assumptions aboutthe conditions for which the modelled responses divide. Theseassumptions should be based on the conditions from which the data areobtained, and need to be re-validated for the calculated genotypic valuesonce the inversion has been carried out.

Implemented thresholds

Implemented thresholds cause problems for algebraic model inversion asdifferent parameter values can produce the same function value and as theabrupt slope change at the location where the threshold is reached violatesthe assumption of differentiability in the Implicit Function Theorem.Implemented thresholds could represent, for example, a maximum valuefor protein deposition, a minimum ratio of lipid to protein retention or acritical value of net efficiency for using ideal protein for protein retention(see Luiting and Knap, Chapter 14, this volume).

Two simple alternatives are proposed to overcome these problems.First, to restrict the domain to one side of the threshold values, based onthe nature of the conditions from which the data are obtained. Forexample, for an experiment involving restricted feed intake, theassumption that the maximum protein retention rate was not achieved bythe animal would be appropriate. Second, more elegantly, to replace thethresholds by mathematical functions that gradually approach anasymptote, as exemplified through the substitution of a linear plateaufunction for protein retention (Whittemore and Fawcett, 1974) by aGompertz function (Emmans, 1988).

The above described generic properties of pig growth modelsdemonstrate the need for model simplification before algebraic modelinversion can be tackled. Functions with inappropriate mathematicalproperties could be replaced by more appropriate ones, or diverse a prioriassumptions must be made, whose validity can only be justified after themodel inversion has been carried out.

Solving the System of Equations

The Implicit Function Theorem states the conditions for the existence of aunique solution, but does not provide an explicit expression of thesolution. In fact, only few non-linear systems of equations can be solved by


analytical means. Most systems require a numerical solver. Finding the solutions of the corresponding system of equations is a

mathematical problem. There is no guarantee that the solutions arebiologically realistic. But if the estimates for genotypic parameters fromalgebraic inversion differ greatly from those expected from empiricalstudies, fundamental flaws in the model equations or in the priorassumptions must be suspected.

Case Study 1: Algebraic Inversion of a Pig Growth Model

The model of de Lange (1995), which was previously used to estimategenotypic parameters from given diet and food intake data (www.defra.gov.uk/science/LINK/agriculture), is a simple mechanistic, deterministic piggrowth model that contains all the features that should be included topredict with reasonable accuracy the performance of pigs under definedconditions. It has two genotypic input parameters LPmin, representing aminimal lipid to protein ratio, and Prmax, the animal’s upper limit toprotein retention. Both parameters are assumed time-invariant. Inaddition to estimates of these parameters, the model requires as input thebody lipid and protein masses at a time t0 and information about foodintake and dietary composition. The model then recursively predicts thepig’s protein and lipid contents together with the body weight at a futuretime.

Derivation of the system of equations

Under the assumption that the body protein and lipid mass of the pig attime t0 are known and the required dietary information is available, thehierarchical model was reformulated into systems of two equations, fromwhich unique values for LPmin and Prmax were obtained. The derivationwas built upon the assumptions of the original research project, i.e. thatinformation about feed intake, diet composition, body weight and backfatdepth were available and that initial body composition could be estimatedfrom initial body weight.

A system of equations with unique solutions for LPmin and Prmax couldonly be obtained if the two constraints C1 and C2 below were satisfied. Thefinal Eqns 9.1a and 9.1b contain LPmin and Prmax as the only unknowns. Allother components are expressed in terms of initial and final body weight(W0 and W1, respectively) or final backfat depth (BF1).

0.95 (W1 – W0) / dt = (0.001 × ((1.189 – E) × PRmax + B(W0))

+ 4.889 × (0.95 W0 / (A(W0) + LPmin) + 0.001 PRmax) 0.855

– 4.889 × (0.95 W0 / (A(W0) + LPmin) ) 0.855 (9.1a)




0.001dt × (B(W0) – E × PRmax) = �8.244 + 2.053 BF1 – 0.95 LPmin ×W0 / (A(W0) + LPmin) (9.1b)

with constraints

BPg (W0) � PRmax (C1)

B(W0) � (LPmin + E) × PRmax (C2)

where dt denotes the time span t1 – t0 between the measurements W0 andW1 and the expressions E, BPg (W), A(W) and B(W) are defined as follows:

E = (Epd – Epe) / Eld,

A(W) = 1.189 + 4.889 × (1.4 + 0.15 × W) –0.145 ,

BPg (W) = 0.85 × [ minimum ( API , ALI / LysBalP ) – 0.9375 W 0.75],

B(W) = 1/ Eld × [EPFI + (Ep – Epe) × API – (0.9375 × (Ep – Epe) + 458) × W0.75].

where API = FI � DProt � AAa is the available protein intake (g/day),ALI = FI x DLys � AAa the available lysine intake (g/day) and EPFI = FI� DDE � Ep � API is the protein-free digestible energy intake (kJ/day).Food intake (FI, kg/day) values and the description and values of theremaining constants are specified in Tables 9.2. and 9.1. respectively.

Solving the equations

Weekly least square means of one of three genotypes from a previousgrowth trial (Green et al., 2003; Whittemore et al., 2003) were used for thiscase study, providing information on nutrient intake and repeatedmeasurements of body weight and backfat depth for a weight rangebetween 25 and 115 kg (Table 9.2). Dietary specifications are in Table 9.1.

For each of the 12 weeks, the weekly least square means of food intake,body weight and backfat depth were substituted into system (Eqns 9.1a, 9.1b),yielding different equation systems for every week. The conditions of the


Table 9.1. Constants of the model. Except for the dietary constants, DProt, DLys and DDE,which were specified in Whittemore et al. (2003), all other constants are taken from de Lange(1995).

Constants Explanation Estimated value

Aaa Post absorptive efficiency for utilizing amino acids and dietary protein for growth 0.85

Dprot Dietary protein content (g/kg) 194Dlys Dietary lysine content (g/kg) 11.4Ep Gross energy content of protein (kJ/g) 23.6DDE Dietary energy content (kJ/g) 14.5LysBalP Lysine content of balanced protein (%) 7Epe Energy cost of available protein excretion (kJ/g) 12.1Epd Energy cost for protein deposition (kJ/g) 43.9Eld Energy cost for lipid deposition (kJ/g) 52.8

Implicit Function Theorem for the existence of a unique solution with theweekly least square means were satisfied. The numerical solver fzero of Matlab(Matlab 6.5, 2002) was used to calculate values for PRmax and LPmin assolutions of the corresponding systems of equations. The weekly solutions arein Table 9.3 (columns 1 to 3). All solutions satisfied constraints C1 and C2.

The value for PRmax obtained through inversion of the de Langemodel ranged between 114 and 171 g/day (Table 9.3), which agrees withestimates provided in the literature, i.e. 99 g/day (SE 4 g/day) to 212 g/day(SE 29 g/day) (Knap, 2000a). Literature estimates for the lipid to protein


Table 9.2. Weekly least square means for daily food intake, body weight andbackfat depth used for the inversion of the model. The values are the results of thestatistical models for ‘Landrace type’ pigs, published in Green et al. (2003).

Week Daily food intake (kg) Body weight (kg) Backfat depth (mm)

1 1.29 30.89 5.302 1.48 35.41 5.773 1.68 40.14 6.394 1.87 45.10 7.045 2.05 50.28 7.726 2.22 55.70 8.437 2.38 61.36 9.178 2.53 67.26 9.949 2.66 73.40 10.75

10 2.77 79.80 11.5811 2.86 86.46 12.4612 2.93 93.37 13.3613 100.56 14.30

Table 9.3. Weekly estimates of the genotypic parameters PRmax and LPmin from algebraicmodel inversion (columns 2 and 3) and inversion through optimization (columns 4 and 5).RMSD is the root of the mean of the squared deviations of predicted body weight and backfatdepths from the observations (Table 9.2) using the optimized parameter values.

Week PRmax LPmin (alg. PRmax LPmin RMSD(alg. inversion) inversion) (optimization) (optimization) (optimization)

1 113.5 0.531 101.5 0.529 < 10�18

2 114.7 0.642 102.6 0.641 < 10–18

3 116.0 0.732 104.5 0.732 8.9 × 10�16

4 117.5 0.810 106.8 0.811 < 10�18

5 120.3 0.880 110.5 0.881 –1.4 × 10�14

6 123.8 0.941 115.0 0.942 < 10�18

7 128.0 0.996 120.3 0.997 < 10�18

8 132.9 1.046 126.4 1.049 < 10�18

9 140.0 1.094 134.9 1.095 –1.2 × 10�14

10 148.6 1.139 144.7 1.141 < 10�18

11 158.3 1.181 155.8 1.184 < 10�18

12 170.7 1.222 169.7 1.225 –3.6 × 10�15

1–12 21.4 –1.895 111.8 1.129 5.70

ratio at maturity vary between 0.97 (SE 0.28) and 5.16 (SE 0.50). Incomparison with these values, the range between 0.53 and 1.22 for theestimates for the minimal lipid to protein ratio obtained from the algebraicmodel inversion also appears realistic. In the last row of Table 9.3,solutions corresponding to a time span of 12 weeks are shown. Thecalculated values are unrealistic, demonstrating that algebraic modelinversion fails if observations are far apart.

Although the solutions of PRmax and LPmin appear realistic, they arenot, as assumed, constant over time. Over the 12 weeks, PRmax and LPminboth increase systematically. This apparent time trend contradicts theassumption that genotypic parameters are time invariant. Agreement ofthe model predictions for body weight and backfat depths with theobserved least square means is only possible if the genotypic parametersare allowed to vary over time, which indicates that the growth trends forbody weight and backfat depth predicted by the model differ from theobserved ones. This suspicion is confirmed in Fig. 9.2, which plots thosegrowth curves corresponding to fixed values of the genotypic parameterstogether with the least square means from the data. For the parametercombinations considered, the predicted backfat depth curves differstrongly from the data. Sensitivity analysis indicates that no combination ofgenotypic parameters can produce a trend similar to the data.

Influence of different types of errors on the solutions

Although the genotypic parameter estimates are accurate solutions of thederived equation system, they may nevertheless not be an accuratedescription of the genotype. The algebraic inversion process integratesvarious sources of error, which must be taken into account when interpretingthe results. The most significant types of error for algebraic model inversionare: (i) modelization errors; and (ii) errors from simplifications of the modelequations and from inverting regression equations.

Realistic time invariant values for the genotypic parameters can only beobtained if the model can reproduce observed trends. This model could notgenerate backfat depth predictions that matched the data over a time spanof 12 weeks. The predicted trends associated with various starting values forgenotypic parameters should be validated before calculating exact estimatesof genotypic parameters through model inversion. In the inversion process,differences between predicted and observed growth trends show up in aprogressive change of the estimated parameters with time.

Most mechanistic growth models incorporate the results fromempirical studies through regression equations. The algebraic inversionprocess often requires rearrangement of these, and thus a change of therole of the dependent and independent regression variables. However,swapping these roles in a least squares approach results in differentequations from those obtained by solving the initial regression equation forthe independent variable, and this introduces more errors.



observed LSMalgebraic inversion, week 12algebraic inversion, week 6inversion through optimization, weeks 1–12inversion through optimization, week 12

110

100

90

80

70

60

50

40

300 1 2 3 4 5 6 7 8 9 10 11 12 13

Week

Bod

y w

eigh

t (kg

)(a)

Fig. 9.2. (a) Predicted body weight for different solutions for the genotypic parameters of themodel. The estimates of the genotypic parameters used to generate these plots arepresented in Table 9.3. (b) Predicted backfat depth for different solutions for the genotypicparameters of the model. The estimates of the genotypic parameters used to generate theseplots are presented in Table 9.3.

observed LSMalgebraic inversion, week 1algebraic inversion, week 12inversion through optimization, weeks 1–12inversion through optimization, week 12

16

14

12

10

8

6

40 1 2 3 4 5 6 7 8 9 10 11 12 13

Week

Bac

kfat

dep

th (

mm

)

(b)

Model Inversion through Optimization

Algebraic model inversion relies upon the assumption that a unique set ofmodel input parameters exists for which the model predictions equal thedata. Uncertainties and errors in the model itself or in the data areignored. Also, if the number of parameters to be determined throughinversion exceeds the number of parameters for which a unique solutionof the inverse model exists, the algebraic approach forces the modeller torestrict the number of unknowns by guessing the values of someparameters. This restriction may lead to poor estimates for the remainingparameters, since they are dependent on these guesses.

By treating the estimation of genotypic parameters by model inversionas an optimization problem, various sources of uncertainty can be takeninto account. Instead of determining the set of genotypic parameters forwhich the model predictions exactly match the data, inversion throughoptimization determines the set of parameters for which the discrepancybetween predictions and data is minimal.

Description of the process

Inversion by optimization is an iterative process, and as such very differentfrom algebraic model inversion. The process starts with an initial guess forthe unknown model parameters. The model then calculates thepredictions associated with these parameter values. In contrast to algebraicinversion, which inverts the model equations, no change in the growthmodel is required. The optimization criterion involves a quantitative measure(such as sum of squares of deviations between predictions and data) thatdescribes the discrepancy between predictions and data. The best set ofmodel parameters has been specified when this measure is minimal.Otherwise, the optimization algorithm determines the next set of modelparameters, for which the process is repeated until a minimum is reached.The process is similar to a trial and error approach, but the optimizationalgorithm searches through the parameter space non-exhaustively butmethodologically, so that the discrepancy gradually decreases until aminimum is reached.

The minimal discrepancy between predictions and data is not known apriori. The minimum is assumed to be achieved when the ‘minimaldiscrepancy’ set of parameters does not change over many iterations, andthe algorithm is then said to have converged.

Common problems

Optimization algorithms differ in their methods for searching throughparameter space, and the most appropriate method differs from oneproblem to another. Many optimization algorithms have been proposed in


the mathematical, computational and applied literature. A review ofexisting algorithms and their application to agricultural models is providedby Mayer et al. (2005) and by Green and Parsons (Chapter 15, thisvolume).

The challenge for model inversion by optimization is not only indetermining the most appropriate optimization algorithm for the specificmodel, but also in establishing an appropriate optimization criterion. Variouscombinations of genotypic parameters may correspond to the same orsimilar discrepancies between predictions and data. In contrast to algebraicmodel inversion, the conditions for a unique ‘minimum discrepancy’parameter set are not mathematically specified. It is generally true that ahigher number of independent observations contributing to the optimizationcriterion increase the chance of obtaining unique parameter estimates, butcertainty can only be achieved by response surface analysis and by repeatingthe process for various starting values for the input parameters.

Case Study 2: Estimating the Genotypic Parameters of the deLange Model by Inversion through Optimization

We applied the differential evolution algorithm (Price and Storn, 1997;Mayer et al., 2005) to obtain estimates for the genotypic parameters LPminand PDmax of the de Lange model.

Weekly estimates for LPmin and PDmax were calculated through theoptimization procedure, using the least square means of body weight asinitial values. Daily food intake was estimated from weekly food intake(Table 9.2). The optimization algorithm calculated the weekly estimates forLPmin and PDmax that correspond to weekly model predictions for bodyweight and backfat with minimal deviation from the data in Table 9.2. Thedeviation between observed and predicted body weight and backfat depthwas represented by the root mean square deviation (RMSD).

The weekly estimates for LPmin and PDmax, and the RMSD are in Table9.3, columns 4 to 6. The LPmin estimates from inversion by optimization arevery similar to the ones from algebraic inversion, whereas some of the weeklyestimates for PRmax are up to 10% lower. The differences in the parameterestimates are probably due to the fact that, in the optimization process, thegrowth model operates on a daily basis, whereas in the algebraic approach,model equations were rearranged to represent 1 week. Taking the differencesin the approaches into account, their genotypic parameter estimates aresimilar, which increases confidence in the validity of either method.

Specifying time invariant values for the genotypic parameters

In contrast to the algebraic model inversion, which could only takeobservations corresponding to two different instances in time into account,observations of body weight and backfat depth for all 12 weeks can be


included in the optimization criterion. The optimization method thenproduces one estimate for each genotypic parameter that corresponds tothe minimal discrepancy between predictions and data during the entire12-week growth period. The LPmin and PRmax estimates are 1.129 and111.8, with a RMSD significantly higher than the RMSDs associated withindividual weeks (Table 9.3). Fig. 9.2a shows that the corresponding bodyweight growth curve is a good approximation of the curve produced by thestatistical model. The fit of the corresponding backfat depth curve to theobserved least squares means (Fig. 9.2b) is however very poor, pointingagain to inappropriate model equations for calculating backfat depth.

Case Study 3: a More Complex Problem for Model Inversion byOptimization

The Pig Genetic Growth Model (PGGM), developed by Knap (1999), is astochastic mechanistic growth model for a population of pigs. It wasdesigned to predict the effects of different environmental conditions(performance testing regimes) on the reliability of estimating the geneticpotential for growth rate, feed efficiency and body composition fromcurrent performance traits. Model parameters describing genetic growthpotential are assumed to represent physiological traits with additive geneticand permanent environmental components.

The four physiological traits specifying the genotype

The model uses four traits to describe the pig’s intrinsic capacity forgrowth and energy utilization. The genetic potentials for protein and lipidgrowth are modelled by Gompertz functions and full allometry betweenbody protein and lipid is assumed. The description of the genotype’sgrowth potential then requires three independent parameters: matureprotein mass (Pmat), the ratio between mature lipid and protein mass(LPmat) and the standardized rate parameter B* = BGomp × Pmat0.27.

The resource-demanding processes other than protein and lipidgrowth are categorized as ‘maintenance processes’. The current version ofthe model explicitly deals with the energy requirements for proteinturnover and thermoregulation, which depend on body composition. Therequirements for all other maintenance processes, including physiologicalservice functions, are combined into a single parameter (MEmaint)calculated as a simple function of metabolic body weight: (MEm0 + b.BW)× BW0.75, where MEm0 is the fourth genotype-specific model parameter.

Introducing variation between individual animals

The phenotypic value for each of the physiological traits can be de-


composed according to

Pij = µ + Ai + PEi + eij (9.2)

where Pij is the phenotype of animal i on day j, µ is the population mean forthe trait, and Ai, PEi and eij are its additive genetic and permanentenvironmental deviations, and its random environmental deviation on day j.

The genetic deviation is determined according to

(9.3)

where rannorAi is a random deviation drawn from the standard Normaldistribution, h2 is the heritability of the trait and σP its phenotypic standarddeviation.

The permanent environmental deviation is determined according to

(9.4)

with rannorPEi also being a random deviation drawn from the standardNormal distribution. The random environmental variation is modelledaccording to

(9.5)

where R represents either a random drawing from the standard normaldistribution or, more realistically, an autoregressive function involvingrandom drawings.

The generated variation in the driving model parameters betweenindividual animals of the population leads to variation in (and covariationbetween) model output traits such as growth rate, feed intake and bodycomposition.

This formulation implies that the same model form applies to bothgenetic and environmental effects. In truth, these are likely to differ.However, power to discover such individual underlying growth models islikely to be very poor, so that the assumption of a single model is probablyinevitable.

Model inversion: methods

The specification of four physiological traits (Pmat, LPmat, B* and MEm0),which describe the genotype of the pig according to Eqn 9.1, each with itspopulation mean, heritability and phenotypic standard deviation, leads to4 × 3 = 12 model parameters to be determined. The parameters areassumed as mutually uncorrelated, so that the covariances between themcan be set to zero. Empirical estimates exist for population means andstandard deviations of the Gompertz growth traits (Knap et al., 2003), butnot for their heritabilities nor for the trait describing maintenance

eij e= ×Rij σ

PE rannor 1 hi PE2

P= × − ×i σ

A rannor hi A2

P= × ×i σ


requirements. Model inversion is thus the only possibility for obtainingthese estimates.

Determining the 12 parameters using inversion through optimizationpresents a 12-dimensional optimization problem. The differentialevolution algorithm above was used due to its efficiency with high-dimensional complex optimization problems (Mayer et al., 2005).

The data used as criteria for estimating the population means, standarddeviations and heritabilities for the four genotypic traits were phenotypicmeans, genetic correlations and heritabilities for the three performancetraits: days to reach 110 kg body weight (DAYS), average daily feed intake(DFI) and backfat depth (BF). These were estimated from data of a PIC pigsireline measured at 110 kg body weight. The statistical estimates for thesemultiple traits constitute multiple objectives for the parameter calibration,which need to be simultaneously achieved. Various methods exist togenerate solutions that simultaneously satisfy multiple goals, some producinga continuous solution space, others individual solutions (e.g. Steuer, 1986).We used a combined objective of minimizing the sum of squared relativedeviations of the phenotypic means, genetic covariances and heritabilitiesderived from model predictions and from data. Alternative objectives, suchas minimizing the maximum of the relative deviations or applyingpunishment functions to the deviations produced similar results.

The stochastic nature of the model implies that its predictions areinfluenced by the specific random drawings used in the simulation. Twosimulations with identical values for all input parameters will producedifferent predictions and possibly different covariance estimates. Theinfluence of individual random drawings can be reduced by increasing thenumber of replicates in the simulated population, but this also increasesmodel runtime and the time of statistical calculations. In the optimizationprocess the model is called many thousands of times and statistical resultsmust be produced for every run, so computing time is a real issue. Fig. 9.3gives the runtime of the optimization process, relative to population size,together with the average coefficient of variation (CV) of the covariancesand heritabilities of the predictions used in the optimization criterion. Theresults given below are based on 7000 replicates (20 days runtime on astandard PC, CV < 10%).

The model inversion aimed to specify the genotypic parametersassociated with a PIC pig sireline. Table 9.4a shows the characterization ofthis genotype in terms of empirical estimates of the heritabilities,correlations and phenotypic means of the three performance traits used inthe optimization procedure.

Model inversion: results

Estimates for population means, CVs and heritabilities for the fourunderlying traits, produced by four optimization runs with differentrandom number sequences and different starting points for the



0.30

0.25

0.20

0.15

0.10

0.05

0.00

runtime

CV of soutions

100000

10000

1000

100

10

00 10000 20000 30000 40000 50000

Population size

Run

time

(day

s) CV

of solutions

Fig. 9.3. Runtime for the optimization process and average coefficient of variation (CV) forthe calculated covariances and heritabilities for the predicted performance traits as affectedby population size.

optimization algorithm are shown in Table 9.5. The solutions of runs Cand D are very similar, whereas runs A and B yield substantially differentresults for some of the parameters. Estimates for population averages inPmat vary from 37 to 56.5 kg, in LPmat from 0.65 to 0.89, and in B* from0.029 to 0.035 kg/day per kg0.73. Except for run B, which gives an averageMEm0 estimate of 506 kJ/kg0.75 per day, three runs produce similarestimates between 638 and 652 kJ/kg0.75 per day.

Knap (2000a) and Knap et al. (2003) estimated average values for Pmat,LPmat and B* from earlier published data on five widely different piggenotypes. Their Pmat estimates range from 20.0 to 40.7 kg, lower than ourpresent estimates. In contrast, their LPmat estimates range from 0.97 to5.16, higher than ours. Their B* estimates range from 0.022 to 0.044kg/day per kg0.73, similar to ours. The genotype simulated here isgenetically more advanced than the ones in the earlier studies, so wewould expect the above Pmat and LPmat differences; in fact, the B* valueswould be expected to be higher, too.

The coefficients of variation produced by model inversion are allbetween 3 and 12%, which agrees with the estimates obtained by Knap(2000b), but are below the empirical estimates reported in Knap et al.(2003), which range between 14 and 27%.

Estimated heritabilities for the four physiological traits vary among theoptimization runs, but exhibit a consistent pattern. In all four runs, LPmathas the highest heritability. The heritability for MEm0 is much lower thanthe heritability of the other three traits. These estimates are slightly lower


Table 9.4. Genetic correlations (upper triangle of the white area), heritabilities (onthe diagonal) and phenotypic correlations (lower triangle of the white area),together with phenotypic means (grey area) for a PIC Sire Line as predicted fromdata analysis and from the growth model combined with optimization routines fromfour different simulations.

(a) Genotype specifications in run A.

Days to 110 kg DFI (kg/day) BF (mm)

Days to 110 kg Data 0.396 –0.725 –0.042Model 0.364 –0.697 –0.044

DFI Data –0.435 0.273 0.405Model –0.853 0.270 0.396

BF Data –0.044 0.237 0.550Model –0.016 0.246 0.554

Phenotyp. means Data 177 2.39 10.3Model 175 2.36 10.25

(b) Genotype specifications in run B.



DFI Data –0.435 0.273 0.405Model –0.694 0.275 0.409

BF Data –0.044 0.237 0.550Model 0.033 0.266 0.563


(c) Genotype specifications in run C.



DFI Data –0.435 0.273 0.405Model –0.896 0.280 0.404

BF Data –0.044 0.237 0.550Model 0.007 0.274 0.536


(d) Genotype specifications in run D.



DFI Data –0.435 0.273 0.405Model –0.668 0.272 0.405

BF Data –0.044 0.237 0.550Model –0.028 0.275 0.553


than those reported by Knap (2000a), who reported literature estimatesfrom 0.1 to 0.7, with the majority lying between 0.1 and 0.4.

Tables 9.4a to 9.4d show that all four optimization runs producedsimilar phenotypic means, genetic correlations and heritabilities for allthree performance traits used in the optimization criterion. In addition tothose criteria used in the optimization process, the model with thespecified parameter estimates also produces realistic phenotypiccorrelations (white fields below the diagonal). Only the phenotypiccorrelation between growth rate and daily feed intake is stronger (in thenegative direction) according to the model, which might indicateinconsistencies in the feed intake data.

The good match between predictions and data implies that, in contrastto the de Lange model, PGGM realistically predicts various traits up to thelevel of their covariation, provided that the genotype is appropriatelyspecified. This increases confidence in its predictions. Nevertheless, despitethis good fit, the inversion process used here does not produce a uniqueset of model parameters that fully characterize the genotype.

Choosing the most appropriate specification of the genotype: stricter criteria

Our optimization criteria exclusively refer to data measured at 110 kgbody weight. The identification of discrepancies in the predictions fromdifferent parameter combinations, and thus of the most appropriatecombination, would require a more extensive description of thephenotype.

The benefit of data covering multiple growth stages is illustrated inFig. 9.4. It shows the predicted trends in average daily gain from the fourparameter combinations A, B, C and D, together with the growth curve


Table 9.5. Estimates of the genetic parameters of the growth model corresponding to a PICSire Line obtained from four simulations.

Simulation results Parameter Pmat LPmat B* MEm0

Run A Phen. mean 56.53 0.89 0.029 637.9h2 0.46 0.47 0.21 0.03Phen. CV 0.03 0.09 0.09 0.03

Run B Phen. mean 50.55 0.78 0.029 505.7h2 0.42 0.51 0.31 0.12Phen. CV 0.07 0.11 0.09 0.08

Run C Phen. mean 38.29 0.68 0.034 650.0h2 0.37 0.58 0.26 0.07Phen. CV 0.03 0.06 0.07 0.03

Run D Phen. mean 37.04 0.65 0.035 652.6h2 0.37 0.52 0.39 0.11Phen. CV 0.05 0.12 0.10 0.07

derived from data of a genotype, bred from the same sireline as above butwith a different damline. Differences between the parameter sets A and Bversus the sets C and D (higher values for Pmat and LPmat) are clearlyreflected in the associated growth curves (upper versus lower curves in Fig.9.4). If genetic correlations together with heritabilities, and repeatedmeasurements from various growth stages, were simultaneously availablefor a genotype (which is not the case here), the most appropriateparameter combination could be chosen according to the model fit toempirically established growth curves. Alternatively, phenotypic growthtrends could be directly included in the optimization criteria usingdynamic control of the objective functions (as pioneered by Kinghorn et al.,2002).

Conclusion

Until now, mechanistic animal growth models have been primarilyrecognized as a valid method for predicting animal performance underconditions that are not covered by available data. The present studysuggests a novel use of such models for quantifying genotypes in a way thatcould be advantageous to animal breeding and management.

Appropriate quantification of the genotype-specific model parameters


AD

G (

kg/d

ay)

Empirical estimates

Model, parameter set A

Model, parameter set B

Model, parameter set C

Model, parameter set D

1.2

1.0

0.8

0.6

0.460

Body weight (kg)

80 100 120

Fig. 9.4. Average daily gain relative to body weight as predicted from empirical studies for acrossbred type and as predicted for the pure bred type by the growth model according to theparameter sets A to D specified in Table 9.5. The crossbred was produced from the samesireline as that used for model inversion, but from a different damline.

is crucial for accurate model predictions and thus for the appropriate useof growth models. Growth models also give a window on to underlyingphysiological traits that are intrinsic drivers of observed phenotype,whatever environment it is expressed in. Their approach can be used formaking genetic evaluation of animals for these underlying traits. Thereare prospects that this will give better gains – through an integration ofdifferent observed traits in a more intelligent manner than the linearstatistical approach that conventional selection index theory in animalbreeding involves, but also through a better choice of observed traits tomeasure (including choices of ages and diets), leading to a more accurateevaluation of both underlying physiological traits, and observed traits asexpressed in different environments, and thus of the genetic potential.

Combined with phenotypic performance data, which are relatively easyto measure, model inversion has been identified as a promising tool toderive the desired specification of the genotype intrinsic physiologicaltraits. The case studies presented here demonstrate that conclusiveestimates for the genotypic specifications are only possible if: (i) the growthmodel simulates the physiological mechanisms of pig growth sufficientlyaccurately that observed growth trends can be reproduced; and (ii) ifsufficient data expressing the genetic potential for growth and energyutilization are available.

Acknowledgements

The authors would like to thank Professor Colin T. Whittemore forinitiating the work on algebraic model inversion and for his useful remarksthroughout the development of this work. We are also thankful to AntheaSpringbett for sharing the concepts and results from the original researchproject on algebraic model inversion and for various inspiring discussions.Many thanks are also due to Dr Darren Green for his comments on anearlier version of this chapter and to Dr David Parsons for sharing hisexperience in constructing a framework for model optimization andcontrol.

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Knap, P.W. (2000b) Stochastic simulation of growth in pigs: relations between bodycomposition and maintenance requirements as mediated through proteinturnover and thermoregulation. Animal Science 71, 11–30.

Knap, P.W., Roehe, R., Kolstad, K., Pomar, C. and Luiting, P. (2003)Characterization of pig genotypes for growth modelling. Journal of AnimalScience 81 (E-suppl. 2), E187-E195. www.asas.org/symposia/03esupp2/jas2593.pdf.

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10 Considerations for RepresentingMicro-environmental Conditionsin Simulation Models for BroilerChickens

O.A. BLANCO AND R.M. GOUS

Animal and Poultry Science, School of Agricultural Sciences andAgribusiness, University of KwaZulu-Natal, Private Bag X01, Scottsville3209, South Africa. [email protected]

Introduction

The thermal relationship between a homeothermic animal and itssurrounding environment presents a challenging level of complexity foranyone attempting to analyse or model it. A conflicting issue, most of thetime overlooked, is the way in which the environment surrounding theanimal is described. The common approach is to account only for thevalues of air temperature (Tair) and relative humidity (RH), whichconstitutes an extremely naive procedure (Charles, 1994; Mitchell, 2005).

Considering that the values of the variables characterizing theenvironment surrounding the animal become meaningful only whenexpressed in the context of the animal (Monteith, 1974), we discourage theadoption of simplistic approaches. Furthermore, if the spatial and temporalvariations of the environmental conditions, as well as the variability of theirbiological implications, are considered it is evident that the way in which theenvironmental conditions are usually expressed should be revised.

There are three objectives to this chapter. First, we wish to review andclarify concepts related to the physiology of heat exchange in broilerchickens; secondly, we aim to give some guidelines for selecting ways inwhich the specification of the environment should be tackled; and finally,and most importantly, we wish to create an awareness of the negativeconsequences of using superficial and improper descriptions of theenvironment on predictions made by models dealing with the energybalance of chickens. In order to accomplish these objectives, this workanalyses the expression of environmental conditions considering thepeculiarities of heat dissipation in broiler chickens.


The Thermal Relationship between the Animal and itsSurroundings

Homeothermic animals are able to keep their body temperature fairlyconstant over a wide range of environmental conditions (Mount, 1979;Mitchell, 2005). Their success depends, on the one hand, on the demandof heat and water vapour that the surrounding environment inflicts on theanimal and, on the other, on the physical characteristics of the animal andits capacity to respond to such an exigency through thermoregulatorymechanisms (Mount, 1979; Mitchell, 2005).

The heat and water vapour dissipated during thermoregulation modifythe climatological conditions in the animal’s immediate environment. Thisbecomes particularly important in animals reared in confined conditions,such as poultry (Charles et al., 1994). Blanco et al. (2004a,b) proposed thatsuch changes in environmental conditions would induce new thermo-regulatory responses in the animal, producing further environmentalmodifications. Charles (1974) proposed a partition of the environmentcentred on the chicken, based on differentiation of the environmentalconditions and on the way in which each of these divisions affects theanimal.

The properties of the mass of air immediately surrounding an animalplay a decisive role in determining the magnitude of the net heatdissipation from that animal. Charles (1974) defined this fraction of theenvironment as the micro-environment. Due to the spatial variability of theenvironmental conditions inside a broiler house (Czaric and Tyson, 1990;Xin et al., 1994), micro-environmental conditions, i.e. the conditions atchicken height, need to be specified at the moment of analysing thethermal balance of the animal.

Charles (1974) referred to the outdoor part of the environment as themacro-environment. The properties of the macro-environmental variableswould influence those of the micro-environment depending on theinsulating properties of the building and its design (Xin et al., 1994).

Finally, the area of transition between the micro-environment and themacro-environment was termed the meso-environment (Charles, 1974).

The environmental conditions should be specified in theenvironmental context that best suit the purposes of the model.

Note: As a convention, the term micro-environment, which comprisesnot only micro-climatological conditions but also aspects such as airpollutants and presence of pathogens, has been used in this work as asynonym of micro-climate.

The Heat Balance of a Farm Animal

Homeothermic animals dissipate heat in the form of both sensible (H) andlatent (λE) heat (Mount, 1979). The heat flow density from the animal tothe environment (expressed normally in W m�2) depends on the structure

Micro-environmental Conditions in Simulation Models 189

and physiological state of the animal (body size, feather cover, respiratoryrate, etc.) and on the thermal gradient (in the case of H) or the vapourpressure gradient (∆eV) (in the case of λE) between the surface of theanimal and the surrounding environment (Mount, 1979). The level ofmicro-environmental radiation affects H, whilst air velocity (u) affects bothλE and H (Monteith and Unsworth, 1990) (see Fig. 10.1).

According to the peculiarities of heat exchange with its surroundings,a farm animal can be modelled as a system with two interfaces, i.e. the‘body surface’ (Ib) and the ‘surface of the anterior respiratory tract’ (Ir)

190 O.A. Blanco and R.M. Gous

Fig. 10.1. Partition of heat dissipated by a chicken. The circular detail shows thecomponents of the heat exchange between breathed air and mucous surface of the upperrespiratory tract, where the double-headed arrow indicates the movement of the circulatingair. λEf: dissipation of latent heat from feathered areas; Hf: dissipation of sensible heat fromfeathered areas; rHRf: thermal resistance of the boundary layer of feathered areas toconvective and radiant heat transfer; rvf: resistance of the boundary layer of feathered areasto water vapour transfer; λEa: dissipation of latent heat from bare appendages; Ha:dissipation of sensible heat from bare appendages; rHRa: thermal resistance of the boundarylayer of bare appendages to convective and radiant heat transfer; rva: resistance of theboundary layer of bare appendages to water vapour transfer; λEr: dissipation of latent heatfrom the surface of the anterior respiratory tract (interface Ir); Hr: dissipation of sensible heatfrom interface Ir; rHRr: thermal resistance of the boundary layer of interface Ir to latent andradiant heat transfer; rvr: resistance of the boundary layer of the interface Ir to water vapourtransfer; Rni: micro-environmental isothermal net radiation; u: micro-environmental airvelocity; C: thermogenic core; Sk: skin; F: feather coat; BL: Boundary-layer (note: due tospace restrictions, it was impossible to represent rva, rHRa, eVa and Ta on the wattles) (basedon Campbell and Norman, 1998 and Blanco et al., 2004a,b).

(Blanco, 2004a,b). A thin layer of air over the surface of each of theseinterfaces, called the boundary-layer (BL), imposes resistance to heat andwater vapour loss to the environment (Monteith and Unsworth, 1990) (Fig.10.1). The micro-environmental variables may impose dissimilar demandson each of the interfaces due to the different values of boundary-layerresistances (Bakken, 1981; Blanco et al., 2004a,b), the various processescontrolling the heat exchange at each interface, and the anatomical andphysiological differences between respiratory tract and body surface.

Sensible heat loss

A homeothermic animal uses three mechanisms for dissipating sensibleheat from its surface, i.e. conduction, convection and radiation.

Conductive heat exchange

Conduction depends on the thermal gradient between the animal and thesurface in contact with it, for example bedding material, as well as on thecoefficient of thermal conductivity of the mass in contact with the animal(Mount, 1979; Monteith and Unsworth, 1990). The amount of heatconducted to the surrounding air is minimal, but the magnitude of theheat transferred to some poorly insulated surfaces, such as floors andwalls, can be quite substantial (Monteith and Unsworth, 1990). The totalheat lost by conduction depends also on the size of the contact areabetween the animal and the contacting surface (Mount, 1968), which isdirectly related to the posture of the animal (Mount, 1968). Since thatposture is unpredictable (Turnpenny, 2000b), Blanco et al. (2004a,b)considered, in the first steps of the construction of their model foranalysing thermoregulatory responses of a broiler, that the animal standson its feet on a surface with very low thermal conductivity, therebyminimizing the heat loss by conduction and ignoring this means of heattransfer.

Convective heat exchange

Convective heat loss depends on the thermal difference between theanimal surface and the surrounding air (or circulating air in the particularcase of the respiratory tract) (Mount, 1979; Wathes and Clark, 1981a;Monteith and Unsworth, 1990; Campbell and Norman, 1998). It is theresult of the combined effect of natural convection, which depends on thebuoyant forces produced by the warming of the air in contact with theanimal surface, and forced convection, which occurs when an airstreamaffects any of the interfaces (Mount, 1979). The BL imposes a resistance toheat transfer by convection (rH) directly proportional to the diameter ofthe animal and inversely proportional to air speed (u) (McArthur, 1981;Monteith and Unsworth, 1990). Therefore, smaller animals, and animals


exposed to higher u, will dissipate more heat by convection per unit ofsurface area.

Radiant heat exchange

The dissipation of radiant heat from a confined animal depends on theemissivities of the surface of the animal and the internal surface of thebuilding, the surface areas of the animal and of the enclosure where theanimal is kept, and the thermal gradient between the surface of the animaland the surrounding environment (Cena, 1974; Wathes and Clark, 1981a;Mitchell, 1985; Campbell and Norman, 1998).

McArthur (1987), in a model of the thermal interaction betweenanimal and microclimate, utilized the parameter isothermal net radiation(Rni) to quantify the net radiant heat exchange between the animal and theenvironment. The parameter represents the net radiation that would beexchanged if the temperature of the animal’s surface were equal to the airtemperature. The mathematical expression for animals housed inbuildings where the solar radiation is negligible is presented in Eqn 10.1.

Rni = ρcp (τe – Ts) (rR)�1 (10.1)

where ρcp is the volumetric heat capacity of the air (kJ m�3 K�1), τe is themean radiative temperature of the environment (°C), Ts is the temperatureof the animal surface (°C), and rR is the thermal resistance of BL to radiantheat transfer (s m�1).

Monteith and Unsworth (1990) performed a more comprehensiveanalysis of this parameter, and the reader is referred to that work forfurther information.

Latent heat loss

Homeothermic animals dissipate latent heat from Ib and Ir (Mount, 1979;Monteith and Unsworth, 1990; Campbell and Norman, 1998; Willmer etal., 2000) (Fig. 10.1). The driving force is the gradient of vapour pressure(eV) between the exposed surface (eVb in the case of the body surface, andeVr in the case of the anterior respiratory tract) and the micro-environmental air (eVair) (Mount, 1979; Monteith and Unsworth, 1990;Campbell and Norman, 1998). (Note that, as will be explained later, thesurface of the animal has been divided into feathered areas and bareappendages, which is the reason why, in Fig. 10.1, eVb is represented byeVf and eVa, which accounts for vapour pressure of the surface offeathered areas and bare appendages, respectively.) The boundary layerscorresponding to the body surface and the surface of the anteriorrespiratory tract impose resistances to water evaporation, which aresymbolized as rvs and rvr, respectively (McArthur, 1981). (The expressionrvs includes the resistance to water vapour transfer from the surface of thebare appendages, or rva, and from the surface of the feathered areas, or


rvf.) The value of rvs (i.e. rva and rvf) is inversely related to u, whilst rvr isinversely proportional to the respiratory rate (RR) (McArthur, 1981;McArthur, 1987; Turnpenny et al., 2000a,b).

Peculiarities of Heat Dissipation in Poultry

Chickens have distinctive anatomical and physiological characteristicsrelated to additional thermoregulatory properties that transform theanalysis of the physiology of their heat exchange into an excitingchallenge.

In the first place, although latent heat loss from both Ir and Ib is asubstantial component of the heat balance of chickens in environmentswhere the sensible heat loss is not restricted (Bernstein, 1971; Marder andBen-Asher, 1983; Mitchell, 2005), chickens are not able to sweat whenexposed to conditions above least thermoregulatory effort (Mount, 1979;Willmer et al., 2000). In such environments, birds rely on active latent heatloss from Ir in order to control their body temperature (Mount, 1979;McArthur, 1981; Barnas and Rautenberg, 1987; Willmer et al., 2000).When the capacity to dissipate sensible heat is reduced, the respiratory rate(RR) increases secondary to an elevation of body temperature (Tb) (Zhouand Yamamoto, 1997). As a consequence, the properties of BL of Ir changeand, as a result, its resistance to water vapour transfer (rvr) is reduced(McArthur, 1981). Finally, the amount of latent heat dissipated from theinterface Ir increases.

A second distinctive feature of commercial chickens is the substantialfeather coat with high insulation properties that covers approximately0.80–0.85 of their body surface area (McArthur, 1981). This coat isresponsible for controlling the sensible heat dissipation from the featheredareas (Richards, 1970, 1974; McArthur, 1981; Wathes and Clark, 1981b).Since the high thermal resistance afforded by this coat cannot be widelyvaried, the bare appendages of the animal, i.e. legs, combs and wattles,play an important role in thermoregulation (Richards, 1974; Bakken,1981; McArthur, 1981; Willmer et al., 2000; Turnpenny et al., 2000a). Thedifferential redistribution of blood to these bare areas, secondary to theautonomic regulation of vasodilation and vasoconstriction in thesubcutaneous arterioles, helps the animal to manage its skin resistance (rs)in order to modify its total sensible heat loss (Mount, 1979; Bakken, 1981).The shape and size of the bare appendages (comparatively smaller thanthe body) result in a high surface:mass ratio, which facilitates the heatdissipation, as well as in a reduced resistance of their BL to convective andevaporative heat transfer (Bakken, 1981; Monteith and Unsworth, 1990).The combination of a lower rH, variable rs, high surface:mass ratio, anddirect exposure of the skin surface of the bare appendages plays animportant role in the determination of the total sensible heat dissipationfrom the animal.


Summary of the Facts to Consider when Modelling the Micro-environmental Conditions Surrounding a Chicken

In view of the concepts previously discussed, several considerations shouldbe made before deciding the way in which to specify the micro-environmental conditions in a simulation model for poultry.

First, in a model dealing with the heat balance of a chicken, theenvironmental variables air temperature (Tair), air speed (u), vapourpressure of the air (eVair) and isothermal net radiation (Rni) need to bespecified in the micro-environmental context.

Secondly, since each micro-environmental variable plays an importantrole in the dynamics of the dissipation of sensible and latent heat from theanimal, neglecting one or more of these variables may negatively affect thefinal estimation of heat production or loss when modelling the heatbalance of the animal.

The important role played by the thermal properties of the chicken, inparticular the thermal and vapour resistances of the BL, should also beconsidered. Monteith (1974) acknowledged that a satisfactory specificationof the environment would account for the close relationship between themicro-environment and the animal interface, whilst Mount (1979)recognized that the ratio of thermal gradient to thermal insulationdetermines the magnitude of sensible heat flow (H) from the body surface.

The role of respiratory thermoregulation in micro-environmentalsituations above least thermoregulatory effort should definitely beconsidered. The importance of evaporative heat loss on heat balanceunder non-stressing conditions should also be contemplated.

In chickens, it is also necessary to take into account the proportion ofthe total body surface represented by bare appendages. These structureshave a decisive influence on the value of the total thermal resistance,through modification of the thermal skin resistance and thecharacteristically reduced thermal resistance of their BL.

Finally, the differences between interfaces, mainly with respect to theproperties of their boundary layers, has been shown to be as important asthe environmental variables themselves (Monteith, 1974), and they shouldbe included in the specification of the environment.

Therefore, it is evident that it is not sufficient to account only for themicro-environmental variables. The following sections deal with issuessuch as what needs to be modelled when specifying the micro-environment, and the format that we consider appropriate in theconstruction of such models.

Modelling the Action of the Micro-environment

As stated above, thermal and vapour resistances of BL regulate heat andvapour dissipation from the surface of the interfaces Ir and Ib. Therefore,it is only by considering the value of the micro-environmental variables in


the context of BL that a proper description of the micro-environment canbe obtained (Monteith, 1974). In doing so, the specification of theenvironment becomes the description of the action of the micro-environment on the animal.

Furthermore, we believe it necessary to differentiate between the actionand the effect of the micro-environment on the animal. Whilst the actionrefers to the value of the micro-environmental variables considered in thecontext of the BL, the effect of the environmental conditions on heatbalance in the animal refers to the activation of thermoregulatorymechanisms and the changes in thermal and physiological parameters ofthe animal, secondary to the micro-environmental action. This is morethan semantic vagary; they are two dissimilar concepts, and they have to beproperly differentiated in order to clarify the aim of the modellingprocedure. Once the magnitude of the action is known, further modellingsteps can be formulated in order to estimate the effect on, for example, heatbalance and the energy requirements of the animal.

A diagram showing the factors considered at the moment of accountingfor the action of the micro-environmental conditions is presented inFig. 10.2.

Regarding the form in which the action of the micro-environmentshould be represented, the adoption of a parametric approach is highlyrecommended, as described below.

Selection of the Proper Parameter for Describing the Action ofthe Micro-environmental Variables on the Animal

There are a great variety of environmental parameters in the literaturedescribing the way in which the micro-environmental variables combineand affect the animal, each of which is suitable for a specific purpose.Therefore, the selection should be performed by means of a carefulanalysis. Even then, it is not guaranteed that the parameter that suits therequirements of the modeller will be found, and pertinent modificationsshould be performed.

Bearing in mind that animal characteristics are as important asenvironmental variables in determining the heat balance of a homeotherm(Monteith, 1974), a reasonable description of the environment shouldneglect neither of these two aspects.

Monteith (1974) and Mount (1979) proposed the following three maincharacteristics that a suitable parameter for specifying micro-environmental conditions should fulfil:

1. Applicability to all the species in any physiological state.2. Validity in both indoor and outdoor conditions.3. Independence from the characteristics of the exchanging interface (i.e.surface of feather cover in feathered regions, skin surface in the bare regions,and the surface of mucous membrane in the upper respiratory tract).


to which we have added three further requisites:

4. That it should account for all the micro-environmental variables.5. That it should consider that the interaction between animal andsurrounding environment is produced through the boundary layer. Thus avariable accounting for the properties of such boundary layer should beincluded in the parameter. 6. If possible, the parameter should account for the interaction of bothinterfaces into which the animal has been divided, i.e. Ir and Ib, and theirrespective micro-environments.

According to these criteria, an initial selection was performed among theparameters reported in the literature, considering those that have beendeveloped following proper scientific procedures. Such parameters wereanalysed and classified in two groups.

The first group recognized is the family of discomfort indices and is ofan empirical nature. These indices usually combine terms accounting for Tair


Fig. 10.2. Diagram showing the components of the action of the micro-environmentand the consequent micro-environmental effect or animal response. rHR: Thermal resistanceof the boundary layer to radiant and convective heat transfer; rv: resistance of the boundarylayer to water vapour transfer. Note that BL is clearly included in the environment.

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

and for the water vapour content of the air. Their empirical nature is theresult of the inclusion of multipliers experimentally derived. Considering theimportance of the physical and thermoregulatory characteristics of thebroiler on the thermal relationship between bird and environment, as well asthe variation of such properties according to factors such as maturity(Poczopko, 1981), breed (Özkan et al., 2002), and adaptation at genetic,phenotypic and epigenetic levels (Nichelman and Tzschentke, 2002), theusefulness of these parameters is very limited, unless new experimentalmultipliers are calculated for each new case. Therefore, these discomfortindices do not fulfil the first criterion of being a suitable parameter.

In addition, the inductive approach used in the construction of theparameters included in this first group neither allows for understanding theanimal–micro-environment interaction, nor for analysing the role of eachvariable as part of such a relationship. This is basically because they havebeen conceived for purposes other than the creation of models for theanalysis of the action and effect of micro-environmental conditions on theheat balance of a broiler. They were originally used for classifying animals asheat stressed and non-heat stressed, according to experimentally determinedcomfort ranges, constituting a safer way of controlling the environment anda moderately accurate way of predicting production results. We have notfound them useful for our model, but do not discard the possibility that suchparameters could be applied in models approaching the relationshipbetween animal and micro-environment from another viewpoint. Examplesof such parameters are the Discomfort Index (Tselepidaki et al., 1995), theThermal Hygrometric Index (Esmay, 1978; Tao and Xin, 2003) and theWind Chill Factor (Siple and Passel, cited by Starr, 1981).

A second group of parameters, which we term a family of equivalenttemperatures, has been identified. These parameters, derived followingthe criteria proposed by Monteith (1974) and Mount (1979), includeenvironmental apparent equivalent temperature (θ*e) (Mount, 1974),environmental temperature (Te) (McArthur, 1981), effective temperature(Tef) (Monteith and Unsworth, 1990), equivalent temperature (Monteithand Unsworth, 1990) and operative temperature (Campbell and Norman,1998). Such parameters are characterized by the deductive approach usedin their construction.

The equations for the parameters of the second group combine thevalue of two or more micro-environmental variables with the factorsaccounting for the physical properties of the animal. These parametershave two advantages over those from the former groups:

1. They have not been developed inductively; hence they do not have anempirical character. Therefore, the three first characteristics of an idealparameter are, at least, partially fulfilled.2. The inclusion of the thermal resistances of the boundary layer in someof these parameters results in a thermal equivalent of the strain imposedby the immediate surroundings on the bird, and accounts therefore for theaction of the environment on the animal.


According to Campbell and Norman (1998), these equivalent temperatures,on the one hand, allow for a better interpretation of the interaction betweenanimal and micro-environment due to their dimension of temperature and,on the other, they facilitate the application of experimental results obtainedin controlled conditions to real situations.

Effective Temperature (Tef) (Monteith and Unsworth, 1990)

Blanco et al. (2004a,b) found effective temperature (Tef) (Monteith andUnsworth, 1990) to be the most suitable parameter for specifying theaction of the micro-environment in meeting their objectives. This 1990version of environmental apparent equivalent temperature (θ*e)(Monteith, 1974) does not include water vapour pressure as a variable, andexpresses the parameter in the animal context by replacing the coefficientsof heat transfer with thermal resistances of BL, which, as expressed above,depends directly on the dimensions of the animals and on the value of thevariable u.

Effective temperature (Tef) follows the mathematical structure of theparameters of the second group, preserved since Monteith (1974), i.e. thecombination of Tair and an increment (expressed in units of temperature),which in this case accounts for the joint effect of u and Rni. The result is thetemperature value that should be reached in a non-radiant environment inorder for an animal to exchange the same amount of sensible heat (H) as itwould if it were situated in a radiant environment (both with identical u)(Monteith and Unsworth, 1990). This parameter includes the thermalresistance of BL to radiant and convective heat (rHR) as a factor. Equation10.2 is the mathematical expression for Tef according to Monteith andUnsworth (1990).

Tef = Tair + ζ = Tair + rHR (ρcp)–1 Rni (10.2)

where Tair is air temperature (°C), ζ is the radiation increment (°C), rHR isthe thermal resistance to radiant and convective heat transfer in theboundary layer (s m�1), ρcp is the volumetric heat capacity of the air (kJ m�3

K�1) and Rni is the isothermal net radiation affecting the animal (W m�2).The second term of the linear Equation 10.2, called radiation

increment (ζ) (Monteith and Unsworth, 1990), expresses, in units oftemperature, the combined action of the micro-environmental radiationair velocity in the context of BL. The factor rHR is the combined resistanceto radiant and convective heat flux imposed by BL. The resistance toradiant heat flux (rR) has a constant value of 2.1 s m�1 for animals with thecharacteristic dimension of a broiler (McArthur, 1981; Monteith andUnsworth, 1990). The resistance to convective heat transfer (rH), whichdiffers from rR, depends on both the dimension and shape of the animal’sbody and on the value of u (McArthur, 1987; Monteith and Unsworth,1990), as well as on the smoothness of the interface (Wathes and Clark,1981a; McArthur, 1987). According to Monteith and Unsworth (1990),


when u is such that the Reynolds number is higher than 103, rH isrepresented by Eqn 10.3.

rH = d (κ Nu)�1 ∝ d0.4 u–0.6 (10.3)

where rH is the thermal resistance of the boundary-layer to convective heattransfer (s m�1), d is the characteristic dimension of the animal (diameterin the broiler, for being considered as a sphere, in m), κ is the thermaldiffusivity of still air (m2 s�1) and Nu is the Nusselt number (non-dimensional value).

For a mature broiler chicken, with a body diameter of approximately0.25 m, rH and rR are of comparable magnitude at the low values of uusually found in a proper tunnel-ventilated broiler house (from 0.25 to3 m/s at chicken level) (Monteith and Unsworth, 1990). Considering that,in the boundary layer, these two resistances are working in parallel, thetotal thermal resistance to radiant and convective heat exchange, rHR, iscalculated, in analogy with Ohm’s law (Wathes and Clark, 1981a;McArthur, 1987; Monteith and Unsworth, 1990; Campbell and Norman,1998), according to Eqn 10.4.

rHR = (rR–1 + rH–1)–1 (10.4)

Equation 10.2 is represented in the diagram of temperature vs heat fluxdensity (Monteith and Unsworth, 1990) in Fig. 10.3 for given values of uand Rni. The slope is directly proportional to rHR. Tef is graphicallydetermined by the intersection between the line with intercept Tair andslope rHR (ρcp)–1, with the Rni flux density.

The impact of the variation in air velocity on the final value of Tef isrepresented in Fig. 10.4. The effect is produced through a modification ofrHR, which changes the slope of equation 10.2.

The variations of Tef secondary to the modifications of Rni for the sameTair and u are shown in Fig. 10.5. Higher values of Rni result in higher Tef,which has important consequences on the control of the macro-


�

Tem

pera

ture

(°C

)

Tef

Tair

⎧⎨⎩

RniHeat flux density (W m–2)

Fig. 10.3. Temperature vs heat flux density diagram for the graphical determination of Tef.Tair: air temperature, Tef: effective temperature, Rni: isothermal net radiation, ζ: Radiationincrement (after Monteith and Unsworth, 1990).


3

2

1

Tem

pera

ture

(°C

) Tef3

Tair

Rni

Heat flux density (W m–2)

Tef2

Tef1

Tef1<Tef2<Tef3

rHR1<rHR2<rHR3

u1>u2>u3

Fig. 10.4. Temperature vs heat flux density diagram for the graphical determination of Tef

considering three different u, with the same Tair and Rni. Tair: air temperature, Tef: effectivetemperature, Rni: Isothermal net radiation, u: air velocity, rHR: thermal resistance to radiantand convective heat transfer through the boundary layer (after Monteith and Unsworth,1990).

Tem

pera

ture

(°C

)

Tef(n-ins)

Tair

Rni(ins)

Heat flux density (W m–2)

Rni(n-ins)

Tef(ins)

Fig. 10.5. Comparison between Tef values reached in two comparable hypothetical houseswith and without insulated roofs in the same season, same air temperature (Tair) and sameair velocity. Rni(ins): isothermal net radiation loaded on chickens under insulated roof; Rni(n-ins):isothermal net radiation loaded on chickens under non-insulated roof; Tef(ins): effectivetemperature for chickens under insulated roof; Tef(n-ins): effective temperature for chickensunder non-insulated roof (after Monteith and Unsworth, 1990 and Blanco et al., 2003).

environmental conditions in a broiler house: for the same value of Tair andu, a broiler exposed to higher Rni, would experience higher Tef.

Limitations of Tef

1. Inability to account for the action of the micro-environmental vapour pressure

The most evident limitation of Tef (Monteith and Unsworth, 1990) is itsinability to account for the action of the micro-environmental vapourpressure. In order to include such a variable, Monteith and Unsworth(1990) returned to the concept of apparent equivalent temperature (Teq)introduced by Monteith (1974). As in the case of the equation developed in1974, this apparent equivalent temperature (here symbolized with Te*) isobtained after the addition of a humidity increment (ξ) to Tair, as shown inEqn 10.5.

Te* = Tair + ξ= Tair + e (Tair) (γ*)–1 (10.5)

where e(Tair) is the vapour pressure of the micro-environmental air (kPa) ata given Tair (°C), and γ* is the psychrometric constant in its apparent form(kPa K�1). The mathematical expression for the apparent psychometricconstant γ* is γ* = γ [ rv (rHR)�1], where γ is the psychrometric constant(=0.066 kPa K�1). The form γ* has the advantage of accounting for thethermal resistance for convective and radiant heat exchange through BL(rHR) and the resistance to water vapour transfer through BL (rv) in a sameterm.

Monteith and Unsworth (1990) obtained an environmental apparentequivalent temperature (Ter*), after combining Te* and a radiantincrement (ζ). The mathematical expression of Ter*, comparable to that forenvironmental apparent equivalent temperature (θ*e) reported byMonteith (1974), is presented here as Eqn 10.6.

Ter* = Te* + rHR (ρcp)–1 Rni = Tair + eVair rHR (rv γ*)�1 + rHR (ρcp)–1 Rni (10.6)

where Ter* is the environmental apparent equivalent temperature (°C).As in the case of θ*e (Monteith, 1974), in steady state conditions, Ter*

can be applied to both interfaces of the system, i.e. Ib and Ir. In theparticular case of Ir, it should be remembered that the value of theresistance to water vapour transfer through its boundary, rvr, depends onthe respiratory rate (RR). McArthur (1981) published an empiricalequation based on experimental data by Hutchinson (1954), reproducedhere as Eqn 10.7.

rvr = [(9.1 × 10�5 RR) + 9.0 × 10�3]–1 (10.7)

Problems appear when attempting to create a unique value of Ter* torepresent the conditions of both interfaces. Since these two interfaces act inparallel, and the conditions affecting each surface are substantially


different, it is almost impossible to find a valid common mathematicalexpression.

The task of finding a common Ter* becomes almost infeasible indynamic models such as that developed by Blanco et al. (2004a,b).According to equation 10.7, rvr depends directly on RR. The value of RR,as well as other physiological parameters, varies according to the bodytemperature (Tb) of the animal, which at the same time depends on themicro-environmental conditions as well as on the time the animal has beenexposed to that environment (Hutchinson, 1954; McArthur, 1987; Zhouand Yamamoto, 1996). Paradoxically, the micro-environmental conditionsaffecting RR are those to be included in Ter*. The derivation of aparameter to account for the action of the micro-environment on bothinterfaces proves to be a situation similar to the old riddle about theontogeny of hen and egg. It is impossible to define what the exact value ofRR, to be used to estimate hB, should be, mainly because it depends on thestill unknown action of the micro-environmental conditions and theirvariations in time, as well as on the consequent changes in Tb.

In models developed to simulate the time-variation of respiratoryparameters, equation 10.7 may be used in the process of modelling theheat dissipation from the interface Ir. But, again, because of the cause andeffect dilemma, the action of the micro-environment on the interface Iband the variable rvr cannot (and should not) be combined in the samegeneral parameter.

The use of Ter* should be limited to situations in which waterevaporation and sensible heat dissipation occur on the same surface. Infact, Monteith and Unsworth (1990) stated that the latent heat dissipatedfrom the respiratory interface should be measured or estimated separately.This is expressed in Eqn 10.8 where a value x, representing the latent heatdissipation from the anterior respiratory tract, is subtracted from the totalheat produced by the animal (M) before estimating the total heatdissipation from the interface Ib.

(1 – x) M = ρcp (Teo* – Ter*) (rHRb)–1 (10.8)

where x is the proportion of metabolic heat (M) that is dissipated as latentheat (both in W m�2), Teo* is the apparent equivalent temperature of theinterface Ib (°C), Ter* is the environmental apparent equivalenttemperature (°C), and rHRb is the thermal resistance to convective andradiant heat transfer through BL of interface Ib.

Campbell and Norman (1998), in the construction of the parameteroperative temperature, managed the latent heat loss in the same manner.In this case, the proportion of the metabolic heat dissipated as latent heatis assumed to be constant, formulating the equation for the animal’s heatbalance based on that proportion of the metabolic heat assumed to bedissipated by sensible means. This parameter has exactly the same form asTef (Monteith and Unsworth, 1990), but in this case the authors haveworked with thermal conductances instead of thermal resistances.

Neither of these approaches gives a solution to the main limitation of


Tef and, consequently, the creation of a parameter combining the action ofthe micro-environmental conditions on both interfaces remains infeasible.

2. Modifications of the total thermal resistance of the boundary layerintroduced by the bare appendages

According to the concepts already discussed in this chapter, the BL of thebare appendages, which has a surface area smaller than the featheredbody, would have a lower thermal resistance to convective and radiant heattransfer than the boundary layer of the feathered body (Bakken, 1981;Monteith and Unsworth, 1990).

Considering that the radiation increment of Tef depends on thethermal resistance of the boundary layer, Eqn 10.2 should be revised.Blanco et al. (2004a,b) expressed rHR as a serial sum of the individualthermal resistances of the feathered body and bare appendages. Eachresistance was multiplied by a factor proportional to the area of total bodysurface area represented by feathers and appendages. Equation 10.9 showsthe modified form of Eqn 10.2.

Tef = Tair + ζ = Tair + (0.85 rHRf–1 + 0.15 rHRa–1)�1 (ρcp)–1 Rni (10.9)

where rHRf and rHRa are the thermal resistances to convective and radiantheat transfer of the boundary-layer of the feathered body and bareappendages, respectively. The numbers 0.85 and 0.15 represent theproportion of the total surface area corresponding to feathered body andbare appendages, respectively. It should be noted that since rHRb and rHRaare working in parallel, they have been added according to Eqn 10.4.

This approach seems to be sensible. The estimations performed byBlanco (2004b) using equation 10.8 have been shown to be reasonablyrealistic.

3. The problem of accounting for the micro-environmental effect without ajoint parameter expressing the micro-environmental action on interfaces Irand Ib

In the development of their simulation model for estimating the effect ofmicro-environmental conditions above least thermoregulatory effort onbroiler chickens, Blanco et al. (2004b) have used the parameter Tef toaccount for the action of the micro-environment.

As previously mentioned, Tef cannot be used for both interfaces of thesystem, i.e. Ir and Ib, in the same equation. Blanco et al. (2004b) haveovercome this limitation by using Tef to account for the action of micro-environment on Ib, considering Ir as a mere ‘regulating device’.Depending on the effect of the micro-environmental conditions on thephysiological parameters (mainly Tb and RR) through the action on Ib, Irdissipates the excessive heat that cannot be lost by sensible means from Ib.


This dynamic model estimates the action of the micro-environmentalvariables on Ib and their effect on the heat balance of a single broiler in 1-scycles. As a first step, the model estimates the experimental Tef(represented as Tef*). After calculating the amount of sensible heatdissipated from Ib for that Tef* (H(Tef*)), the heat excess (HE) is calculatedby subtracting H(Tef*) from the sensible heat hypothetically lost from Ib atleast thermoregulatory effort (H(TNT)). If HE is higher than the capacity ofthe respiratory tract for dissipating latent heat (λEr), which depends on theRR, the model calculates the heat excess and re-estimates Tb, RR and rvr.These outputs are used in the following cycle of simulations. Fig. 10.6synthesizes in a flux diagram the main steps of this model.

Taking this approach, a parameter for estimating the action of themicro-environmental conditions on interface Ir is not necessary. Instead,when considering the evaporation from interface Ir as a process secondaryto the variation of Tb, the modeller would only need to know the values ofeVair and RR.


Boundarylayer

Micro-environmental

variables

Reestimation

of rvr

Tb RR

Informationused in the

next cycle ofestimations

OUTPUTTbRR

Recalculationof RR

Recalculationof Tb

Estimationof S

(S=H-λEr)

Estimation oflatent heat

dissipation fromrespiratoryinterface

(λEr)

Estimationof HE

Estimationof H frominterface

‘bodysurface’

1 s cycle

Estimationof TNT

Tef

Model of a thermoregulating broiler

Fig. 10.6. Diagram of a simulation model for estimating the effect of micro-environmentalconditions on the heat balance of a broiler, including an alternative approach for estimatingthe latent heat dissipation from the respiratory tract. The estimations are performed onceevery second, as indicated by the circular arrow; Tef: Effective temperature estimated for aparticular broiler under given environmental conditions; TNT: particular value of Tef at whichthe animal is under least thermoregulatory effort; H: sensible heat loss; HE: Heat excess; λEr:latent heat loss from the respiratory tract; S: heat storage; Tb: body temperature; RR:Respiratory rate; rvr: resistance of the boundary-layer of interface Ir to water vapour transfer.

Conclusions

The authors of this chapter consider that the way in which micro-environmental conditions are usually accounted for in simulation modelsneeds to be revised.

In the first place, and bearing in mind the differentiation of theenvironment directly surrounding the animals, micro-environmentalconditions should always be considered in models strongly influenced bythe heat exchange between animal and environment as, for example, thosedealing with heat balance and energy utilization.

Secondly, considering the importance of each of the micro-environmental variables on the heat exchange between animal andenvironment, models should at least consider Tair, eVair, u and Rni in orderto produce balanced estimations.

A third point to take into account: since the BL of the animal plays afundamental role in the relationship with its surroundings, itscharacteristics should be considered when accounting for theenvironmental conditions. The description of the micro-environmentalconditions in the context of the BL allows for the estimation of what wehave termed micro-environmental action. This can be a starting point forfurther modelling procedures in order to estimate the consequent effect ofthose micro-environmental conditions on the heat balance of the chicken.

Regarding mathematical expressions that account for the micro-environmental action, two groups of parameters have been identified inthe literature. Among the parameters belonging to the group of equivalenttemperatures, effective temperature (Tef) (Monteith and Unsworth, 1990)best suited the needs of the authors of this chapter. Although most of theparameters of this group adequately account for the micro-environmentalaction by considering the properties of the boundary layer, they need to beadapted to the following peculiarities of the thermoregulatory processes ofnon-sweating animals such as poultry:

1. Water vapour dissipation is important from both the body surface andthe upper respiratory surface.2. Both body surface and mucous membranes of the upper respiratory tractare separate interfaces of a system tract (Ib and Ir, respectively).3. Because different factors control heat and vapour exchange, the action ofthe environment on those two interfaces cannot be included in the sameparameter.4. As RR is directly related to the value of Tb, which is a product of theaction of the environmental conditions to be specified by the parameter,the formulation of a parameter accounting for the action of the micro-environment in both interfaces is infeasible.

An alternative approach in dynamic models would be to estimate the latentheat loss from the respiratory tract as a consequence of the effect of themicro-environmental conditions on the sensible heat dissipation. By doingso, the introduction of a respiratory component on a parameter accounting


for the action of the micro-environment would not be necessary, since thelatent heat loss from the respiratory tract could be estimated byconsidering the value of the resulting respiratory rate and the gradient ofvapour pressure between the circulating air and the surface of the anteriorrespiratory tract.

Finally, we strongly believe that encouraging the interaction betweenanimal scientists and environmental physiologists would be a fruitfulmeans of improving the way in which the environmental conditions arespecified in models dealing with the energy balance of poultry.

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11 Using Physiological Models toDefine Environmental ControlStrategies

M.A. MITCHELL

Roslin Institute, Roslin, Midlothian, EH25 9PS, [email protected]

Introduction

Biologists develop and use mathematical models to understand observedphenomena more fully, to characterize mechanisms and to predict thebehaviour of systems under a range of conditions or in the face of changinginputs. Models may be derived from theory or empirical data or both, butultimately should be applicable to ‘real world’ situations and systems.Models may be generally classified according to their theoretical origins, thenature of the input-output variables and probability components and theirdescriptive or predictive functions. Thus models describing a process orresponse may be regarded as analytical, numerical or observational.Analytical models are based upon fundamental equations, with someapproximations, to provide an explicit closed form solution. Numericalmodels are derived from first principles and may be detailed and complexwhilst observational models are inferred from measured data (Gershenfeld,1999). Such approaches may require the application of establishedmathematical techniques including linear and quadratic programming andordinary and partial differential equations or more novel methodologiessuch as neural networks. Other model descriptions, frequently encounteredin biology and agriculture, include the terms static and dynamic. Staticmodels have the mathematical form that relates a dependent to anindependent variable each taking different numerical values. Dynamicmodels incorporate an element of time and frequently describe a timecourse of events or responses. Dynamic models are commonly representedin their differential form, i.e. by one or more first order differentialequations (France and Thornley, 1984). Finally models may be stochastic(probabilistic), being based upon random trials, or deterministic, whererandom phenomena are excluded. The selection of appropriate models isbased upon a range of criteria including goodness of fit, freedom from


systematic errors and simplicity. A given model is usually fitted and theoptimal parameters determined by minimization of an objective function,usually the sum of squared errors (Garfinkel and Fegley, 1984).

Models of all types are commonly applied in animal biology andagriculture and are employed to describe a wide range of processesincluding growth and the influence thereon of genetics, nutrition andhusbandry (Wellock et al., 2003a, 2004a); reproductive performance; theeffects of environmental and other stressors upon animal production andwell-being (Wellock et al., 2003b, 2004b); behavioural and physiologicalneeds; factors influencing animal health; toxicity and environmentalhazard and management and risk extrapolation. The outputs of suchmodels may provide the basis for the setting of standards, optimumpractices and nutritional strategies, operational control systems andpractical guidelines and legislation. In the current review attention isfocused particularly upon the thermal environments to which livestock areexposed and the modelling of animal responses in the context ofenvironmental specification and control.

Animals and the Thermal Environment

A major factor influencing both the efficiency of production of animals andtheir welfare is the thermal environment. Problems may be encountered inboth extensive outdoor systems and in more intensive artificial or‘controlled’ environments. An important objective of modern sustainableproduction systems should be the matching of environmental conditions tothe biological needs or requirements of the animals (Wathes, 1994;Mitchell and Kettlewell, 2004a). Such an approach should minimize thestress to which livestock are exposed and reduce the physiologicalhomeostatic demands that are imposed. It is clear that modelling ofanimals’ responses to the thermal environment, and the concomitantdevelopment of models describing the thermal environment and itscomponents, will facilitate the design of effective control systems basedupon definition of acceptable ranges and limits for thermal loads andoptimum thermal micro-environments.

Livestock housing offers an opportunity to control the internalenvironment and to maximize productivity if optimum conditions can beachieved. Intensive systems, however, have attendant problems associatedwith the precise specification of those conditions, animal welfare standardsand the impact upon the external environment. Even in ostensibly‘environmentally controlled buildings’ animals may be subject to adversethermal loads during demanding meteorological conditions (Seedorf et al.,1998). It is proposed that future design and management of livestockenvironments should involve fully integrated systems and that these shouldincorporate elements of the animals’ responses to rate limiting environmentalcomponents in addition to other production and environmental concerns(Frost et al., 1997, 2003; Wathes et al., 2001). Even in the specific case of the

210 M.A. Mitchell

thermal micro-environment the responses of housed livestock are complexand dynamic. Animals housed under intensive conditions may havelimitations imposed upon the behavioural responses that individual free orwild animals might exploit in the face of environmental challenge. Also,genetic selection for desirable production traits may result in alteredhomeostatic capabilities or in more extreme cases pathologies that limitadaptive responses. Specification of practical environmental conditions andcontrol criteria should be cognizant of these issues in addition to utilizingmodels of the animals’ physiological and behavioural reactions andrequirements. The development of truly integrated control systemsincorporating comprehensive simulation models of all the inputs in aproduction system is dependent upon characterization and mechanisticmodelling of each of the sub-processes that must be combined to representthe larger more complex system. The thermal micro-environment is one suchsub-process. It in turn consists of interactive components each of which mayexert either a direct influence upon the animal or a summative effect inconjunction with other variables. Each sub-process analysis should also beregarded in a more holistic context since biological responses to thermalinputs may be markedly affected by non-thermal environmental variables.

The Thermal Micro-environment and Ventilation

In intensive system livestock buildings ventilation is the primary controllerof thermal conditions, although the major source of heat and moisture maybe the animals. The ventilation system must regulate the air temperatureand moisture content, provide air mixing and appropriate velocities of airmovement at animal level and remove air-borne contaminants. The controlstrategy may be based upon simple measures such as air temperature withcorrectly sited sensors or may involve simultaneous measurement of severalenvironmental inputs and processing through predetermined set pointsand models based upon environmental, production or biologicalrequirements. Future control system algorithms may incorporateinformation relating to physiological characteristics of the animals as well ascontrol variables such as heat, moisture and carbon dioxide balance (Allisonet al., 1991; Frost et al., 1997; Pedersen et al., 1998; Aerts et al., 2003). Theapplication of fuzzy logic based control systems (Gates et al., 2001) andComputational Fluid Dynamics (CFD) should facilitate ever greatersophistication and accuracy of ventilation of livestock housing provided theappropriate optimum set points and acceptable ranges of theenvironmental variables have been clearly defined.

Defining the Optimal Thermal Conditions

Several approaches have been adopted to determine the required thermalconditions in livestock houses that are consistent with optimal productivity,

Using Physiological Models to Define Environmental Control 211

health and welfare. Clearly the heat exchange between an animal and itsimmediate environment and the thermoregulatory responses to theimposed conditions are the major consideration when determiningoptimum temperature and humidity ranges in addition to predictions ofeffects upon production parameters. Thus, in cattle, dynamic models ofresponses to thermal loads have been developed based upon fractalanalysis of tympanic temperature responses that allow identification of theenvironmental temperature at which heat stress is apparent (Hahn, 1999).The fractal dimensions for body temperature may be employed tocategorize thermal stress (environmental temperature) from slight throughmoderate to severe. Measurements of respiration rate changes were usedto further refine this ‘stress’ model. Dynamic responses provide the basisfor evaluating stress thresholds and differentiation of stress levels in cattleand therefore can be used as criteria for environmental management(Korthals et al., 1997; Hahn, 1999). In pigs, stochastic models have beendeveloped and evaluated that predict the effects of the thermalenvironment upon food intake, daily weight gain, food conversionefficiency and metabolic heat production (Wellock et al., 2003a). The modelindicated that within the apparent zone of thermal comfort there are notemperature effects upon the production variables. A heat balance modelof the pig proposed by Fiahlo et al. (2004) and derived from first principlesof heat and mass transfer, simulates heat loss, heat balance and deep bodytemperature responses in animals exposed to different thermalenvironments. It is suggested that this model might be integrated into amore comprehensive physiological model of the pig for precise definitionof optimum production environments and limits for imposed thermalloads. Important advances in understanding the relationships betweenanimals and their thermal environments can be made through entirelytheoretical models of heat exchange which cannot always be evaluated bycomparison with experimental or empirical data. An idiosyncratic,although useful, example has been presented by Phillips and Heath (2001)in which the heat loss from ‘Dumbo’ (© Walt Disney Company) has beenmodelled. Using fundamental principles, these authors have demonstratedthat Dumbo may often be at risk of losing more heat than he can produceat rest and therefore will be at risk of hypothermia. The large pinnae areaassociated with this character may have evolved to favour heat loss duringthe hypermetabolism of flying!

Mathematical models describing both evaporative and non-evaporativeheat losses from livestock in relation to the thermal environment have beendeveloped (e.g. Ehrlemark, 1993). Such models provide valuable predictivedata based on the thermal properties of the animals but without referenceto the internal mechanisms of the thermoregulatory systems. The modeloutputs can underpin determination of the thermoneutral zone and uppercritical temperature and ultimately may be employed as the basis for controlsystems or algorithms. Thermal balance models for livestock, includingcattle and sheep (outdoors) and pigs and chickens (indoors), have also beendescribed by Turnpenny et al. (2000a,b). These mathematical models,

212 M.A. Mitchell

examining the effects of temperature, vapour pressure, wind speed andsolar radiation, were also derived from heat transfer principles andincorporated physiological and thermoregulatory responses to thermalchallenge. The outputs of the models were successfully validated bysimulating the experimental thermal conditions, for each species, used byprevious workers. Whilst the models may be improved by incorporation ofdata from more modern commercial strains of livestock, valuable outputsare the prediction of thermal comfort zones for each species and thesensitivity of heat exchange to individual environmental components suchas humidity that may be important in commercial production conditions.From these models the prediction of upper and lower critical temperatures,evaporation thresholds and thermoneutral zones facilitates the definition ofoptimum ‘in house’ thermal micro-environments.

Stress and the Thermal Environment

It is apparent that the imposition of thermal challenges upon an animalconstitutes a stress. It may be argued that minimizing stress by controllingthe thermal micro-environment to within the thermoneutral zone thephysiological needs of the animal will be met and both productivity andwelfare will in turn be optimized. Thermal stress is often defined by someindex incorporating two or more of the primary components of the thermalenvironment, e.g. temperature, water vapour pressure, radiant temperatureand air velocity (Budd, 2001). It may be suggested that thermal stress, ormore correctly strain, should be quantified by means of animal responses,particularly those associated with physiological stress mediators and thehomeostatic systems directly influenced by the stress stimulus (Von Borell,2001). Integration of physiological stress indices with concurrent behaviouralobservations will allow identification of thermal conditions that imposeminimum threat to homeostasis and least risk of undue stress and thus, bydefinition, the optimum thermal environment. Stress assessment willtherefore identify combinations of temperature, humidity, air movement andradiant exchange that produce discomfort or distress and, as a corollary,those combinations constituting thermal ‘comfort’.

Thermal Comfort

The term ‘thermal comfort’ has evolved in the discipline of human thermalphysiology. The ‘Zone of Thermal Comfort’ in man is defined as

the range of ambient temperatures, associated with specified mean radianttemperature, humidity and air movement within which a human in specifiedclothing expresses indifference to the thermal environment for an indefiniteperiod.

(Commission for Thermal Physiology of the International Union ofPhysiological Sciences, 2003)


Models of thermal comfort have been developed based upon humanheat and mass balance and physiological responses to the thermalenvironment. These models range from simple one-dimensional steadystate simulations to complex, transient, finite element codes withthousands of nodes (Jones, 2002; Tanabe et al., 2002; Zhang et al., 2004;Kaynakli and Kilic, 2005). The limitations of these models lie in theaccuracy of the inputs and the difficulty in relating the comfort perceptionsto the physiological variables simulated in the thermal models. Calibrationof models in terms of the perceived comfort is often performed in humansby means of the Predicted Mean Vote (PMV), as proposed by Fanger(1970, 1973) and Kjerulfjensen et al. (1975). PMV is a simple numeric scale(�3 to +3) used to designate perceived thermal comfort from cold to cool,slightly cool, neutral, slightly warm, warm to hot. PMV is often related tothe Predicted Percentage Dissatisfied (PPD). For a numerical deviation inPMV of ±1.5 approximately 50% of individuals are dissatisfied. Attemptshave been made to develop sensors or physical models which can integratethe effects of temperature, humidity and air movement to yield ‘standardeffective temperatures’ or ‘equivalent temperatures’ and through this topredict PMV (Ye et al., 2003; Mendes and da Silva, 2004). Clearly suchsystems can form the basis of environmental control. A recent study hasemployed thermodynamic analysis of human heat and mass transfer usinga two-node thermal model to identify the combinations of thermalvariables at which energy consumption for physiological and metabolicfunctions is minimal (Prek, 2005). It was demonstrated that expectedthermal sensation expressed as PMV exhibited a strong correlation withenergy consumption. In man it is thus possible to base environmentalspecifications both upon physiological or metabolic response models andupon human perceptions of thermal comfort. It has been shown, using astatic linear model, that thermal comfort in humans is heavily determinedby skin temperature whilst physiological adaptive responses aredetermined by changes in core temperature (Bulcao et al., 2000). Suchstudies and all other human models using subjective correlates ofenvironmental and physiological variables can provide a mechanisticunderstanding of thermoregulatory responses and definition of ‘thermalcomfort zones’.

In livestock, however, it is not possible to directly ask the animals for asubjective assessment of thermal comfort and thus to determine PMV orPPD. Other approaches are possible that can indirectly determine comfort.Behavioural methods, including passive avoidance and continuous choice,have been applied to assess aversion to multiple concurrent stressors inpoultry (Abeyesinghe et al., 2001a,b; MacCaluim et al., 2003). The stressorsincluded thermal variables. This approach might form the basis of abehavioural model yielding preferred temperature-humidity combinationsand those producing mild to severe aversion and thus constitutingunacceptable thermal loads in commercial practice.

At present, models utilizing energy balance, thermal exchange andphysiological and stress responses are more likely to be employed to assess

214 M.A. Mitchell

thermal comfort in livestock and to form the basis of environmentalcontrol systems. The comprehensive models described by McArthur (1987,1991) and Turnpenny et al. (2000a,b) may facilitate determination ofthermoneutral zones and upper and lower critical temperatures and thusthermal conditions in which heat or cold stress may occur. Randall (1993)used models of heat, moisture and carbon dioxide production of pigs,cattle and sheep to recommend appropriate thermal envelopes to ensure‘comfort’ during transportation of the animals. The study demonstratedthe profound effects of humidity upon thermal comfort, particularly athigher dry bulb temperatures, and stressed the importance of control ofthe thermal environment by appropriate ventilation strategies. Otherstudies examining the thermal environment during transport haveemployed physical models to assess thermal comfort (Webster et al., 1993;Weeks et al., 1997). A model chicken was constructed to simulate heatexchanges between poultry and the transport environment. Measurementsof sensible heat loss from the model at different temperatures werecompared with published estimates of thermoneutral heat production toestimate the range of thermal stresses experienced by chickens in transit. Itwas concluded that thermal conditions ensuring comfort rarely occurredin commercial transport. This model was also used to compare thermalcomfort upon different vehicle types and the efficacy of ventilationregimes.

Indices of Thermal Loads

It is abundantly clear that the heat and mass exchange between an animaland its immediate environment is dependent not only upon the dry bulbtemperature but upon the water vapour pressure or density, air movementand radiant temperature. Whilst it is possible to model the effects of eachvariable upon animal performance, physiological and metabolic responsesand thermal comfort, it is often desirable to develop a single integratedindex of imposed thermal load that will allow prediction of the biologicalresponse. Various indices have been proposed for man and other animalswith a particular focus upon the prediction of the risk of heat stress or coldstress. The situation may be summarized thus:

Ta is only one of several physical factors determining heat exchange with theenvironment which occurs via ‘dry’ (conduction, radiant, convection) and ‘wet’(evaporation) mechanisms. In addition to depending upon Ta each mechanismalso depends upon one or more of the following physical factors, humidity, airvelocity, barometric pressure, contact with housing structures and material e.g.bedding/litter and effective radiant field.

(Romanovsky et al., 2002)

The age, physiological status, acclimation state, diet and food intake andbehavioural freedom of the animals will all contribute to the integratedheat exchange of the animals and thus to any assessment of desirablethermoneutral conditions.


It may be concluded that a more integrated and biologicallymeaningful index of the thermal environment is essential to defineoptimum thermal conditions or thermal comfort zones. Simple measuresof Ta as dry bulb temperature must no longer be considered adequate.There have been many attempts to incorporate the various factors intomore comprehensive indices of environmental thermal load and theconsequent effects upon thermal balance of the animal. Theoretical modelshave been developed which allow prediction of thermal balance and bodytemperature in livestock (including poultry) over a wide range of practicalthermal environments into which the influence of humidity and airmovement can be incorporated (Turnpenny et al., 2000a,b; Fialho et al.,2004). Temperature-humidity indices have been proposed as the maindescriptor of factors influencing heat exchange (e.g. Hubbard et al., 1999).The Wet Bulb Globe Thermometer (WBGT) has been employed for asimilar purpose (Schroter et al., 1996), although alternative measures tothe WBGT integrating humidity and temperature effects have beenproposed more recently, such as the environmental stress index or ESI(Moran et al., 2001, 2003). An effective temperature index for poultry wasproposed by Tzschentke and Nichelmann (2000) that incorporated theeffects of only temperature and air speed. Effective temperature wasoriginally designed for use in man and was intended to identifycombinations of temperature, humidity and air movement that producedthe same ‘sensation of cold or warmth’. This strategy may be very useful inanimals if physiological measures and behavioural assessments are used todetermine the biological equivalence of different permutations of therelevant thermal factors (vide infra). The importance of this moreintegrated environmental description has been emphasized in recentindustry and practical publications (e.g. Garden, 2004; Hulzebosch, 2004).Indeed, a practical effective temperature scale for broiler productionenvironments has been produced by Barnwell (1997). This study tabulatestemperature, humidity and air speed and on the basis of thermalequivalence indicates the necessary air velocities required to produce theoptimum conditions (an effective temperature of 21°C). It is tempting tosuggest that similar studies could accurately define the biologicallyoptimum conditions in terms of these environmental variables and thusprovide insight into the effective temperature equivalents of the truethermo-neutral zone (TNZ). Another approach has been the developmentof ‘standard operative temperatures’ integrating several environmentalvariables including temperature, humidity, air movement and solarradiation. The values represent an index of potential heat flow between ananimal and its environment (Beaver et al., 1996) and require accuratemeasurement of all the relevant parameters in the productionenvironment. Physical models have been employed to derive standardoperative temperatures (e.g. O’Connor, 2000; Bartelt and Peterson, 2005)and the application and performance of such models has been reviewedrecently (Dzialowski, 2005). Devices have been developed for fieldmeasurement of standard operative temperature for selected avian species

216 M.A. Mitchell

(Bakken et al., 2001) and the principles involved in the design ofenvironmental control systems. Tao and Xin (2003) have proposed atemperature-humidity-velocity index as a basis for management decisionsand control strategies in commercial broiler chicken production.

Physiological Response Modelling: Transport ThermalEnvironments

A specific animal production thermal environment that has presentedmany challenges to the industry and researchers alike is that encounteredduring transportation of livestock. It has been stated that in order todefine comfort zones for animals in transit all the relevant thermal factorsmust be taken into account (Randall, 1993).

In order to address these issues, physiological response modellingmust first involve full characterization of the commercial transportenvironment and identify the stressors most likely to compromise thewelfare of the transported animals. Laboratory based studies then producequantitative, predictive response models over ranges of magnitude ofindividual stressors such as thermal loads. The selection of an appropriatespectrum of physiological variables, which reflect disturbances in all themajor homeostatic systems, is crucial. Measurements must indicate notonly the adequacy of homeostatic responses but the homeostatic effortrequired for maintenance of controlled variables. Homeostatic responsesmay be categorized as adequate compensation, inadequate compensationor decompensation approximately corresponding to mild, moderate andsevere physiological stress. Thus models may contain assessments ofcardiovascular, respiratory, thermoregulatory and metabolic function inaddition to indices of hydration, electrolyte and acid-base or blood gasstatus and the degree of any tissue dysfunction or pathology. Both pointmeasurements and continuous monitoring of physiological variablesshould be employed. Radio-telemetric systems have been developed forthe continuous remote monitoring of physiological variables for use inboth laboratory and commercial transport studies (Kettlewell et al., 1997;Mitchell et al., 2001a). Point measures and continuous remote monitoringhave been applied to studies in poultry, pigs and calves and the findingsused as the basis of recommendations for ‘thermal comfort zones’ and‘thermal limits’ for animals in transit.

In the case of poultry, birds are transported from hatchery to farm, forrelocation and to slaughter (Mitchell and Kettlewell, 2004a,b). Duringthese journeys the birds may be exposed to hostile thermal micro-environments resulting in mortalities, pathology, production losses andreduced welfare (Mitchell and Kettlewell, 2003). Research in this arearequired the development of an index of thermal load upon broilers intransit that integrated the two most essential variables of this uniqueenvironment, namely temperature and humidity. This index could then beemployed to establish the biological equivalence of different temperature-


humidity combinations through physiological modelling (Mitchell andKettlewell, 1998). In these studies models incorporating the use ofApparent Equivalent Temperature (AET) have been employed to definethe ‘thermal comfort zones’ for birds under commercial conditions. Clearlythermal environments which cause deep body temperature to approachthe upper or lower lethal limits will increase mortality and must beregarded as totally unacceptable. Other thermal loads, however, will resultin the bird exhibiting a range of thermoregulatory responses aimed atminimizing the change in deep body temperature. The adequacy of theseresponses may be judged by measurement of deep body temperature andthe thermoregulatory effort involved can be assessed from physiologicalmonitoring of panting rate in the heat, shivering rate in the cold, changesin metabolic rate and disturbances in blood gases and acid-base balance.The physiological stress response model may thus be based upon therelationships between these responses and a single integrated index of thethermal load imposed upon the birds. The hypothetical relationshipbetween a given physiological variable, thermal load and the severity ofstress is shown in Fig. 11.1.

Studies were undertaken to determine the stress imposed uponbroilers by different thermal loads and to define thermal comfort zones forbirds in transit. Broiler birds were held in commercial transport crates andplaced in controlled climate chambers for a period of 3 h (typical ofcommercial journeys). Various combinations of temperature and humiditywere employed in the range 10–35°C and 30–95% RH. Thermoregulatorysuccess (deep body temperature) and thermoregulatory effort (blood pHand gas disturbances) were correlated with the actual imposed thermalload (temperature-humidity combination).

AET was used as an index of thermal load. This parameter is derivedfrom the temperature, water vapour pressure and the corrected

218 M.A. Mitchell

Integrated Index of thermal load

Mild

Moderate

SeverePhy

siol

ogic

al s

tres

s

Fig. 11.1. Physiological stress response vs integrated thermal load.

psychrometric constant (Eqn 11.2) and describes the total heat exchangebetween a wetted surface and the environment (Eqn 11.1).

θ*app. = T + ( e/γ* ) (11.1)

where θ*app = AETT = absolute temperature (K)e = water vapour pressure (mbar)γ* = corrected psychrometric constant (mbar/K)

γ* = γ (rv/rh) (11.2)

where rv = the resistance to water vapour transfer (s/m) rh= the resistance to heat transfer (s/m).

AET may be calculated from the dry bulb temperature and the relativehumidity (RH) alone (Eqn 11.3).

(11.3)

where

T = Observed temperature (°C)K = T corrected to Kelvin (°C + 273.16)Φ = Observed relative humidity (RH/100).

The derivation and application of AET is perhaps best describedgraphically (Fig. 11.2). If a sample of air at 18°C (t) and 10 mbar vapourpressure (e) is represented by point X then the line YXZ with a slope of -γyields the wet bulb temperature Y (12°C) and the equivalent temperature Z(33.3°C). The line QX gives the dew point temperature (7.1°C) and the lineXP gives the saturation vapour pressure (20.6 mbar). If water vapour wascondensed adiabatically from a sample of saturated air (point Y) then thetemperature and water vapour pressure changes are described by the lineYX. When all the water vapour has condensed (e = 0) then t = Z(Equivalent Temperature). In the calculation of AET the correctedpsychrometric constant replaces γ as described above.

Using the AET approach, the combinations of temperatures andhumidities that produce equivalent biological effects were determined. Therelationship between change in deep body temperature and AET ispresented in Fig. 11.3. It is clear that the response to thermal load issimilar to the hypothetical curve presented in Fig. 11.1 and as such allowsdefinition of temperature-humidity combinations imposing mild, moderateand severe physiological stress. Similar response patterns were observedfor changes in blood pH and pCO2 which are used to assess homeostatic orthermoregulatory effort.

Physiological stress response modelling, exploiting the concept of AET,has thus allowed identification of ‘safe’, ‘alert’ and ‘danger’ combinations oftemperature and humidity which equate to mild, moderate and severe

AET TK

Log K K K

= + ⋅⋅ +( )

− ⋅ −( )10

0 93 0 0006363601 0 472

30 5905 8 2 0 0024804 3142 3110. . . .

. . .

( )+ /Φ


Q

Y

P

X

M Z0

10

20

30

10 20 30

Slope–γ

0

Temperature (°C)

Vap

our

pres

sure

(m

bar)

Fig. 11.2. The curve PQ gives saturation vapour pressure as a function of ambienttemperature. Point X represents a sample of air at 18°C and 10 mbar vapour pressure. Theslope of the line YZ, passing through X, corresponds to the psychometric constant. Othersymbols are explained in the text.

220 M.A. Mitchell

0

1

2

3

0 20 40 60 80 100

AET (°C)

Cha

nge

in b

ody

tem

pera

ture

(°C

)

Fig. 11.3. Relationship between change in deep body temperature and AET.

physiological stress. The model thus permits the definition of thermalcomfort zones for broilers in transit as presented in Fig. 11.4. Attemperature-humidity combinations yielding AET values of 40°C or less,thermal stress will be minimal in transit. At temperature-humiditycombinations giving AETs between 40 and 45°C moderate thermal stresswill occur with some degree of hyperthermia and acid-base disturbances.At AETs of 65°C or greater physiological stress may be deemed severe and

mortalities will increase. Such thermal loads must be consideredunacceptable.

In a parallel series of experiments the effects of low environmentaltemperatures accompanied by wetting and air movement were examined.The experimental protocol was as for heat stress but the temperature rangeemployed was �4°C to +12°C with a constant air speed (supplied from alaminar flow cabinet) of 0.7 m/s. For each temperature employed, birdswere either exposed to dry conditions or were intermittently wetted byspraying for 1 min every 30 min. The experimental conditions were basedupon characterization of the environments on typical commercial broilertransporters in the UK. Measurements of deep body temperature weremade before and after exposure to each temperature-air speed-wettingcombination. In addition some birds were surgically implanted with deepbody temperature data loggers to allow continuous recording of thisvariable. The degree of physiological stress imposed was assessed by theextent of the reduction in body temperature in each set of conditions.

In the cold stress studies, surface wetting (at constant air speed of 0.7m/s) had a profound effect upon thermoregulatory success with anincreasing degree of hypothermia across the whole range of chambertemperatures employed. At 12°C the fall in rectal temperature in wettedbirds was 3.03 ± 1.75°C, an additional decrease of 2.1°C compared to thecorresponding ‘dry’ group. In wetted birds the relationship between thechange in rectal temperature (Tr) and Te could be described by:

y = (3)(1013)(e–0.1065K) (11.4)wherey = change in Tr, °CK = Te corrected to Kelvin.


0

20

40

60

80

100

10 15 20 25 30 35 40

Dry bulb temperature (°C)

Rel

ativ

e hu

mid

ity (

%)

SAFE

ALERT

DANGER

Fig. 11.4. ‘Thermal Comfort Zones’ for broiler transport. Safe limit AET = 40°C; danger limitAET = 65°C or greater.

Marked hypothermia was therefore induced at all other chambertemperatures and ranged from a reduction of 4.4 ± 3.2°C at Te = 8°C to amaximum and life threatening fall of 14.2 ± 5.4°C when Te = �4°C. Aslethal deep body temperature in the fowl is 24°C then from the derivedrelationship between environmental temperature and the change in coretemperature (Fig. 11.5) it is apparent that a lethal hypothermia will occurin all wetted birds when Te = �9.5°C and marked elevations of mortalitieswill be observed if Te falls to only +1.0°C. The findings from this modeldefine the lower limits for temperature exposure in transported broilers inwet and in dry conditions (Hunter et al., 1997; Mitchell et al., 1997, 2000,2001a). Improved ventilation strategies based upon the outputs of thismodel can reduce the risk of cold stress and all the sequelae in terms ofanimal welfare, product quality and animal mortality.

Conclusions

In summary, physiological modelling evaluates both homeostatic successand homeostatic effort and through the determination of biologicalequivalence of thermal loads consisting of different combinations oftemperature and humidity or other environmental parameters can definethermal comfort zones. AET has been used already in a technical manual(Ross Tech 99/34, 1999) as a guide to the temperature profiles for broilerrearing taking into account the important interactions of temperature andhumidity in determining heat exchange. Incorporation of air movementinto a similar model of broiler house environments (see Tao and Xin, 2003;Yahav et al., 2004) should provide the sound scientific basis for setting in-house thermal conditions to optimize not only productivity but also bird

222 M.A. Mitchell

Environmental temperature (K)

265 270 275 280 285 2900

10

15

5

Cha

nge

in b

ody

tem

pera

ture

(°C

)

Fig. 11.5. Relationship between change in deep body temperature in wetted birds andenvironmental temperature (K).

comfort and welfare. Physiological models may be complemented bybehavioural studies in which birds’ preferences for temperature-humiditycombinations may be assessed by established choice techniques(Abeyesinghe et al., 2001a,b; MacCaluim et al., 2003). Bird monitoring andaccurate measures of bird responses to well defined thermal loads will playan increasing role in the development of advanced automatedenvironmental control and management systems (Frost et al., 1997; Naas,2002; Aerts et al., 2003; Taylor et al., 2004).

The novel experimental modelling approaches described herein haveprovided data which are specific to transportation conditions and directlyapplicable to commercial practice. Using physiological response modelling(Mitchell et al., 1996, 2001b; Mitchell and Kettlewell 1998, 2004a,b) theoptimum thermal envelope for broiler carriage has been defined in termsof the ‘physiological thermal comfort zones’ and factors precipitating orcontributing to the incidence of thermal stress have been identified. Theoutputs of the models have been employed as the basis for environmentalcontrol strategies on animal transport vehicles using mechanical ventilationsystems with the controlled capacity to remove the imposed heat andmoisture loads thus matching the ‘on-board’ thermal environments to thephysiological requirements of the ‘passengers’ (Kettlewell and Mitchell,2001a,b; Kettlewell et al., 2001a,b; Mitchell and Kettlewell, 2004a,b,c). Itmay thus be proposed that this very successful physiological modellingapproach may be applied to other areas of animal production in order todefine the optimum thermal conditions in terms of biological response andrequirements and to underpin the development of integrated monitoringand control systems for livestock environments.

Acknowledgements

The work described in this review was supported by DEFRA. The author isgreatly indebted to Peter Kettlewell and Richard Hunter for their effortsand inputs in all of the research projects in this area and to all the staffinvolved at the Roslin and Silsoe Research Institutes for their technicalassistance, which ensured the successful completion of the modellingresearch programme.

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228 M.A. Mitchell

12 Modelling Egg Production inLaying Hens

S.A. JOHNSTON AND R.M. GOUS

Animal and Poultry Science, School of Agricultural Sciences and Agribusiness,University of KwaZulu-Natal, Private Bag X01, Scottsville 3209, South [email protected]

Introduction

The processes of ovulation and oviposition in domestic hens have been thesubjects of much interest and of numerous investigations by poultryscientists over the past century. The associated temporal relationshipsmake an intriguing study, both for the modeller aiming to predict rate oflay and for the physiologist attempting to integrate the hormonal andneurological pathways. Although tremendous progress has been made inrecent years in understanding the hormonal control, mainly due to theadvent of radioimmunoassay techniques, some aspects of the hen’sreproductive system continue to elude scientific explanation.

Domestic hens lay their eggs in sequences; a sequence being made upof a number of consecutive daily ovipositions followed by one or morepause days, when no egg is laid. The first egg of a sequence is usually laidearly in the morning, roughly 8 h after the onset of darkness. Eachsubsequent oviposition occurs progressively later in the day, at intervalsslightly longer than 24 h, on successive days. The difference in times of dayat which eggs are laid on consecutive days is known as the lag, as is thecorresponding delay in the ovulation cycle (Fraps, 1955). Total lag is ameasure of the proportion of the day used for egg laying and can beregarded as an indication of the length of the open period for luteinizinghormone (LH) release and hence ovulation (Lillpers and Wilhelmson,1993). The reason why hens lay eggs in sequences is that the ovulatorycycle is due to the interaction of two asynchronous physiological systems(Etches, 1984; Johnson, 1984). These are the maturation of the largestovarian follicle and a circadian rhythm that restricts the preovulatory surgeof LH to a limited portion of the day. Ovulation occurs when thematuration of a follicle coincides with a certain phase of the circadianrhythm.


Much controversy surrounds the issue of whether circadian rhythmsare indeed involved in timing the preovulatory surge of LH, sinceconclusive evidence is still lacking in poultry. Such evidence would lendweight to the mathematical theory of the ovulatory cycle proposed byEtches and Schoch (1984). In their model, the concentration of theregulator substance is assumed to have a circadian rhythm, beingreinitiated at the same time daily. Birds are known to have a circadianrhythm in photosensitivity that is involved in their reproductive responsesto light (Siopes and Wilson, 1980). This may be partially attributed tomelatonin, the pineal hormone thought to link the reproductive system tothe light:dark cycle, because it has a circadian rhythm of release thatentrains to the light:dark cycle (Menaker et al., 1981). However, efforts torelate the pineal gland to photoperiodic control of LH have failed thus far(Liou et al., 1987). In the meantime, it is convenient to assume that therestriction of LH release to a limited period of the day is brought about bya hormone or neurotransmitter that has a circadian rhythm of secretion oractivity.

A number of publications have shown that either a single or twomathematical functions may be used to describe the egg production curve(Johnston, 1993). The Adams-Bell model, for example, uses a logisticgrowth curve to describe the initial rise to peak and a negative linearfunction to mimic the decline in egg production post peak (Adams andBell, 1980). These empirical models show no awareness of the underlyingreasons for the shape of the curve, nor do they take into account the factthat rate of egg production for the flock is derived from individualperformances.

Rate of lay is determined by the ovulation rate, which varies amongstindividuals and over time. The ovulation rate, in turn, is established by aninteraction between the rate of follicle maturation and the rhythmic releaseof LH. It therefore makes sense that a model designed to predict the eggproduction of a flock of hens should start by predicting the ovulation ratefor each hen. There are two main benefits to this approach. First, the largenumber of variables that play a role in egg production are accounted for inthe model. In this manner the process of egg production is acknowledgedas being an extremely complex one. Secondly, the variation betweenindividuals within a population is brought to light. Most poultry producersrecord performance indicators in terms of means (e.g. mean egg weight,rate of lay, egg output and feed intake) without having the vaguest idea ofthe extent of the variation within the flock. The peril is that unsatisfactoryperformances from some individuals may be masked by the populationmeans, with the result that overall flock performance efficiency is reduced.In a stochastic model, each variable has an associated standard deviation orcoefficient of variation. These are either measured during experimentationor derived from published scientific papers, failing which educated guessesneed to be made by the modeller.

The development of a mechanistic model of this nature thereforerequires a thorough understanding of the system to be modelled, which in

230 S.A. Johnston and R.M. Gous

turn entails a comprehensive review of the available literature. During thisprocedure, several unknown quantities usually become evident. These mayrelate to the response of a selected strain to environmental stimuli (e.g.how the age at first egg for the strain is affected by different lightingprogrammes), or to the values of constants (e.g. the constants defining therelationship between yolk weight and albumen weight) and of the variablesrequired by the model (such as the prevalence of double-yolked or soft-shelled eggs during the course of the laying cycle). The modeller is thuslikely to challenge current knowledge and to direct further researchtowards providing precise answers to relevant questions.

The Ovulatory Cycle

A mathematical model of the hen’s ovulatory cycle

Based on the work of Fraps (1955), a mathematical model of the ovulatorycycle was presented by Etches and Schoch (1984), to provide support forthe theory of two independent biological systems interacting to producethe observed pattern of sequential laying in commercial hens. The modelwas able to predict times of ovulation close to actual times of ovipositionrecorded under experimental conditions for different sequence lengths, onthe assumption that the ovulatory and ovipository cycles were displaced bythe oviducal term. Furthermore, the accepted features of lag weredemonstrated by the mathematical model. The calculated lag betweenpredicted ovulation times decreased initially between successive ovulations,was minimal for mid-sequence ovulations and increased towards the end ofa sequence, so that the greatest lag was between the penultimate and lastovulations. The predicted total lag given by their model for the differentsequence lengths fell within the prescribed 8- to 10-h open period. Totallag was also positively related to sequence length, with a two-ovulationsequence having a relatively short total lag of 4 h 32 min and a nine-ovulation sequence, 8 h 7 min. Mean lag was negatively related to thesequence length, so that longer sequences had comparatively shorterintervals between successive ovulations (Fig. 12.1).

A three-compartmental model was used to describe how theproduction of a hypothetical regulator substance could restrict the releaseof LH to a limited period of the day. The regulator is assumed to beproduced in compartment one and instantaneously released intocompartment two at regular intervals determined by a circadian oscillator.The regulator is then released into compartment three at a given rate andcleared from this compartment at a different rate. The concentration ofthe substance (Fraps’ threshold of response of the neural component) incompartment three at time t depends on the rates at which it is enteringand leaving the compartment and is given by:

R3(t) = a1 •e ��1 (t-S1) – a2 •e ��2 (t-S1) (12.1)

Modelling Egg Production in Laying Hens 231

where a1 is a constant and S1 is the time of day when the cycle is completedand the regulator function is reinitiated. The events leading up toovulation take place some hours beforehand, but the inclusion of theparameter S1 shifts the curve so that R3(t) exceeds a threshold value fromabout 07:00 to early afternoon, not during the night. Thus the curve givenby Eqn 12.1 also represents the period of the day during which ovulationmay take place. The values of the parameters �1, �2 and S1 and of theconstant a1 used to predict ovulation sequences of varying lengths aregiven in Table 12.1.

The value of a2 depends on the values allocated to parameters �1 and�2 and may be calculated from the function

a2 = (a1�(a1.e (�λ1 . 24) )) / (1�e (�λ2 . 24)) (12.2)

when the light:dark cycle is of 24 h duration.The second equation in the ovulation model of Etches and Schoch

(1984) represents the maturation of the largest ovarian follicle (Fraps’excitation hormone concentration) and takes the form of a Gompertzfunction:

G(t) = b1.e�b2 e�b3 (t�S2) (12.3)

where S2 represents the time taken after the previous ovulation toreinitiate G(t). This interval is necessary because the follicle is not sensitiveto gonadotrophic stimulation for a number of hours after the previousovulation. The values for the parameters b1, b2, b3 and S2 to predictsequences of different lengths are shown in Table 12.1.

Follicle maturation refers to the competence of the follicle to ovulate inresponse to an LH surge, rather than to an increase in weight or diameterof the follicle. This phase is brought about by a number of physiological


Fig. 12.1. The observed (shaded columns) and predicted (blank columns) mean lag for eightsequence lengths (data from Etches and Schoch, 1984).


Table 12.1. The values of the parameters and constants used by Etches and Schoch (1984),University of Guelph data, to predict the times of ovulation and oviposition.

Seq. length a1 �1 �2 S1 b1 b2 b3 S2

2 2.175 0.14 0.25 8.0 0.75 4.5 0.22 17.03 2.175 0.14 0.25 7.5 0.75 5.1 0.27 17.04 2.175 0.14 0.25 6.75 0.75 5.2 0.30 17.05 2.175 0.15 0.285 6.5 0.75 5.15 0.315 17.56 2.175 0.15 0.285 6.5 0.76 5.05 0.32 17.57 2.175 0.15 0.285 6.5 0.78 5.2 0.325 17.58 2.175 0.15 0.285 6.5 0.78 5.15 0.33 17.59 2.175 0.15 0.285 6.5 0.785 5.17 0.334 17.5

processes. For instance, the granulosa cells in hierarchical folliclesdifferentiate so that they are capable of secreting progesterone (Johnson,1996), the hormone needed to initiate and maintain the ovulation-inducing surge of LH. Prior to ovulating, the F1 follicle changes from anFSH- to a LH-dominated phase (Tilly et al., 1991). It is of interest to notethat the rate of maturation of follicles is affected by advancing hen age,since Johnson et al. (1986) found that the sensitivity of the follicle to LHand hence its ability to ovulate, declines with age.

At the time of day when the two functions intersect, ovulation takesplace. This is based on the hypothesis that a sufficient concentration of theregulator coincides with a sufficient concentration of receptor to induceovulation (Etches and Schoch, 1984). The intersection is brought about byusing a mirror image of the curve produced by Eqn 12.1, so that themoment of ovulation occurs when G(t) � (1 � R3(t)) = 0. The greater theconcentration of regulator and the more advanced the stage of folliclematuration, the greater is the likelihood of intersection of the two curves.The earlier in the day each consecutive ovulation occurs, the shorter thelag and hence the longer the sequence is likely to be (Johnston and Gous,2003).

A graphical representation of an ovulation sequence may be achievedby plotting the two functions given by Eqns 12.1 (in the form 1 � R3(t))and 12.2 on the same axes, with time of day along the x-axis. Where thetwo curves intersect, ovulation takes place. Fig. 12.2 shows the series ofevents over a 6-day period for a three-ovulation sequence.

On day 2 the predicted ovulation time is 08:31. On days 3 and 4ovulations occur at 11:30 and 15:22, respectively, resulting in corre-sponding lag values of 2 h 59 min and 3 h 52 min. The two functions donot meet on day 5; hence there is no ovulation, resulting in a pause day.Day 6 sees the start of a new sequence, with an ovulation taking place at08:31. The total lag for the three-ovulation sequence is thus 6h 51 min andthe mean lag is 3 h 25 min.

Credit is therefore due to Etches and Schoch (1984) for successfullyachieving their objective, which was to show mathematically why hens laytheir eggs in sequences. Indirect support is given to the theory of a

circadian rhythm restricting the release of LH to a portion of the day,although the hypothesis still needs to be confirmed.

Although this model satisfactorily accounts for the pattern ofsequential laying, it does have limitations, because the table of values usedfor the parameters in the model restricts the simulated sequences to two tonine ovulations. Most individuals in a population of hens produceconsiderably longer egg sequences around peak rate of lay. If the ovulatorymodel is to be used to predict flock egg production, it needs to be able toreproduce these longer sequences. The way to do this is to replace thetable of values with a set of continuous functions; one function for each ofthe seven parameters in the ovulatory model. In addition, a method ofintroducing inter-sequence pauses longer than 1 day needs to be found,because experimental observations on individually-caged birds indicatethat a number of hens do pause for several days at a time (Johnston, 2004).

An enhanced version of the ovulatory model

The first step in amending the model is to convert sequence length to acontinuous variable, namely ovulation rate. For example, a sequence oftwo ovulations followed by a single pause day gives an ovulation rate of0.667 (two divided by three) and a nine-ovulation sequence, 0.90 (nineovulations in 10 days). A long sequence of 119 eggs in 120 days isequivalent to an ovulation rate of 0.992. A relationship may now beestablished between the ovulatory cycle parameters and ovulation rate.


Fig. 12.2. An illustration of the asynchronous cycle of ovulation for a three-egg sequence;ovulation occurs when the regulator concentration 1�R3(t) (solid line) intersects with folliclematuration G(t) (dotted line).

The ovulatory cycle parameters are able to change predicted ovulationrate by changing the lag between successive ovulations. As the ovulationrate approaches 1.0 (for very long sequences), increasingly smaller changesto the values of the parameters are required to cause increasingly smallerdecreases in lag values. If, as is seen in Fig. 12.1, mean lag decreases at adiminishing rate as the sequence length or ovulation rate increases, theparameters themselves presumably need to show a diminishing rate ofchange with increasing rate of ovulation. This trend is evident in the valuesfor b3 (the rate parameter in the Gompertz equation representing folliclematuration) given in Table 12.1. Three of the other parameters, i.e. λ1, λ2and S2, were each allocated two values by Etches and Schoch (1984). Itseems reasonable that these and the remaining three parameters (S1, b1and b2) should also alter gradually to bring about steady changes insequence length or ovulation rate. A Gompertz function of the form

y = A + C . exp (�exp (�B . (x�M))) (12.4)

fulfils the requirements. It has two asymptotes, so that as the ovulation rateapproaches zero the parameter values remain positive and as the ovulationrate approaches 1.0, the parameter values continue to increase but at adiminishing rate. The procedure used to solve simultaneous equations forthe seven ovulatory cycle parameters is discussed by Johnston and Gous(2003). The values allocated to the parameters A, C, B and M from Eqn12.4 are listed in Table 12.2.

Figure 12.3 illustrates the values for the rate parameter b3 given byEtches and Schoch (1984) and the fitted Gompertz function that may beused to predict the value of b3 required for any ovulation rate from 0.5 (aone-ovulation sequence) to 1.0. Fig. 12.4 shows that, although acontinuous function is now used to predict �2 rather than the two valueslisted in Table 12.1, the range in the values for two- to nine-ovulationsequences remains the same as used by Etches and Schoch (1984).

The set of continuous functions, representing the changes required tothe values of the different parameters, makes the prediction of anysequence length or ovulation rate possible.


Table 12.2. Values assigned to the Gompertz function parameters for each of the sevenovulatory cycle parameters.

Parameter B M C A

λ1 8 0.66667 0.020456 0.132475λ2 8 0.66667 0.071596 0.223662S1 8 0.66667 �3.068414 9.128776b1 8 0.66667 0.071596 0.723662b2 6.148166 0.708292 21.097792 0.760415b3 8 0.66667 0.233199 0.134213S2 8 0.66667 �3.596213 17.080953


Fig. 12.3. The curvilinear relationship between b3 and ovulation rate, showing the fittedGompertz function (—) and the given parameter values (�).

Fig. 12.4. The values for λ2 given by Etches and Schoch (1984) () and the Gompertzfunction for predicting λ2 from ovulation rate (—).

A Mechanistic, Stochastic Population Model

Age at first egg

The starting point for any layer model aiming to predict flock eggproduction is to estimate the mean age at first egg. This is because a hen’schronological age determines her ovulation rate and yolk weight, as well asthe incidence of internal ovulations, soft shells and double-yolked eggs.Sequence length and rate of lay are therefore also influenced by the meanage at sexual maturity. Although other factors do play a role, light is the

single most important factor determining the age at sexual maturity inpullets (Lewis et al., 1997). The Bristol-Reading model (Lewis et al., 2002)predicts the mean age at first egg of a flock of pullets, based on the genotypeand the lighting programme applied during rearing. The function

SD = �8.76 + 0.124 . mean AFE (12.5)

estimates the associated standard deviation and predicts that delayedphotostimulation causes an increase in the standard deviation about themean. The model also calculates the proportion of the flock capable ofresponding to photostimulation and, depending on the age at photo-stimulation, produces either a normal or a bimodal distribution of ages atfirst egg.

The distributions of ages at first egg for three theoretical Hy-LineBrown flocks, photostimulated at either 12, 15 or 18 weeks of age, areillustrated in Fig. 12.5. The mean ages at first egg (± SD) as predicted bythe Bristol-Reading model are 117.0 (± 5.75), 129.4 (± 7.29) and 142.04days (± 8.85), respectively.

Internal cycle length

A hen has an internal cycle length, which is expressed as the intervalbetween successive ovulations. For example, if an ovulation occurs on day1 at 08:00 and on day 2 at 10:00, then the internal cycle length is 26 h.


Fig. 12.5. Theoretical distributions of ages at first egg for Hy-Line Brown pulletsphotostimulated at 12 weeks (hatched columns), 15 weeks (blank columns) and 18 weeks(solid columns).

This interval is determined by the synchrony between the follicularhierarchy and the circadian rhythm of LH release. A hen that has aproperly maintained hierarchy containing sufficient follicles, capable ofmaturing at the rate of one every 24 h, will have an internal cycle of 24 hand will lay an egg every day. With advancing age the follicles take longerto mature, with the result that the internal cycle length increases. Theremay also be age-related changes to the circadian clock system (Turek et al.,1995). Emmans and Fisher (1986) proposed that the change in a hen’sinternal cycle length (ICL) over time may be calculated from the following:

ICL = ICLo – Lag + 1/((1/Lag) – kt) (12.6)

where ICLo = initial internal cycle length, k = a decay factor and t = timefrom first egg, in days. If the internal cycle length is less than or equal tothe 24 h daylength or external cycle length (EXCL), rate of ovulation orrate of lay (R) is given by:

R = 24/EXCL (12.7)

If the internal cycle length is greater than the external cycle length:

R = Lag/((ICL – EXCL) (1+ (Lag/(ICL-EXCL)))) (12.8)

These functions allow a decrease in egg production with advancing henage, but they do not permit the simulation of the shorter egg sequencesproduced by many hens at onset of lay. It is evident from trials thatinvolve recording time of lay that these short egg sequences are not alldue to internal ovulations (Lewis and Perry, 1991; Johnston, 2004). Itwould appear that there may be insufficient FSH at sexual maturity tomaximize follicle growth and to promote recruitment into the hierarchy(Zakaria, 1999). In order to reproduce these short sequences, the internalcycle length initially needs to be longer than 24 h, before decreasing withadvancing time from first egg to close to or below the daylength andsubsequently increasing. Quadratic-by-linear equations of the form:

ICL = A + B/(1 + D. x) + C . x (12.9)

where x = time from first egg (in days), give the required curvilinear shape. The theoretical relationship between internal cycle length and time

from first egg for two individuals is illustrated in Fig. 12.6. The predictedrates of lay for the same two hens are illustrated in Fig. 12.7. Because theinitial internal cycle lengths are longer than 24 h, both of these birds willlay a few short egg sequences before producing their prime sequences.

Quadratic-by-linear functions therefore have the advantage over thefunction given by Emmans and Fisher (1986) (Eqn 12.6), in terms of beingable to produce short ovulation sequences at onset of lay. Table 12.3 listspossible values of the parameters that may be substituted in Eqn 12.9, topredict changes in internal cycle length over time for Hy-Line Silver andHy-Line Brown birds. These values have been found to produceacceptable rates of lay and sequence lengths for the two strains (Johnston,2004).



Fig. 12.6. Curvilinear relationships between ICL and time from first egg for two hens.

Fig. 12.7. The rates of lay for two hens, using the internal cycle lengths shown in Fig. 12.6.

Table 12.3. Parameter values for the quadratic-by-linearfunctions to predict ICL for Hy-Line Silver and Hy-LineBrown hens.

Variable Hy-Line Silver Hy-Line Brown

A 22.4416 22.5416B 2.0469 2.0469D 0.02279 0.02279C 0.011 0.011418

In order to introduce variation in the rate of change in internal cyclelength within a population, a coefficient of variation of 1% may be used togenerate normal distributions for each of the four parameters. The rates oflay of individual hens will then differ; a small proportion of the flock willlay exceptionally long sequences and a proportion will produce shortsequences, even at peak egg production.

Linking ovulation time to sunset

The ovulatory cycle parameter S1 (from Eqn 12.1) determines the timewhen the circadian rhythm for the regulator concentration function isreinitiated. Because of the phase-setting effect of sunset, S1 needs to belinked to the time that the lights are turned off in the poultry house, sothat predicted ovulation and oviposition times are relative to the onset ofdarkness. The predicted mean time of lay on 15- to 16-h photoperiods isabout 13–14 h after sunset, as reported by Lillpers (1991) and Patterson(1997), although as the duration of the scotoperiod increases, the intervalbetween dusk and the mean oviposition time increases (Etches, 1996).

The open period for LH release is thought to commence about 2-hafter sunset and to last for about 8–9 h (Williams and Sharp, 1978). Thepreovulatory surge of LH can take place at any time during the openperiod. Between 4 and 6 h after the LH peak, ovulation occurs. There is acorresponding open period of about 8–9 h during which ovulation cantake place. Presumably the earliest ovulations at the start of a sequencetake place about 6–8 h after the onset of darkness. In a population modeleach hen may be allocated a unique value for the sunset-ovulation intervalby creating a normal distribution, using a mean of 7 h and a coefficient ofvariation of 5%. Suggested temporal relationships between the onset ofdarkness, LH release and ovulation are shown in Fig. 12.8.

The method used to link S1 to the onset of darkness is explained indetail by Johnston (2004). Briefly, the ovulatory cycle parameter S1 is itself


18:00 24:00 6:00 12:0021:00

Lights off

9:00

Open period for LH release

3:00

Time of day

Open period for ovulation

Fig. 12.8. An illustration of the temporal relationships between lights off (21:00), the start ofthe open period for LH release (23:00) and the start of the open period for ovulation (04:00).

described by four parameters A, C, B and M. Instead of using the value forA given in Table 12.2 (i.e. 9.128776), the formula

A = lights off + sunset-ovulation interval – daylength + 3 (12.10)

where daylength = 24 h, is applied. If, for example, the lights are turnedoff at 21:30 (i.e. 21.5 h) and the sunset-ovulation interval for a given hen is7.25 h (7 h 15 min), then A = 21.5 + 7.25 – 24 + 3 = 7.75. Thismodification still allows the value of S1 to change with rate of ovulation, sothat longer sequences are linked to an earlier initiation of the circadianrhythm, but the circadian rhythm itself will now phase-shift in accordancewith the time the lights are turned off.

Predicting the ovulation rate

An ovulation needs to occur the day before the hen lays its first egg. Atsexual maturity the time from first egg is zero, and this determines thebird’s initial internal cycle length (Eqn 12.9), which in turn determines theovulation rate (using Eqns 12.7 and 12.8). A normal distribution of lagvalues with, for example, a mean of 8.5 h and a coefficient of variation of2%, introduces further variation. The ovulation rate establishes the time ofeach consecutive ovulation by using the appropriate values for the sevenovulatory cycle parameters. In a flock of hens, the mean ovulation rate atonset of lay will be determined by the distribution of ages at first egg andalso by the initial sequence lengths, or individual ovulation rates. Thepredicted flock ovulation rate over a laying cycle for a hypothetical flock ofbirds is illustrated in Fig. 12.9. In this example the ovulation rate reaches apeak 9 weeks after the onset of lay.


Fig. 12.9. The predicted ovulation rate for a theoretical flock of 100 Hy-Line Silver hens.

In theory, the ovulation rate and the rate of lay are identical unless internalovulations occur, or the production of double-yolked or soft-shelled eggscauses interruptions to egg sequences. Johnston (2004) found that 8% ofdouble yolks and 18% of soft shells were associated with pauses in eggsequences, and these percentages increased with earlier photostimulation.

Predicting time of lay

The time that an egg is laid is determined by the time of the associatedovulation (Gilbert and Wood-Gush, 1971), which means that, except forthe terminal egg of a sequence, the ovulation times may be used toestimate oviposition times. Oviposition normally occurs about half an hourbefore the next ovulation, with a range of 7–75 min (Warren and Scott,1935; Fraps, 1955). A normal distribution of oviposition-ovulation intervalsmay be produced using a mean of 30 min and a coefficient of variation of30%, so that the range of intervals is from 3 to 57 min. In a population,each hen may therefore be allocated a different value for the interval andthis value may change daily. This interval needs to be subtracted from thepredicted ovulation time to give the estimated time of the associatedoviposition.

Estimation of the oviposition time for the last egg of a sequence needsto be handled in a different way, because there is no associated ovulation.The relationship between the lag for the last two eggs of sequences andsequence length is illustrated in Fig. 12.10.


Fig. 12.10. The relationship between sequence length and lag (the oviposition interval minus24 h) for the last two eggs of a sequence. Data from Morris, unpublished (×) and Johnston,2004 (�). The solid line shows the fitted linear-by-linear function.

Shorter sequences tend to have longer intervals between the last twoovipositions. The large variation in lag for the longer egg sequences is dueto the fact that the sample sizes are very small.

A fitted linear-by-linear equation of the form

y = 1.75 – 0.9 / ( 1 – 1.969 . x ) (12.11)

predicts the lag between the last two ovipositions of a sequence (y, h) fromovulation rate (x) which, in the population model, determines sequencelength. Consequently for an ovulation rate of 0.75 (a three-ovulationsequence), the lag for the last two eggs is estimated to be 03 h 33 min.

The predicted distribution of oviposition times for a theoretical flock of100 Hy-Line Silver hens is illustrated in Fig. 12.11. The distribution isbimodal, because the shorter sequences that come with advancing age leadto an increasing number of late afternoon ovipositions (Foster, 1968). Themean time of lay is 10:28, 12 h 58 min after the sunset signal at 21:30.

Predicting internal ovulations

Prior to the rupture of the follicle and the release of the ovum, the follicle isusually engulfed by the infundibulum so that ovulation occurs directly intothe infundibulum. This process is under hormonal and neurological controland its effectiveness may therefore be impaired at puberty and with ageing(Gilbert, 1972). Internal laying occurs when, for some reason, an ovum isnot grasped by the infundibulum and therefore remains in the body cavity.The yolk material is usually resorbed within 24 h (Sturkie, 1955).


Fig. 12.11. Frequency distribution of the predicted times of lay for a theoretical flock of 100Hy-Line Silver hens for 500 days, with sunset at 21:30.

The frequency of internal ovulations within a population may beestimated by studying times of lay from individually caged birds, althougha physiological measurement, such as a change in body temperature, isrequired to confirm that ovulation has occurred.

The percentage of internal ovulations is expected to decrease with agein the early stages of lay. Pullets subjected to early photostimulation andhence coming into lay at a young age are more likely to exhibit asynchronybetween ovary and oviduct. However, older hens are also increasinglyprone to internal ovulations. A quadratic-by-linear function such as

y = �58.08 + 67.17 / (1 + 0.001585 . x) + 0.04426 . x (12.12)

where y = % internal ovulations and x = hen age in days, may be used todetermine the percentage of internal ovulations expected at a particularage for Hy-Line Silver hens. For example, at 126 days of age 3.5% of totalovulations are expected to occur internally. Similarly the per cent internalovulations for Hy-Line Brown birds may be predicted from the quadratic-by-linear function

y = �29.78 + 38.32 / (1 + 0.002352 . x) + 0.02659 . x (12.13)

These functions are based on the findings of Johnston (2004) for the twostrains of laying hens at onset of lay. No useful information is available onthe precise frequency of internal ovulations for different breeds and atspecific ages in older hens, so the predicted increase in per cent internalovulations towards the end of the laying cycle, used to derive thesefunctions, is conjecture. The curves given by these functions are shown inFig. 12.12. In addition, 48% of Hy-Line Silver and 28% of Hy-Line Brownbirds were thought to be prone to internal ovulations. In a populationmodel, a proportion of the flock needs to be identified and marked as


0

1

2

3

4

5

6

12 17 22 27 32 37 42 47 52 57 62 67 72

Age (weeks)

% In

tern

al o

vula

tions

Fig. 12.12. The relationship between expected per cent internal ovulations and hen age forHy-Line Silver (solid line) and Brown (dotted line) birds.

potential internal ovulators. Equations 12.12 and 12.13 may be used in apopulation model to produce random internal ovulations over time withinthe designated proportion of the flock.

Double-yolked eggs

The occurrence of double-yolked eggs in young hens at onset of lay is acommon phenomenon and may be attributed to some irregularity in theprocess of ovulation or in the regulation of the follicular hierarchy. Themost likely cause is simultaneous development and ovulation of two ova(Christmas and Harms, 1982). The earlier the pullets are brought into lay,the greater the incidence of double yolks. Johnston (2004) found that 36%of the experimental hens laid one or more double yolks, the proportionbeing the same for both strains of Hy-Line birds.

An exponential function, based on the experimental data, may be usedto predict the per cent double yolks for both strains of Hy-Line birds:

y = �0.000475 + 8786.66 . (0.9403199 x) (12.14)

where y = % double-yolked eggs and x = hen age, in days. The curvegiven by this equation is shown in Fig. 12.13. Hy-Line pullets receivingincreasing daylength at 12 weeks and coming into lay at about 15 weeksmay be expected to produce 13.7% double yolks. At 18 weeks of age, thepredicted per cent double yolks drops to 3.8%.

The distribution of double yolks up to 70 weeks of age within atheoretical flock of Hy-Line Silver hens photostimulated at 18 weeks isillustrated in Fig. 12.14. Twelve hens laid one double-yolked egg and nine


Fig. 12.13. An illustration of the relationship between expected per cent double yolks andhen age for Hy-Line birds.

hens laid two double-yolked eggs. Only 23% of the population produceddouble yolks. This proportion is substantially lower than anticipated, themodel having identified 36 of the 100 hens as potential multiple ovulators,but the figure is presumably influenced by the relatively short periodallocated to the production of double yolks. These 37 double-yolked eggsaccounted for 0.11% of the total eggs laid to 70 weeks of age.

Soft-shelled eggs

Soft-shelled eggs have been found to be associated with short ovulationintervals (van Middelkoop, 1972). If two or more ovulations occur within a24-h period, the resulting eggs are unlikely to have normal shells unless adouble-yolked egg is produced. Premature expulsion of eggs from theuterus may also lead to the production of soft-shelled eggs.

Older hens have a higher incidence of soft shells or breakages, due tothinner shells, than young hens. This is as a result of their changinghormone profiles and decreased ability to transport calcium at theduodenum (Hansen et al., 2003). The reduced populations of oestrogenreceptors mean that old hens are less efficient, both in their absorption ofdietary calcium and in their utilization of calcium in the uterine fluid forshell formation. Premature photostimulation of pullets also causes anincrease in the number of soft-shelled eggs (Johnston, 2004).

Johnston (2004) reported that 38% of Hy-Line Silver and 26% of Hy-Line Brown birds produced soft-shelled eggs at onset of lay. Althoughthese proportions will vary according to nutritional and environmental


Fig. 12.14. The distribution of double yolks in a theoretical flock of 100 Hy-Line Silver hensphotostimulated at 18 weeks of age.

factors, it is useful to have some value for the purpose of testing the model.Many hens lay normal-shelled eggs throughout their laying year. Thepopulation model therefore needs to set apart a proportion of the hensthat will randomly produce soft-shelled eggs.

Two line-plus-exponential functions, derived from experimental data(Johnston, 2004), may be used to predict the percentage of soft shells forthe Silver and Brown birds, respectively:

y = �0.8006 + 1202.6 . (0.952622 x) + 0.0036895 . x (12.15)

y = �0.8134 + 714.6 . (0.953762 x) + 0.0037948 . x (12.16)

where y = % soft shells and x = hen age, in days. The curves given bythese functions are shown in Fig. 12.15. Hy-Line Silver birds that arephotostimulated at 12 weeks and come into lay at about 15 weeks of agemay be expected to produce 6.9% soft shells in the first week of lay. At 18weeks the frequency will be reduced to 2.3%.

A hypothetical distribution of soft shells within a population of 70-week-old Hy-Line Silver hens photostimulated at 18 weeks of age is shownin Fig. 12.16. Three birds laid one soft-shelled egg each and one bird laideight. A total of 141 soft shells (0.43% of total eggs) was produced by 36%of the hens; 64 of the 100 hens did not lay any soft-shelled eggs. Fig. 12.17illustrates how the per cent soft shells changed during the course of thelaying year for the same flock. Because the pullets were photostimulated atthe recommended age, there were very few soft shells at onset of lay. Anincreasing number were produced towards the end of the productiveperiod.


Fig. 12.15. An illustration of the relationship between expected per cent soft shells and henage for Hy-Line Silver (solid line) and Brown (dotted line) birds.


Fig. 12.16. The distribution of soft shells in a theoretical flock of 100 Hy-Line Silver hensphotostimulated at 18 weeks of age.

Fig. 12.17. The per cent soft shells produced over a full laying cycle, by a theoretical flock of100 Hy-Line Silver hens photostimulated at 18 weeks.

Predicting egg weight

In a layer model, egg weight may be predicted as a unit or as the sum ofthe weights of the three components – yolk, albumen and shell. In view ofthe fact that the proportions of the components change with advancing ageand that the three components have very different chemical compositions,a model that predicts the weights of each separately may be of moreinterest to a nutritionist making a study of the hen’s changing nutritionalrequirements.

At a given age, and over a range of egg weights, the weights of all threecomponents increase as egg weight increases, with the proportion ofalbumen increasing at the expense of yolk and shell. In a sample of eggscollected on a specific day from a single-age flock, it may therefore beexpected that the larger eggs will contain proportionately more albumenthan the smaller eggs. As the laying cycle progresses and egg weightincreases, the component weights all increase, but the percentage of yolkincreases to the detriment of albumen and shell. These proportionalchanges need to be accounted for by the layer model, and this isaccomplished via allometry. A satisfactory method for estimating theweights of the three egg components is given by Hussein et al. (1993).

Allometric functions of the form

y = a. x b (12.17)

are used by biologists working with variables that are scaled relative tobody size. Allometry refers to non-isometric scaling, i.e. changes in size ofirregular-shaped organisms. A useful property of allometric functions isthat when the two variables x and y are plotted on logarithmic coordinates,the result is a straight line:

ln y = ln a + b. ln x (12.18)

The exponent b from Eqn 12.17 represents the slope of the straight lineobtained in a logarithmic plot. Emmans and Fisher (1986) proposed thatalbumen and shell weights may be predicted from these allometricfunctions:

AW = a1 . YW b1 (12.19)

and

SW = a2 . ECW b2 (12.20)

where AW = albumen weight, YW = yolk weight, SW = shell weight andECW = the weight of the egg contents, yolk plus albumen. Egg weight isgiven by YW + AW+ SW.

The first step in predicting egg weight is to predict the weight of theyolk. This may be achieved by using a Gompertz function (Eqn 12.4) or alogistic function:

y = A + C / (1 + exp (–B . (x –M))) (12.21)


where y = yolk weight, in grams and x = hen age, in days. The parametersof both functions need to be defined for each genotype, because strainsdiffer both in their initial yolk weight and in their rate of increase in yolkweight with advancing hen age. In addition, the values allocated to each ofthe parameters may need to be adjusted from time to time in line withgenetic advancements, since the component weights are likely to beaffected. The relationship between yolk weight and hen age, for threecommercially available genotypes, is illustrated in Fig. 12.18.

It is interesting to note that, although the eggs from Hy-Line Brownhens are heavier, they have a smaller proportion of yolk than those fromHy-Line Silver hens. Some suggested values of the parameters are given inTable 12.4.

The next step is to predict albumen weight from yolk weight, usingEqn 12.19 and substituting the relevant values for the two parameters forthe specific genotype. Subsequently, shell weight may be estimated from theweight of the egg contents (yolk plus albumen) using Eqn 12.20. Finally, eggweight is calculated as the sum of yolk, albumen and shell weights. Thesuggested values for the allometric function parameters for the same threestrains of bird are summarized in Table 12.5. The method used to derive thevalues for the parameters is explained by Johnston (2004).


Table 12.4. Values of the parameters derived for the logistic (Amber-Link) and Gompertz(Hy-Line Silver and Brown) functions used to predict yolk weight from age.

Strain A C B M

Amber-Link �224.7 243.2 0.01268 �116.4Hy-Line Silver �51107 51123 0.01771 �370.1Hy-Line Brown �101.1 116.0 0.01972 �15.36

Fig. 12.18. The curvilinear relationship between yolk weight and hen age, for Amber-Link(bold line), Hy-Line Silver (solid line) and Hy-Line Brown (dotted line) hens.

The positive relationship between the percentage of yolk and timefrom first egg, for a simulated flock of 100 Hy-Line Silver hensphotostimulated at 18 weeks of age is illustrated in Fig. 12.19. Figure 12.20shows how the percentage of albumen decreases as the same flockprogresses in its laying cycle. The strong positive relationship betweenalbumen weight and egg weight, for eggs produced by hens at 163 days ofage (23.2 weeks), is illustrated in Fig. 12.21.

A population model that makes use of Eqns 12.19 to 12.21,substituting the relevant parameter values for the genotype, is able tocorrectly predict changes in the egg component weights and proportionswith advancing hen age. Moreover, the relationships between the weightsof the three components and egg weight, at a given hen age, are accurate.Variation in yolk, albumen and shell weights within the population may beintroduced by allocating standard deviations to each of the parameterslisted in Tables 12.4 and 12.5.


Table 12.5. Estimates of the parameter values in the allometric functions used to predictalbumen and shell weight.

Parametera1 (albumen) b1 (albumen) a2 (shell) b2 (shell)

Hy-Line Silver 9.473515 0.5044 0.138207 0.9180Hy-Line Brown 10.8906 0.5020 0.133187 0.9310Amber-Link 10.9900 0.4491 0.33875 0.6896

Fig. 12.19. An illustration of how predicted mean yolk percentage increases with age, for ahypothetical flock of 100 Hy-Line Silver hens.


Fig. 12.20. An illustration of how predicted mean albumen percentage decreases with agefor a hypothetical flock of 100 Hy-Line Silver hens.

Fig. 12.21. A scatter diagram illustrating the positive relationship between albumen weightand egg weight (r2 = 0.99), for a hypothetical flock at 163 days of age.

Mean sequence length

The mean sequence lengths for two theoretical flocks, both photostimulatedat 18 weeks, one consisting of 100 Hy-Line Silver hens and the other of 100Hy-Line Brown hens, are shown in Fig. 12.22. It may be seen that thepredicted mean sequence length for both strains is initially short at onset oflay, owing to the quadratic-by-linear function used to predict changes ininternal cycle length. The maximum mean sequence lengths are 86.7 and76.8 days for the Hy-Line Silver and Hy-Line Brown flocks, respectively.The trends simulated by the model are similar to those observed in practiceand reported by Johnston (2004) and Lewis and Perry (1991). As expected,the model predicts that the Silver strain has slightly longer mean sequencelengths than the Brown strain for most of the laying cycle.

The predicted sequence lengths per bird over an extended layingperiod may be imported into the Sequence Analyzer program (Zuidhof etal., 1999). This software calculates (as well as other variables) the meansequence length, the number of sequences, the prime sequence length andthe mean pause length for each bird, and is useful for comparing theperformances of individuals or groups of birds subjected to differenttreatments. The performance indicators for the same Hy-Line Silver andBrown flocks discussed above are summarized in Table 12.6. The Silverstrain tends to have longer prime sequences and to lay fewer but longersequences than the Brown strain. These factors contribute to the higherrate of lay seen in the Hy-Line Silver hens. The large standard deviationsindicate the huge amount of variation between individuals in terms ofsequence lengths.


Fig. 12.22. Predicted mean sequence lengths for 100 Hy-Line Silver (solid line) and 100 Hy-Line Brown (dotted line) hens.

A mean pause length of 1.16 days was reported by Robinson et al.(2001) for SCWL hens. Johnston (2004) found mean pause lengths of 1.59and 1.51 days for Hy-Line Silver and Hy-Line Brown birds, respectively.The model of Etches and Schoch (1984), both in its original and in itsrevised form, does not create pauses longer than 1 day. In the populationmodel, however, a few longer pauses are introduced by the inclusion ofrandom internal ovulations.

Discussion

The improved mathematical model of the ovulatory cycle provides theideal starting point for a layer model. It is capable of producing ovulationsequences of any length and of restricting the total lag between the firstand last ovulations of a sequence to between 8 and 10 h. The predictedovulation times are therefore constrained to occur within an 8–10 h openperiod. The model provides a sound mathematical explanation for thelong-observed phenomenon of sequential laying in domestic hens. On itsown, however, the ovulatory model is not able to show changes inovulation rate with advancing hen age. This is brought about by utilizingthe theory of Emmans and Fisher (1986), namely that a hen has aninternal cycle length that increases with time from first egg, causing theovulation rate and rate of lay to decline. The assumption is made that allhens commence laying by producing their prime sequence, which is notalways the case.

The quadratic-by-linear functions, used in the model to predictchanges in internal cycle length in ageing hens, are able to reproduceshorter sequences at onset of lay. This is because the functions allow theinternal cycle length to decrease towards 24 h in the first few weeks of lay,before increasing. However, the primary disadvantage of these quadratic-by-linear functions is that it is relatively difficult to find suitable values forthe four parameters that enable the population model to produce anacceptable mean sequence length and rate of lay for the genotype. It is feltthat, while these quadratic-by-linear functions give the desired result, animproved or simplified method of creating shorter sequences needs to befound.

It may be helpful to develop a model of the follicle hierarchy, the sizeof the hierarchy being determined by the processes of recruitment andatresia. The absence or presence of a mature follicle may then dictate


Table 12.6. Summary of mean sequence characteristics (± SD) for the theoretical flocks.

Prime sequence Number of SequenceStrain length sequences length Pause length

Hy-Line Silver 82.76 (±60.20) 27.41 (±9.15) 13.60 (±5.56) 1.02 (±0.03)Hy-Line Brown 72.70 (±61.69) 28.47 (±9.82) 13.02 (±5.90) 1.02 (±0.03)

whether or not ovulation takes place. If young hens have fewer follicles inthe hierarchy at onset of lay, the result would be shorter sequences.Another benefit to be derived from modelling the hierarchy is that yolkweight may be predicted with a greater degree of accuracy. The folliclesmay be allowed to continue to accumulate yolk up to the precise time ofovulation. In this way the yolk of the first egg of a sequence is likely to beheavier than in subsequent eggs.

It would be useful to know why some birds have inter-sequence pauseslonger than one day. These may well be due to inadequate maintenance ofthe follicular hierarchy, but there may also be times during the laying cyclewhen the preovulatory surge of LH does not proceed as expected. Stressesthat are imposed on the hens over a number of days, such as thewithdrawal of feed, cause apoptosis and subsequent cell proliferation in thetissues of the anterior pituitary, with corresponding changes to the LHsecretions (Chowdhury and Yoshimura, 2002). Short-term stresses mayalso have the ability to prevent the secretion of LH. The current modelpresumes that the circadian rhythm of LH release continues withoutinterruption. A method of blocking the rhythm of the regulator substancecan be found such that, for one day or a number of days, ovulation will nottake place. This will allow the model to respond to a limiting environmentby altering rates of ovulation and lay. Accordingly, pauses longer than oneday can be introduced into sequences. Increasing the incidence of internalovulations or allowing soft-shelled and double-yolked eggs to disrupt eggsequences will also result in longer inter-sequence pauses, as long as two ormore disturbances occur on consecutive days. A well-designed trial,focusing on the poor producers, could provide valuable information on theunderlying reasons for their low rate of lay.

The proportional changes in yolk, albumen and shell with increasingage have been observed and accepted by poultry scientists for more thanhalf a century (Romanoff and Romanoff, 1949; Harms and Hussein, 1993).It is important to be able to model these changes successfully, so thatincreases in egg weight with advancing hen age are brought about byincreases in the three components occurring at different rates. Theparameters in the allometric functions need to be carefully defined foreach genotype, since strains differ in the weights and proportions of yolk,albumen and shell and this may entail different nutritional requirements.Moreover, it is necessary to reassess the information every few years inorder to keep pace with genetic advancements.

A great many factors are taken into account by the layer modelpresented in this chapter. The mean age at first egg is calculated from thelighting programme applied during rearing. Ovulation times are predictedfor a theoretical flock of 100 birds over a laying year. The flock ovulationrate is seen to increase rapidly to reach a peak about 8 weeks from onset oflay, before declining in a linear fashion. Oviposition times are predictedfrom the associated ovulation times. For all but the last egg of a sequence,oviposition occurs roughly half an hour before the associated ovulation.The lag between the penultimate and ultimate eggs of a sequence is


calculated from an equation relating the length of the interval to ovulationrate; short sequences have a longer interval between the last twoovipositions. The open period for LH release entrains to the onset ofdarkness, so that mean time of lay occurs 13–14 h after sunset. The user isable to observe the effect of different times of sunset on the mean time oflay. The distribution of oviposition times is seen to be unimodal andpositively skewed in young flocks, when a greater proportion of the eggsare laid in the morning, and bimodal in older flocks, when due to theshorter sequences, comparatively more eggs are laid in the afternoon. Flockrate of lay follows a similar pattern to ovulation rate, and also follows thetrend given in breed manuals. Yolk weight increases with hen age.Allometric functions are used to predict albumen weight from yolk weight,and shell weight from the combined weight of yolk plus albumen, using theparameters appropriate for the genotype. Egg weight is calculated as thesum of the three component weights and may be seen to be in line withbreed standards. The model correctly predicts the increasing proportion ofyolk and the decreasing proportions of albumen and shell with advancinghen age. Random occurrences of internal ovulations, restricted to aproportion of the flock, cause interruptions to egg sequences. The numberof internal ovulations in the population is higher at the beginning and atthe end of the laying cycle, when asynchrony between ovary and oviduct ismore likely. Double-yolked eggs are produced by a proportion of the flockat the start of the laying period; the earlier the hens are brought into lay,the greater the incidence of double yolks. A number of hens are prone tolaying soft-shelled eggs, with a greater frequency occurring at onset of layand in older hens. The mean sequence length is initially low, but it increasesto about 70–80 eggs at peak rate of lay and subsequently decreases.

To broaden the scope of the model, a number of parameters still needto be defined for a selection of genotypes. For instance, the LohmannSilver and Brown strains possess a reasonably large share of the SouthAfrican market for commercial pullets and layers and yet little academicresearch seems to have been conducted with these hens. They mayrespond to environmental stimuli in a similar manner to the Hy-Linebirds, but this needs to be tested. No information appears to be availableon the weights of the egg components for the Lohmann birds. In a slightlydifferent vein, it is not known whether yolk, albumen and shell weights canbe manipulated by the environment, although yolk weight is stronglyinfluenced by hen age. Thus, while the model addresses many issuesassociated with egg production, it is hoped that it may be continuallyimproved as new information comes to light.

Despite the fact that several improvements can still be made to thelayer model, it is hoped that the model in its current form will be of benefitto sections of the poultry community. As a teaching aid to poultry sciencestudents it may be invaluable, given its ability to illustrate the complexitiesof egg production and to draw attention to the extent of variation within apopulation. By allowing the user to change various inputs, the modeldemonstrates the ability of hens to respond to their environment. The egg


producer may be interested in predicting the response of the birds, interms of laying performance, to changes in the lighting programmeapplied during rearing. The importance of applying stimulatorydaylengths to pullets at the recommended age for the breed is underlinedby the effect of age at photostimulation on the incidence of internalovulations, soft shells and double-yolked eggs. He or she would also gain abetter understanding of the process of egg production and the effect thatpoor layers may have on flock efficiency. The producer may benefit fromseeing how mean time of lay is influenced by hen age and the time thelights are switched off at night; daily egg collections could then be timed sothat the majority of eggs are collected as soon as possible after being laid.The model may also be used to predict voluntary food intake on a dailybasis and over the laying year; food intake being less on a day when no eggis laid. The nutritionist may be interested in estimating the nutrientrequirements of laying hens according to the predicted weights of yolk,albumen and shell. Ultimately, this model may assist nutritionists tooptimize the nutrient requirements for the various commercially availablestrains. With a few modifications, the population model may be adaptedfor use with broiler breeder hens that have notoriously erratic eggproduction cycles, with long and frequent pauses between egg sequences.

References

Adams, C.J. and Bell, D.D. (1980) Predicting poultry egg production. Poultry Science59, 937–938.

Chowdhury, V.S. and Yoshimura, Y. (2002) Cell proliferation and apoptosis in theanterior pituitary of chicken during inhibition and resumption of laying.General and Comparative Endocrinology 125, 132–141.

Christmas, R.B. and Harms, R.H. (1982) Incidence of double yolked eggs in theinitial stages of lay as affected by strain and season of the year. Poultry Science61, 1290–1292.

Emmans, G.C. and Fisher, C. (1986) Problems in nutritional theory. In: Fisher, C.and Boorman, K.N. (eds) Nutrient Requirements of Poultry and NutritionalResearch. Butterworths, London, pp. 9–39.

Etches, R.J. (1984) Maturation of ovarian follicles. In: Cunningham, F.J., Lake, P.E.and Hewitt, D. (eds) Reproductive Biology of Poultry. Longman Group, Harlow,UK, pp. 51–73.

Etches, R.J. (1996) Reproduction in Poultry. Cambridge University Press, Cambridge,UK.

Etches, R.J. and Schoch, J.P. (1984) A mathematical representation of the ovulatorycycle of the domestic hen. British Poultry Science 25, 65–76.

Foster, W.H. (1968) The effect of light-dark cycles of abnormal lengths upon eggproduction. British Poultry Science 9, 273–284.

Fraps, R.M. (1955) Egg production and fertility in poultry. In: Hammond, J. (ed.)Progress in the Physiology of Farm Animals. Butterworths, London, pp. 661–740.

Gilbert, A.B. (1972) The activity of the ovary in relation to egg production. In:Freeman, B.M. and Lake, P.E. (eds) Egg Formation and Production. BritishPoultry Science, Edinburgh, UK, pp. 3–17.


Gilbert, A.B. and Wood-Gush, D.G.M. (1971) Ovulatory and ovipository cycles. In:Bell, D.J. and Freeman, B.M. (eds) Physiology and Biochemistry of the DomesticFowl, Vol. 3. Academic Press, London, pp. 1353–1378.

Hansen, K.K., Kittok, R.J., Sarath, G., Toombs, C.F., Caceres, N. and Beck, M.M.(2003) Estrogen receptor-α populations change with age in commercial layinghens. Poultry Science 82, 1624–1629.

Harms, R.H. and Hussein, S.M. (1993) Variations in yolk: albumen ratio in heneggs from commercial flocks. Journal of Applied Poultry Research 2, 166–170.

Hussein, S.M., Harms, R.H. and Janky, D.M. (1993) Research Note: Effect of ageon the yolk to albumen ratio in chicken eggs. Poultry Science 72, 594–597.

Johnson, A.L. (1984) Interactions of progesterone and luteinizing hormone leadingto ovulation in the domestic hen. In: Cunningham, F.J., Lake, P.E. and Hewitt,D. (eds) Reproductive Biology of Poultry. Longman Group, Harlow, UK,pp.133–143.

Johnson, A.L. (1996) The avian ovarian hierarchy: a balance between follicledifferentiation and atresia. Poultry and Avian Biology Reviews 7, 99–110.

Johnson, P.A., Dickerman, R.W. and Bahr, J.M. (1986) Decreased granulosa cellluteinizing hormone sensitivity and altered thecal estradiol concentration inthe aged hen, Gallus domesticus. Biology of Reproduction 35, 641–646.

Johnston, S.A. (1993) Simulation modelling as a means of predicting theperformance of laying hens. MSc Agric thesis, University of Natal, South Africa.

Johnston, S.A. (2004) A stochastic model to predict annual egg production of aflock of laying hens. PhD thesis, University of KwaZulu-Natal, South Africa.

Johnston, S.A. and Gous, R.M. (2003) An improved mathematical model of theovulatory cycle of the laying hen. British Poultry Science 44, 752–760.

Lewis, P.D., Morris, T.R. and Perry, G.C. (2002) A model for predicting the age atsexual maturity for growing pullets of layer strains given a single change inphotoperiod. Journal of Agricultural Science 138, 441–458.

Lewis, P.D. and Perry, G.C. (1991) Oviposition time: correlations with age, eggweight and shell weight. British Poultry Science 32, 1135–1136 (Abstr.).

Lewis, P.D., Perry, G.C. and Morris, T.R. (1997) Effect of size and timing ofphotoperiod increase on age at first egg and subsequent performance of twobreeds of laying hen. British Poultry Science 38, 142–150.

Lillpers, K. (1991) Genetic variation in the time of oviposition in the laying hen.British Poultry Science 32, 303–312.

Lillpers, K. and Wilhelmson, M. (1993) Genetic and phenotypic parameters foroviposition pattern traits in three selection lines of laying hens. British PoultryScience 34, 297–308.

Liou, S.S., Cogburn, L.A and Biellier, H.V. (1987) Photoperiodic regulation ofplasma melatonin levels in the laying chicken (Gallus domesticus). General andComparative Endocrinology 67, 221–226.

Menaker, M., Hudson, D.J. and Takahashi, J.S. (1981) Neural and endocrinecomponents of circadian clocks in birds. In: Follett, B.K. and Follett, D.E. (eds)Biological Clocks in Seasonal Reproductive Cycles. Wright, Bristol, UK,pp. 171–183.

Patterson, P.H. (1997) The relationship of oviposition time and egg characteristicsto the daily light:dark cycle. Journal of Applied Poultry Research 6, 381–390.

Robinson, F.E., Renema, R.A., Oosterhoff, H.H., Zuidhof, M.J. and Wilson, J.L.(2001) Carcass traits, ovarian morphology and egg laying characteristics inearly versus late maturing strains of commercial egg-type hens. Poultry Science80, 37–46.


Romanoff, A.L. and Romanoff, A.J. (1949) The Avian Egg. John Wiley, New York.Siopes, T.D. and Wilson, W.O. (1980) A circadian rhythm in photosensitivity as the

basis for the testicular response of Japanese quail to intermittent light. PoultryScience 59, 868–873.

Sturkie, P.D. (1955) Absorption of egg yolk in the body cavity of the hen. PoultryScience 34, 736–737.

Tilly, J.L., Kowalski, K.I. and Johnson, A.L. (1991) Stage of ovarian folliculardevelopment associated with the initiation of steroidogenic competence inavian granulosa cells. Biology of Reproduction 44, 305–314.

Turek, F.W., Penev, P., Zhang, Y., Van Reeth, O., Takahashi, J.S. and Zee, P. (1995)Alterations in the circadian system in advanced age. In: Chadwick, D.J. andAckrill, K. (eds) Circadian Clocks and Their Adjustment. Wiley, Chichester, UK,pp. 212–234.

van Middelkoop, J.H. (1972) The relationship between ovulation interval of WhitePlymouth Rock pullets and the laying of abnormal eggs. Archiv fürGeflügelkunde 6, 223–230.

Warren, D.C. and Scott, H.M. (1935) The time factor in egg formation. PoultryScience 14, 195–207.

Williams, J.B. and Sharp, P.J. (1978) Control of the preovulatory surge ofluteinizing hormone in the hen (Gallus domesticus): the role of progesteroneand androgens. Journal of Endocrinology 77, 57–65.

Zakaria, A.H. (1999) Ovarian follicular growth in laying hens in relation tosequence length and egg position in various sequence lengths. Archiv fürGeflügelkunde 63, 264–269.

Zuidhof, M.J., Bignell, D. and Robinson, F.E. (1999) Egg Production and SequenceAnalyzer Software. Alberta Poultry Research Centre, Alberta Agriculture, Foodand Rural Development, University of Alberta, Canada.


13 Comparison of Pig Growth Models– the Genetic Point of View

P. LUITING AND P.W. KNAP

PIC International Group, Ratsteich 31, D-24837 Schleswig, [email protected]

Introduction

Application models of growth in pigs were pioneered by Whittemore andFawcett (1976) and further developed by Moughan and Smith (1984),Black et al. (1986), Emmans (1988, 1997), Pomar et al. (1991), TMV(1991), De Greef (1992), Ferguson et al. (1994), Whittemore (1995) andmany others. All these models are dynamic (describing the growthprocess over time), deterministic (non-stochastic), and semi-mechanistic(more or less based on biological growth mechanisms, focusing on theaccretion of several body components). Many of these biologicalmechanisms are driven by one or more parameters that are specific tothe genotype (breed, strain, etc.) to be simulated. Proper simulation ofthat genotype then requires quantification of those parameters, whichrequires experimental effort. Therefore, these parameters are of primaryinterest for animal breeders who use the model for their particularpurposes.

The above mentioned publications describe the mechanisms thatform the core of their models with different notation andargumentation; as a consequence, the exact differences and similaritiesbetween these approaches are often unclear and we attempt here toclarify some of these issues. Section 1 of the present text describes themain common mechanisms of the various models and their genotype-specific aspects. Section 2 describes the details of implementation ofthese mechanisms, and attempts to derive a common denominator.Section 3 discusses the differences between the various models from thepoint of view of adequacy and complexity of the description of thegenotype.

Given the large amount of water in the mammalian body, theprediction of body water mass is perhaps the most critical factor of pig


growth simulation. Emmans and Kyriazakis (1995) focus on this issue inquantitative detail, and this is the only such treatment of the matter that weare aware of; we do not deal with it any further.

Main Common Mechanisms

All the models discussed here distinguish three processes that requireenergy: protein deposition (PD), body maintenance, and lipid deposition(LD), all three on a daily basis. The driving factor is PD; it is predictedfirst, after which it determines all other factors in the simulation. Themetabolizable energy (ME) requirements for body maintenance (MEm) arepredicted from metabolic body weight or from body protein mass: MEm =α × BW� or MEm = α × P�, where α and � are constants. It follows that atknown energy intake (MEI), LD is predicted as the item that balances therequirements of the law of conservation of energy:

(13.1)

where LD = lipid deposition (kg per day), MEI = ME intake (MJ per day),MEm = ME required for maintenance (MJ per day), PD = proteindeposition (kg per day), EP and EL = combustion energy contents of bodyprotein and lipid, respectively (MJ per kg), and kP and kL = efficiencies ofuse of ME for PD and LD, respectively.

All models assume EP, EL, kP, kL, α and � to be constant, although theyvary somewhat with regard to their values. Genetic variation in theseparameters is presumed absent.

All models calculate water and ash deposition from PD, using empiricalequations with constant parameter values. Empty body weight gain (BWG)is calculated by summation of the four components; adjustment for acertain amount of gut fill leads to daily growth:

(13.2)

All models define an initial status with the starting values for bodyprotein, lipid, ash and water mass. The predicted deposition values areadded to the current values of body component mass, and next day’scalculation is performed. This process is repeated until the desired endstatus is reached. The models vary somewhat with regard to the water-and ash-related empirical equations and/or their parameter values, withregard to the magnitude of gut fill, and with regard to the initial bodycomponent mass assumptions. Genetic variation is presumed absenthere.

empty BWG PD LD waterdeposition ashdepositionBWG (empty BWG) (1 gutfill correction factor)

= + + += × +

MEI ME PD E / k LD E / k

LDMEI- ME (PD E / k )

E / k

m P P L L

m P P

L L

= + × + × →

= − ×

Comparison of Pig Growth Models 261

Most models treat feed intake as a known input parameter. However,some models predict voluntary feed intake as an output parameter basedon MEm, desired PD, desired LD and Eqn 13.1. The prediction of desired PD and desired LD is described, respectively, in the two sectionsbelow.

Prediction of Protein Deposition

The main feature of PD is that it is sourced from the digestible crudeprotein intake (DCPI). Like MEm, protein requirements for bodymaintenance (Pm) are predicted from metabolic body weight or from bodyprotein mass: Pm = γ × BWδ or Pm = γ × Pδ, where γ and δ are constants. Itfollows that at known DCPI, PD can be predicted as:

(13.3)

where eP = material efficiency with which protein is utilized abovemaintenance, DCPI = digestible crude protein intake (kg per day), and Pm= protein required for body maintenance (kg per day).

The material efficiency with which protein can be utilized abovemaintenance (eP) is assumed to have a constant maximum value (maxep) ofabout 0.83, see Fig. 13.1. The various models vary somewhat with regardto the magnitude of this maximum value for eP, and of γ and δ. Geneticvariation is again presumed absent.

All models described here recognize two situations where eP is lowerthan its maximum value, i.e. where part of the protein supply is used as asource of energy rather than amino acids: (i) PD is at its maximum (section 1);and (ii) ME supply is insufficient (section 2).

PD e (DCPI P )P m= × −

262 P. Luiting and P.W. Knap

Pm DCPI

ep = maxep

PD

Fig. 13.1. Protein deposition (PD) in relation to digestible crude protein intake (DCPI). Pm

denotes the protein requirement for body maintenance, eP is the material efficiency of proteinutilization. In this range of DCPI, eP attains its maximum value maxeP.

Maximum protein deposition

All models assume a genetically determined upper limit to a pig’s rate ofprotein deposition: maxPD. This is the protein deposition that the pigseeks to realize: maxPD equals the pig’s desired level of PD. By analogy,the DCPI level that is required to just achieve maxPD is the desired DCPI:

When realized DCPI exceeds desired DCPI, the surplus of digestedprotein is used as an energy source. This reduces the material efficiency eP,calculated as:

(13.4)

Adding this relation to Fig. 13.1 results in Fig. 13.2. The various modelsuse different definitions for the genetic factor(s) that describe maxPD. The obtained value for maxPD is used to determine desired DCPI =

+ Pm, which is compared to DCPI. If DCPI < desired DCPI,

PD is estimated with Eqn 13.3; otherwise, PD = maxPD.

Insufficient energy supply

All models assume implicitly an intrinsic lower limit to a pig’s MErequirements in order to reach maxPD: minMEImaxPD. From the law ofconservation of energy, all models then assume an intrinsic lower limit to apig’s LD coinciding with maxPD:

maxPDmaxeP

eoutputinput

PDDCPI P

maxPDDCPI P

max e , for DCPI > desired DCPIPm m

P= =−

=−

<

eoutputinput

PDDCPI P

maxPDdesired DCPI P

maxePm m

P= =−

=−

=


Pm DCPI

maxPD

PD

ep = maxep

ep < maxep

Fig. 13.2. An extension of Fig. 13.1. PD has an upper limit (maxPD), reached at DCPI =desired DCPI. At higher DCPI levels, eP is lower than its maximum value.

(13.5)

where minLDmaxPD is the lower limit to LD coinciding with maxPD.The relation of PD and LD with MEI is shown in Fig. 13.3 . At MEI ≤

minMEImaxPD, LD must compete for resources with PD so its realized levelis an indication of the genotype’s priorities for this resource allocation. AtMEI > minMEImaxPD all surplus energy goes to LD, and this is genotype-independent. So we have a genetically controlled part for LD belowminMEImaxPD and a genetically controlled part for PD above it. It followsthat the point of intersection represents: (i) the pig’s ambition for proteindeposition; and (ii) its genetic priorities for resource allocation between PDand LD, and minMEImaxPD must then be the lower limit to the energyintake that the pig seeks to realize.

Another consequence is that PD is not the only genetically determinedfactor that drives the system: below minMEImaxPD, the desired LD level isjust as important. Thus a genotype must be characterized by a desired PD(= maxPD) and a desired LD coinciding with it (= minLDmaxPD).Dependent on environmental conditions, it may well be that neither ofthem ever gets phenotypically expressed.

Whereas at MEI > minMEImaxPD the surplus energy is fully used forLD, the energy deficit at MEI ≤ minMEImaxPD is not fully accounted for byreducing LD but also by reducing PD. Part of DCPI is then used as anenergy source and not for protein deposition. This leads to PD < maxPD,and it reduces eP to:

(13.6)

Adding this relation to Fig. 13.2 results in Fig. 13.4.

eoutputinput

PDDCPI P

PDdesired DCPI P

max e for PD < maxPDPm m

P= =−

=−

<

minMEI ME (maxPD E / k ) (minLD E / k )maxPD m P P maxPD L L= + × + ×


minMEImaxPD MEI

PD LD

PD

b0

maxPD

minLDmaxPD

b1

LD

Fig. 13.3. Protein (PD) and lipid deposition (LD) in relation to ME intake (MEI). For PD <maxPD, PD = f(MEI) = b1 × (MEI – b0). Above that level (i.e. above MEI = minMEImaxPD andLD = minLDmaxPD), all surplus energy is used for LD.

The various models use different definitions of the function f(MEI):PD = b1 × (MEI – b0) that describes the reduction of PD at MEI <minMEImaxPD, see the section on ‘Insufficient energy supply’ in ‘Modelcomparison’ above.

The value for PD that was obtained from DCPI (in the section on‘Maximum protein deposition’ in ‘Main common mechanisms’ above)

is used to determine desired MEI = + b0, which is

compared to MEI. If MEI < desired MEI, PD is estimated via f(MEI);otherwise, PD from DCPI remains unchanged.

Model Comparison

The main issue from the above section is: body protein deposition (PD)takes place at a low material efficiency when it is limited either by thegenetic maximum to PD or by insufficient energy supply. The question isthen how the various models parameterize these relations. We deal nextwith maximum protein deposition, with insufficient energy supply, andgive a brief comparison of how some of these models describe voluntaryfood intake.


Three different methods are used for the definition of maxPD. The simplest method makes the assumption that maxPD has a constant

value throughout the growth period, at least up to commercial slaughter

PD (from DCPI)b1


Pm DCPI

PD

maxPD

PD =

f(MEI)

eP = maxeP

eP < maxeP

eP < maxeP

Fig. 13.4. An extension of Fig. 13.2. At insufficient ME supply, PD has an upper limit thatdepends on ME intake (MEI) and eP is lower than its maximum value.

weights (Whittemore and Fawcett, 1976). Hence, different genotypes canbe characterized by different values for this single parameter. The othertwo methods make maxPD depend on body weight or stage of bodydevelopment, describing a pattern where maxPD increases rapidly early inlife, plateaus during the growth period and then decreases towards zero atmaturity. Two types of functions are used to model this trend, as shown inFig. 13.5.

First, hyperbolic or parabolic equations of maxPD in terms of BW, inboth cases with two genetic parameters.

Walker and Young (1993) used a skew-hyperbolic relation with BW:

maxPD = BW � e(c + d � BW) (13.7)

Thorbek (1975) and Whittemore and Fawcett (1976) used a quadraticrelation with metabolic body weight:

maxPD = f � MBW2 – g � MBW (13.8)

Second, derivatives of sigmoid curves for potential protein growth, basedupon the idea that the effect of BW on maxPD reflects the effect ofphysiological development. Emmans (1988) used the Gompertz function;this equation has two genetic parameters, the rate parameter BGomp andthe mature body protein mass Pmature:

(13.9)

Black (1988) used the Richards function, modified to replace one of thetwo instances of protein mass by BW:

(13.10)

This equation has a high information requirement for characterization ofthe genotype: four genetic parameters (k, S, a and Pmature).

maxPD= k (BW+S) [(P P) / P ]= k (BW S) 1P

Pa

mature maturea

mature

× × − × + × −⎛

⎝⎜⎞

⎠⎟

maxPD=B P ln(P /P) = B PP

Pln

PPGomp mature Gomp mature

mature mature

× × × × ×⎛

⎝⎜⎞

⎠⎟1 /


maxPD

Walker & Young (1993)eqn (7)

Thorbek (1975)eqn (8)

maxPD

P/Pmat

Black (1988)eqn (10)

Emmans (1988)eqn (9)

BW

Fig. 13.5. Various functions to describe the course of maxPD in relation to body weight (BW)or body protein mass (P) as a proportion of its mature value (Pmat).


All models described here use a function f(MEI) that describes thereduction of PD for MEI < minMEImaxPD. This function is not alwaysexplicit, but may follow implicitly from other, explicitly defined, relations.Table 13.1 introduces these structures. Method 1 explicitly defines a valuefor minLD/PD, and implicitly describes f(MEI) as a linear regression lineof PD on MEI with b0 = MEm. Methods 2 and 3 define f(MEI) explicitlybut differently. Methods 4 and 5 explicitly define a function for eP and avalue for minL/P, respectively, leading implicitly to a function PD =f(MEI).

Method 1 was published earliest, and some subsequent methods give,in addition to their explicit element f(MEI), also their own implicit valuefor minLD/PD, for comparison purposes. We include minLD/PD in Table13.1 for the same reason, although it is not required for a comparison ofthese five methods when f(MEI) has already been described.

The general form of f(MEI) is PD = b1 × (MEI – b0), where b0 is an x-intercept and b1 represents the reduction of PD at MEI < minMEImaxPD.The general form of minLD/PD is derived as follows. Substituting f(MEI)into Eqn 13.1 gives:

so that

LDMEI ME (PD E / k )

E / kMEI ME [b (MEI b ) E / k ]

E / k

1 b E / kE / k

MEIME b b E / k

1 b E / k

m P P

L L

m 1 0 P P

L L

1 P P

L L

m 0 P P

1 P P

1

= − − × = − − × − ×

= − × × − − × ×− ×

⎛

⎝⎜⎞

⎠⎟


Table 13.1. Methods for the reduction of protein deposition at MEI < minMEImaxPD.

Method minLD/PD PD = f(MEI) Third function

1 Whittemore explicit definition implicit descriptionMoughan constant → Lin(MEI)

2 Black implicit description explicit definitionDe Greef nonLin(MEI) ← Lin(MEI)

3 Van Milgen implicit description ← explicit definitionnonLin(MEI) Quad(MEI)

4 Emmans and implicit description ← implicit description ← explicit definitionKyriazakis nonLin(MEI, DCPI) Lin (MEI), nonLin(DCPI) eP = Lin(MEI/DCPI)

5 De Lange implicit description ← implicit description ← explicit definitionnonLin(MEI) Lin(MEI, L, P) minL/P = constant

Lin(): linear function. nonLin(): nonlinear function. Quad(): quadratic function.References in the text.

(13.11a)

which can usefully be rearranged as

(13.11b)

Method 2 introduced the parameter ‘marginal minLD/PD’ (margminLD/PD):the ratio between the regression coefficients of LD and PD on MEI, at MEI <minMEImaxPD. We show in Appendix 13.1 that this parameter equals the first

term in Eqn 13.11b: margminLD/PD = . We present

the implicit values of margminLD/PD as well as minLD/PD for the purpose ofcomparison between the models.

The methods are discussed in detail in the following five sections andin Table 13.2.

1 b E / kb E / k

1 P P

1 L L

− ××

minLD / PD1 b E / k

b E / k1

ME1 b E / k MEI b

1 P P

1 L L

m

1 P P 0

= − ××

× − −− ×

×−

⎛

⎝⎜⎞

⎠⎟b0 1

minLD / PD

1 b E / kE / k

MEIME b E / k

1 b E / k

b (MEI b )

1 b E / kb E / k

MEIME b E / k

1 b E / kMEI b

1 P P

L L

m 1 P P

1 P P

1 0

1 P P

1 L L

m 1 P P

1 P P

0

=

− × × − − × ×− ×

⎛

⎝⎜⎞

⎠⎟

× −=

= − ××

×− − × ×

− ×−

b

b

0

0


Table 13.2a. The forms of regression coefficientsa b0 and b1 for the methods in Table 13.1.The forms of margminLD/PD and minLD/PD are in Table 13.2b.

Method b0 b1

1 Whittemore MEm

Moughan

2Black

g1 g2De Greef

3 Van Milgen MEm

4Emmans and

0Kyriazakis

5 De Lange MEm + (minL/P × P – L) × EL / kL

a PD = b1 × (MEI – b0).References in the text.

1E / k minLD / PD E / kP P L L+ ×

g (MEI ME g )

4 maxPDg

MEI ME g

2 m 1

12 m 1

× − − =

= − × × − −( )

� × −DCPI PDCPI

m

1E / k minL / P E / kP P L L+ ×

Com

parison of Pig G

rowth M

odels269

Table 13.2b. Continuation of Table 13.2a: the forms of margminLD/PD and minLD/PD for the methods in Table 13.1.

Method

1 = minLD/PD g1

2

3 margminLD/PD

4

5 minL/P

margminLD / PD

1minL / P P L (E / k minL / P E / k )

minL / P MEI [ME minL / P P L E / k ]P P L L

m L L

×

+× −( ) × + ×

×− + × −( ) ×

⎛

⎝⎜⎞

⎠⎟1

margminLD / PD 1 b E / k

b E / k1 P P

1 L L

= − ××

minLD / PD margminLD / PD 1ME

1 b E / k MEI bm

1 P P 0

= × − −− ×

×−

⎛⎝⎜

⎞⎠⎟

b0 1

1 g E / kg E / k

2 P P

2 L L

− ××

margminLD / PD 1ME g

1 g E / k MEI gm

2 P P 1

× − −− ×

×−

⎛⎝⎜

⎞⎠⎟

1 1

1E / k

14 maxPD

gMEI ME g

E / kL L

12 m 1

P P× − × × − −( )−

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

1E / k

1 DCPIDCPI P

E / kL L m

P P× ×−( ) −

⎛

⎝⎜⎞

⎠⎟�margminLD / PD 1

ME

1DCPI P

DCPIE / k

1MEI

m

mP P

× −− ×

−( ) ××

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟�

1. Whittemore and Fawcett (1976)

These authors assumed that an intrinsic minimum amount of lipiddeposition must accompany each unit of protein deposition, implying thatthere is an intrinsic lower limit to the ratio between lipid and proteindeposition (minLD/PD), which is defined as a genetically determinedconstant throughout the growing period (g1 in Table 13.2).

Substitution of minLD/PD × PD for LD into Eqn 13.1 shows thatf(MEI) is assumed to be a linear regression of PD on MEI:

(13.12)

It follows that b0 = MEm, b1 = 1/(EP/kP + minLD/PD × EL/kL). The linearregression coefficient b1 is therefore also assumed to be a geneticallydetermined constant throughout the growth period.

2. Black et al. (1986)

Black explicitly assumed f(MEI) to be a linear regression of PD on MEI:PD = b1 × (MEI – b0), and b0 and b1 are assumed to be geneticallydetermined constants throughout the growth period (g1 and g2 in Table13.2). In contrast to Whittemore’s model (Eqn 13.12), the x-intercept is notassumed to be in MEm; all its estimated values are lower than MEm. Theargumentation for b0 < MEm is that when MEI = MEm, protein depositionis often positive and lipid deposition is often negative (i.e. lipid iscatabolized). Moreover, Black’s model does not require an intrinsicminimum amount of lipid deposition that must accompany each unit ofprotein deposition. Hence minLD/PD is not a constant; it decreases whenMEI decreases, see Table 13.2. It is genetically determined through b0 andb1. By contrast, margminLD/PD is a constant in this model.

The entity margminLD/PD (the ratio between the regressioncoefficients of LD and PD on MEI) was introduced by De Greef (1992) as agenetically determined constant throughout the growth period. We show inAppendix 13.1 that, because of Eqn 13.1, the regression of LD on MEI canbe fully expressed in terms of the one for PD, which removes the need forDe Greef ’s two additional genetic parameters (e.g. c0 and c1 in LD = c1 ×[MEI – c0]). This makes De Greef ’s model collapse entirely to Black’s one;the only novelty is that it makes the margminLD/PD parameter explicit.

3. Van Milgen et al. (2000)

Like Black, these authors explicitly assumed a regression function forf(MEI): PD = b1 × (MEI – b0), with an x-intercept b0 = MEm just as inWhittemore’s model. Their regression coefficient b1 is in itself a linearregression on (MEI – MEm) and can be written, in our notation, as b1 =g2 × (MEI – MEm – g1). This way, f(MEI) has the form of a quadraticregression of PD on (MEI – MEm):

MEI ME PD E / k minLD / PD PD E / k

PD1

E / k minLD / PD E / kMEI ME

m P P L L

P P L Lm

= + × + × × →

=+ ×

× −

( ) (

( )

)


(13.13)

Parameters g1 and g2 are defined as genetically determined constants. Eqn13.13 is defined as having its maximum value at maxPD; this makes one ofthe two parameters (g1, g2) redundant, as follows.

Solving Eqn 13.13 for dPD / d(MEI – MEm) = 0 gives minMEImaxPD:

(13.14)

After substitution of minMEImaxPD from equation 13.14 for MEI inequation 13.13, maxPD can be solved for in order to express b1 in terms ofmaxPD and g1 (instead of g1 and g2):

(13.15)

It follows that b1 is not a constant but a function of MEI. It is geneticallydetermined through maxPD and g1.

Like b1, minLD/PD is not a constant but a function of MEI; it isgenetically determined through maxPD and g1 (see Table 13.2). Note thatin this model, margminLD/PD equals minLD/PD and is therefore not aconstant either, in contrast to model 2.

4. Kyriazakis and Emmans (1992)

The reduction in eP with decreasing MEI given a certain amount of DCPIwas represented by these authors in terms of a linear regression of eP onthe ratio between the food ME content and food digestible protein content(MEC / DCPC, which equals MEI / DCPI), forced through the origin:

(13.16)

The parameter µ is explicitly assumed to be a constant, not geneticallydetermined. Following Eqn 13.16, f(MEI) has the form PD = b1 × (MEI –

b0) with b0 = 0 and . The regression coefficient b1 is

then a non-linear function of DCPI, not genetically determined. Table 13.2

bDCPI P

DCPI1m= × −

�

eMEIDCPI

PDDCPI P

MEIDCPI

PDDCPI P

DCPIMEIP

m

m= × →−

= × → = × − ×� � �

b4 maxPD

gMEI ME g1

12 m 1= − × × − −( )

maxPD g (minMEI ME ) g g (minMEI ME )

g (g / 2) g g (g / 2) 0.25 g g g4 maxPD

g

2 maxPD m2

1 2 maxPD m

2 12

1 2 1 2 12

212

= × − − × × − =

= × − × × = − × × → = − × →

dPDd(MEI ME )

2 g MEI ME g g 0

minMEI MEg g2 g

g / 2

minMEI ME g / 2

mm

maxPD m1 2

1

maxPD m 1

−= × × − − × =

→ − =××

=

→ = +

2 1 2

2

( )

PD b (MEI b ) g MEI ME g ) MEI ME

g (MEI ME ) g g (MEI ME )1 0 m m

m2

m

= × − = × − − × − =

= × − − × × −2 1

2 1 2

( ( )


shows that minLD/PD is not a constant, but a non-linear function of MEIand DCPI, not genetically determined. It also shows that margminLD/PDis not a constant either, but a non-linear function of DCPI, not geneticallydetermined.

5. De Lange (1995)

De Lange assumed that an intrinsic minimum amount of lipid mass (L)must accompany each unit of protein mass (P), hence that there is anintrinsic minimum lipid to protein ratio in the body (minL/P), which isgenetically determined. Therefore, minLD can be written as minLD =minL/P × (P + PD) – L. The equivalent of Eqn 13.12 is then:

(13.17)

It follows that f(MEI) is implicitly defined as a linear regression with aregression coefficient b1 that is a genetically determined constant, just asminL/P. Its x-intercept b0 is a function of P and L, and it is geneticallydetermined through minL/P. When the actual amount of body lipid exceedsits intrinsic lower limit, then (minL/P × P – L) � 0, so that b0 � MEm.

Table 13.2 shows that minLD/PD is a function of P and L, and (non-linearly) of MEI; it is genetically determined through minL/P;margminLD/PD is a constant, this time equal to minL/P.

Prediction of voluntary food intake

Two of these models predict voluntary food intake, and they do so fromthe combination of maintenance requirements and desired PD and LD.Desired LD is defined in both cases via an additional equation. The formsof these equations (and their difference between the two models) aresimilar to the associated definitions of maxPD, as follows.

Emmans (1988) used again the derivative of the Gompertz growthfunction to describe desired LD. This equation has two genetic parameters:the rate parameter BGomp (equal to the one for maxPD in Eqn 13.9), andmature body lipid mass Lmature.

desired LD = BGomp � L � ln(Lmature / L) (13.18)

Black (1988) used again the derivative of a modified Richards growthfunction to describe the desired increase of net energy (NE) in the body:

desired NE = k × (BW + S)a × [(NEmature – NE)/NEmature]

which gives

(13.19)desiredLDdesiredNE maxPD E

EP

L

= − ×

So b =ME +(minL / P P – L) E / k , and b =1

E / k minL / P E / k0 m L L 1

P P L L

× ×+ ×

PD1

E / k minL / P E / kMEI [ME (minL / P P L) E / k ]

P P L Lm L L=

+ ×× − + × − ×( )


Discussion and Conclusions

Apart from several empirical relations, the models described here containthree truly mechanistic elements in the form of Eqns 13.1, 13.2 and 13.3.All genetic factors enter this mechanistic system through eP in Eqn 13.3:maximum protein deposition (maxPD) and protein deposition atinsufficient energy supply.

The differences and similarities between the various models withregard to these genetic factors are summarized and discussed below.


The genetic aspects of the five discussed methods are summarized inTable 13.3.

Black et al. (1986), Moughan and Verstegen (1988) and Emmans andKyriazakis (1997) refer to several studies that show an effect of body weighton maxPD. Although measurement of maxPD seems to be difficult and notvery reliable, especially in the early increasing phase, the trend of‘increasing rapidly early in life, plateauing during the growing-fatteningstages and then decreasing towards zero at maturity’ is generally accepted.Hence inclusion of this effect of body weight on maxPD makes the modelvalid over a wider growth trajectory than with the assumption of a singleconstant maxPD value as in method 1 in Table 13.3.

The hyperbolic, parabolic and sigmoid-derived equations are allempirical, and it is probably possible to find functions from all these threeclasses that fit the observed pattern very well. However, the derivatives ofthe sigmoid functions have a more general character and useful propertieslike allometry. Disadvantages of Black’s modified Richards curve (method5) are the large number of genetic parameters and the unclarity of hismodification. The inclusion of BW has strange consequences; for example,if a pig has a higher BW at a given P because it has more fat in its body,then its predicted maxPD will be higher. The derivative of the Gompertz


Table 13.3. Methods to describe maximum protein deposition.

Method na maxPD Type

1 WhittemoreMoughan 1 g1 constant

2 WhittemoreThorbek 2 f (g1, g2) hyperbola

3 Walker and Young 2 f (g1, g2) skewed parabola

4 Emmans 2 f (BGomp, Pmature) Gompertz

5 Black 4 f (k, S, a, Pmature) modified Richards

a Number of genetic parameters.References in the text.

curve with two genetic parameters (method 4) seems to be the preferredmodel. An additional advantage is the smooth connection with Taylor’sgenetic size scaling principles, see Emmans (1988, 1997).


The genetic aspects of the five discussed methods are summarized in Table13.4 and Fig. 13.6.

De Greef and Verstegen (1992) showed that minLD/PD decreases withdecreasing MEI. This makes method 1 (with a single constant value for thegenetic parameter minLD/PD, g1 in Table 13.4) unsuitable.


Table 13.4. Methods to describe protein deposition at MEI < minMEImaxPD.

Method na b0 b1 margminLD/PD minLD/PD

1 WhittemoreMoughan 1 MEm g1 f(g1) g1

2 BlackDe Greef 2 g1 f(g2) g2 f(g1, g2, MEI)

3 Van Milgen 1 MEm f(g1, maxPD, MEI) f(g1, maxPD, MEI) f(g1, maxPD, MEI)

4 Emmans and Kyriazakis 0 0 f(DCPI) f(DCPI) f (DCPI, MEI)

5 De Lange 1 f(g1, P, L, MEm) f(g1) f(g1) f(g1, MEI)

a Number of genetic parameters.References in the text.

MEm

PD

maxPD

0

L/P > minL/P

high L/P

MEIb0 < MEm

L/P = minL/P

low

DCPI

MEm MEI

PD

maxPD

0

high

DCPI

41

b0 < MEm

2

3

31

4

Fig. 13.6. Methods to describe protein deposition with insufficient ME supply, as in Table 13.3.Left: (1) Whittemore, Moughan; (2) Black, De Greef; (3) Van Milgen and Noblet; (4) Emmansand Kyriazakis. Right: De Lange. References and explanation of symbols in the text.

Table 13.2 shows that method 2 makes minLD/PD dependent on MEI,for which it requires two genetic parameters (g1 and g2 in Tables 13.2 and13.4). The reason given by Black et al. (1986) for this is that when MEintake is just sufficient to achieve zero energy retention (maintenanceenergy intake, MEm), protein deposition is positive and lipid deposition isnegative (i.e. lipid is catabolized). This feature has been emphasized bymany authors (e.g. ARC, 1981; Close and Fowler, 1982; Walker and Young,1993; NRC, 1996; Van Milgen and Noblet, 1999). Thus, the line describingPD as a linear function of MEI has an x-intercept lower than MEm (b0 <MEm): the assumption that the ME requirement at zero PD equals MEm (b0= MEm) is therefore invalid.

Method 3 incorporates the effect of MEI on minLD/PD in a differentway. It requires two genetic parameters, one of which was shown, in Eqn13.15, to collapse to maxPD; therefore Table 13.1 gives only g1. This is anadvantage over method 2 with its two required genetic parameters.However, f(MEI) is a quadratic regression of PD on MEI with an x-intercept equal to MEm (see line (3) in Fig. 13.6), which is (like for method1) in conflict with the above mentioned finding of b0 < MEm. This makesmethod 3 also unsuitable.

Method 4 does not include any genetic parameters, which makes it aninconvenient method to model animals that differ in their geneticallydesired lipid deposition at MEI < minMEImaxPD. This may be caused bythe fact that this method was based on data collected on very young pigs(4, 6 or 8 weeks after 12 kg body weight, up to 20–50 kg end weight).Emmans (1997) notices that ‘all genotypes are thin when they are veryimmature’ and that this means that the body lipid to protein ratio showslittle variation at a low degree of maturity. This should make it verydifficult to detect genetic variation in this trait at that stage.

Method 4 presents two more complications. First, when an efficiencyparameter (i.e. output/input) such as eP is expressed in terms of MEI, itwould make sense to regress eP on MEI / (DCPI – Pm) where thedenominator properly represents ‘input’. However, the regression wasdone on MEC / DCPC, which equals MEI / DCPI. Of course, Pm is small incomparison to DCPI (especially in very young animals) so the error isprobably small.

Second, the above regression was forced through the origin, definingb0 = 0. This approach has one parameter less to be estimated, animportant advantage when analysing a small dataset. However, such anassumption about an intercept (with notoriously large standard errors ofthe regression estimates) is very difficult to falsify, and the defaultapproach should be that the intercept is non-trivial (e.g. Neter et al., 1985,pp. 163–164). At least there seems to be no valid biological reason to set b0to zero. Inclusion of Pm as suggested above, and allowance for a non-zerointercept in the regression, would make method 4 collapse to method 2. Allthis makes method 4 unsuitable.

Method 5 has several advantages over the other methods: only a singlegenetic parameter is involved and, just as in method 2, minLD/PD depends


on MEI and is not constant, and b0 � MEm. There are two more reasonswhy this method is attractive.

First, b0 depends on P and L in such a way that b0 approaches MEmwhen [minL/P × P – L] approaches zero, i.e. when L/P approaches minL/P.This is illustrated in Fig. 13.7. When a pig that used to be fed at a highMEI level (so that it is on a high PD metabolism, and has a high L/P level)is suddenly brought to a low MEI level (for example, MEI = MEm as inFig. 13.7), it will not directly reduce its PD metabolism to zero, but willcatabolize body lipid to support its protein retention. In Fig. 13.6 thisinitial situation is represented by the base of the arrow at the upperregression line with a high L/P level (b0 < MEm). When this low MEI levelcontinues, the resulting lipid catabolism reduces L/P until it has reachedminL/P (through subsequently lower regression lines in Fig. 13.6), and PDmetabolism follows the arrow to approach zero as represented by theregression line with b0 = MEm. Black et al. (1986) describe a similar effectof b0 approaching MEm during a long period (100 days) of insufficientenergy supply. But they had to add yet another empirical equation tomethod 2 to quantify this effect; method 5 does not require that.

It also follows that methods that set b0 = MEm (methods 1 and 3 inTable 13.4) implicitly assume a steady state situation where metabolism hasbeen adapted to a low MEI level, another reason why they are less suitable.Second, the concept of minL/P in method 5 is more elegant (because moremechanistic) than the empirical approach of the linear regressionparameters in method 2. It operates on the same level as Emmans’s (1988,1997) system of potential body protein mass and desired body lipid mass,


PD

maxPD

LD

PDLD

C MEIMEm0 A B

A

B

minMEImaxPD

minLDmaxPD

L/P = minL/P

L/P > minL/P

⎫⎬⎭

⎫⎬⎭

Fig. 13.7. An extension of Fig. 13.3. The PD system is the same as in the right-hand plot ofFig. 13.6. Each PD line has an associated LD line which changes to a steeper slope in thepoint minMEImaxPD where PD and LD reach maxPD and minLDmaxPD, respectively. See thetext for scenarios A, B and C.

which presumes that both entities follow Gompertz functions in relation toage, characterized by three genetic parameters: mature body protein mass(Pmature), mature body lipid mass (Lmature), and a common specific growthrate parameter BGomp.

In Emmans’s system as extended by Ferguson et al. (1994), the pig’sdesired lipid deposition at any point in time makes up for the deficitbetween desired lipid mass (which follows the above geneticallydetermined Gompertz pattern) and actual lipid mass (which may deviatefrom it for a variety of reasons). Hence for a given level of desired lipidmass, desired lipid deposition will be lower for higher values of actual lipidmass. Similarly, in method 5, minLDmaxPD equals [minL/P × (P + maxPD) –L] which for a given level of minL/P is lower for higher values of L, andhence for higher values of L/P.

In the example in Fig. 13.7, the pig with the highest actual L/P level(farthest removed from the minL/P line) reaches its maxPD at MEI level A,where its LD = minLDmaxPD level is lower than for the pig with the loweractual L/P which reaches its maxPD and minLDmaxPD values at MEI level B.

The connection between Emmans’s system and method 5 can beextended as follows.

(13.20)

with as an ‘auxiliary variable’ (Emmans, 1997).

More generally, the right-hand term in Eqn 13.20 is a non-linear functionof (P/Pmature) with genetic parameter (Lmature /Pmature). Like maxPD it variesthroughout the growth period.

It follows from the above that the two terms in inequality (Eqn 13.20)behave the same way, and that one serves as a boundary value for the other. This would suggest a functional relationship between the two entities

minL/P and , which merits further study.

As a consequence, minLDmaxPD must be seen as the lower limit todesired LD. In Fig. 13.7 this leads to the situation where voluntary MEI >minMEImaxPD so that desired LD > minLDmaxPD, indicated by the circlesfor PD (at maxPD) and LD (at desired LD) when the genotype withminMEImaxPD = B realizes a voluntary MEI = C. In that case we can write:

voluntary MEI = MEm + maxPD × EP/kP + desired LD × EL/kL =

= MEm + maxPD × EP/kP + minLDmaxPD × EL/kL + extra LD × EL/kL

(13.21)

The last term (extra LD) must then be due to either: (i) a drive towards anLD (desired LD) higher than minLDmaxPD; or (ii) a drive towards a higher

desired Ldesired P

= ×⎛

⎝⎜⎞

⎠⎟1 46

0 23

..

LP

mature

mature

minL / Pdesired Ldesired P

LP

PP

mature

mature mature

1

≤ = ×⎛

⎝⎜⎞

⎠⎟

−


MEI than minMEImaxPD. Both would lead the pig to realize a datapoint (as inFig. 13.7) beyond the maxPD level; Campbell et al. (1983, 1985), Campbelland Taverner (1988) and Dunkin and Black (1987) have shown that thisactually happens. Option (ii) can more appropriately be expressed as:

(13.22)

It follows that whereas the trajectory for MEI < minMEImaxPD is controlled bya genetic drive for lipid deposition (expressed as minL/P), the trajectory forMEI � minMEImaxPD is controlled by a genetic drive for protein deposition(expressed as maxPD) and a genetic drive for either lipid deposition or‘luxury’ ME intake (which would lead to extra LD through Eqn 13.22).

Final remarks

MEm is quantitatively quite large, and it depends on many environmentalfactors. Hence, errors in its estimation may have considerable effects onmodel predictions. All models described here assume that MEm is notsubject to genetic variation. This assumption is probably false (see Knap,2000, p. 164) and MEm must be characterized for the genotype to besimulated. The system of protein deposition, lipid deposition andmaintenance can be kept internally consistent if MEm and Pm are thenexpressed in terms of P/Pmature (e.g. for growing animals, MEm = α ×

P = according to Emmans, 1997), similar to maxPD

and desired LD (Eqns 13.9 and 13.18). Apart from the models mentionedin the section on ‘Prediction of voluntary food intake’ in ‘Modelcomparison’ above, most models do not simulate voluntary food intake buttreat it as an input parameter. For pig breeding applications, wherevoluntary food intake is of true interest, this is unproductive; this againrequires inclusion of MEm as a genotype characteristic in the model, on thesame level as maxPD and desired LD.

Finally, all models assume EP, EL, kP and kL to be constants withoutgenetic variation; evidence to support or falsify this assumption is virtuallyabsent (see Luiting, 1990, for an overview in poultry, and Emmans, 1997).

Conclusions

For the purposes of animal breeding, desirable features of a growth modelare: (i) that it is consistent with real-life data; (ii) that it is internallyconsistent; (iii) that it has a small number of genotype-specific parameters;and (iv) that it is able to predict voluntary food intake. Given the shortageof reliable data that span a sufficiently wide range of P/Pmature on modern

� × ×PP

Pmature

mature0.73

extra LD voluntary MEI (ME maxPD E / k minLD E / k )

E / km P P maxPD L L

L L

= − + × + ×


genotypes, item (i) will always be hard to meet, and not necessarily as ashortcoming of the models. For the description of maxPD, method 4 ofTable 13.3 seems the most appropriate method to meet the other criteria.With respect to feature (ii) it is best combined with method 5 of Table 13.4for the description of PD at MEI < minMEImaxPD. An additional advantageof this combination of methods is that it provides a smooth and consistentconnection with Taylor’s genetic size scaling principles.

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Emmans, G.C. and Kyriazakis, I. (1995) A general method for predicting theweight of water in the empty bodies of pigs. Animal Science 61, 103–108.

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Knap, P.W. (2000) Variation in maintenance requirements of growing pigs inrelation to body composition; a simulation study. PhD dissertation,Wageningen Agricultural University, Wageningen, Netherlands.

Kyriazakis, I. and Emmans, G.C. (1992) The effects of varying protein and energyintakes on the growth and body composition of pigs. 2: The effects of varyingboth energy and protein intake. British Journal of Nutrition 68, 615–625.

Luiting, P. (1990) Genetic variation of energy partitioning in laying hens: causes ofvariation in residual feed consumption. World’s Poultry Science Journal 46, 133–152.

Moughan, P.J. and Smith, W.C. (1984) Prediction of dietary protein quality basedon a model of the digestion and metabolism of nitrogen in the growing pig.New Zealand Journal of Agricultural Research 27, 501–507.

Moughan, P.J. and Verstegen, M.W.A. (1988) The modelling of growth in the pig.Netherlands Journal of Agricultural Research 36, 145–166.

Neter, J., Wasserman, W. and Kutner, M. (1985) Applied Linear Statistical Models.Irwin, Homewood, Illinois.

NRC (1996) Nutrient Requirements of Beef Cattle. National Academy Press,Washington, DC.

Pomar, C., Harris, D.L. and Minvielle, F. (1991) Computer simulation of swineproduction systems. 1: Modeling the growth of young pigs. Journal of AnimalScience 69, 1468–1488.

Thorbek, G. (1975) Studies on energy metabolism in growing pigs. 2: Protein and fat gain ingrowing pigs fed different feed compounds. Efficiency of utilization of metabolizable energyfor growth. Report 424, Statens husdyrbrugsforsøg, Copenhagen, Denmark.

TMV (1991) Technisch model varkensvoeding: informatiemodel. Research report P1.66,Research Institute for Pig Husbandry, Rosmalen, Netherlands.

Van Milgen, J. and Noblet, J. (1999) Energy partitioning in growing pigs: the use ofa multivariate model as an alternative for the factorial analysis. Journal ofAnimal Science 77, 2154–2162.

Van Milgen, J., Quiniou, N. and Noblet, J. (2000) Modelling the relation betweenenergy intake and protein and lipid deposition in growing pigs. Animal Science71, 119–130.

Walker, B. and Young, B.A. (1993) Prediction of protein accretion, support costsand lipid accretion in the growing female pig and dry sow. Agricultural Systems42, 343–358.


Whittemore, C.T. (1995) Modelling the requirement of the young growing pig fordietary protein. Agricultural Systems 47, 415–425.

Appendix 13.1

In addition to a linear regression of PD on MEI with linear regressioncoefficient r and x-intercept s, De Greef (1992) assumes a ‘constant’ linearregression of LD on MEI with linear regression coefficient t and x-intercept v:

(13.A1)PD r (MEI s)LD t (MEI v)

= × −= × −


He defines the ratio between the two linear regression coefficients as themarginal minLD/PD ratio and assumes that this parameter is a geneticallydetermined constant, which makes minLD/PD dependent on MEI:

(13.A2)

However, because of the law of conservation of energy, the linearregression of LD on MEI can be written in terms of the parameters of thelinear regression of PD on MEI; De Greef does not mention this:

(13.A3)

This shows that t is a function of r, and that v is a function of r, s and MEm,which automatically makes both t and v constants too. As a consequence,the ratio between t and r (i.e. marg minLD/PD) is a constant with value (1 –r × EP / kP) / (r × EL / kL).

Hence given that r = b1 and s = b0, substitution in Eqn 13.A2 showsthat De Greef ’s minLD/PD equals the one of Black (see Table 13.2):

LDMEI ME (PD EP / k )

E kMEI ME (r (MEI s) E / k

E k

1- r E / kE / k

MEIME r s E / k

1- r E / k

t (MEI v)

m P

L L

m P P

L L

P P

L L

m P P

P P

/)

/

=− − ×

= − − × − × =

= × × − − × ××

⎛

⎝⎜⎞

⎠⎟=

= × −

=

minLD / PDt (MEI v)r (MEI s)

tr

MEI vMEI s

margminLD / PDMEI vMEI s

= × −× −

= × −−

= × −−


= − ××

×− + − − × ×

− ×

⎛

⎝⎜⎞

⎠⎟

−=

= − ××

× +

− × × − + × ×−

1 b E / kb E / k

MEIME b b E / k

1 b E / k

MEI b

1 b E / kb E / k

b b E / k ME b b E / k1 b

1 P P

1 L L

m 0 1 P P

1 P P

0

1 P P

1 L L

0 1 P P m 0 1 P P

b b

b

0 0

0

1 11 P P

0

1 P P

1 L L

m 0

1 P P 0

E / kMEI b

1 b E / kb E / k

1ME b

1 b E / k1

MEI b

×−

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

=

= − ××

× − −− ×

×−

⎛

⎝⎜⎞

⎠⎟

minLD / PD margminLD / PDMEI vMEI s

1 r E / kr E / k

MEIME r s E / k

1 r E / kMEI s

1 b E / kb E / k

MEIME b b E / k

1 b E / kMEI

P P

L L

m P P

P P

1 P P

1 L L

m 0 1 P P

1 P P

= × −−

=

= − ××

×− − × ×

− ×−

=

= − ××

×− − × ×

− ×−

=b0

(13.A4)

14 Mechanistic Modelling at theMetabolic Level: a Model ofMetabolism in the Sow as anExample

J.P. MCNAMARA

Department of Animal Sciences, Washington State UniversityPO Box 646351, Pullman WA 99164-6351, [email protected]

Introduction

Models are representations of reality. The fields of nutrition, metabolismand biomedicine have used models to aid in research and its applicationsince before World War II (see Black et al., 1986; Baldwin, 1995; NRC,1998, 2001). A model may also be defined as an ordered way of describingknowledge of some real system. Much research into nutrition of farmanimals since the early 1900s has been used, directly or ‘by default’, tobuild, evaluate and improve models of nutrient requirements. An examplewould be the Net Energy System, first fully described by Lofgreen andGarrett (1968) as applied to beef cattle nutrition. Since then, this modelsystem and others derived from it has been used to determine energyrequirements of many animal species, and to determine energy values offoods and feeds (NRC, 1998, 2001).

An early model in energy metabolism was the linear equation of fastingheat production = 0 + 70 kcal/kg BW0.75. Energeticists such as Brody,Kleiber and Blaxter asked questions about the commonality of energy useby organisms. This model was derived from empirical data and spurreddecades of discussion, experimentation and further more detailed andmechanistic model building, encompassing new information as it becameavailable. These lines of research led to practical empirical models used infood production and human nutrition as well as to mechanistic researchinto the control of energy metabolism in animals. It was the effort ofdescribing increasingly complex chemical knowledge in strict mathematicalterms, in an iterative fashion as more knowledge became available, and


applying the knowledge in the real world as appropriate, that has lead togreat efficiencies and improvements in nutrition.

Billions of US dollars, represented as conservation of resources anddecreased costs of raising feed for livestock and of the labour for feeding oflivestock, have been saved by application of these nutritional models (NRC,1998, 2001). If we assume that application of practical models andresultant changes in ration formulation and feeding has gained a costsaving of $0.50 per market pig, and an average of 100 million pigs killed inthe US each year for the last 20 years, that is a saving of about US$1billion. If we make a liberal estimate of 30 states with two pig nutritionistsper state at a salary of $40,000 and each had a total of $100,000 in totalresearch support for 20 years, that is about $168 million. Not a bad returnon investment. And this is only for pigs.

Our ability to describe metabolic transactions, and their resultant effecton nutrient requirements is critical to raising food-producing animals inefficient ways around the globe. As our knowledge of variation in geneticand environmental situations continues to increase, this author takes thephilosophy that it is only through continuing to develop models ofincreasing complexity, ever grounded in validated research data, that wewill continue to improve our true knowledge, wisdom and theirapplication to feeding the world.

Another use of such models is in teaching. The more complex modelshave great utility for demonstrating to students how the complex systemworks. In addition, when used in a teaching programme which alsoexposes students to practical models used in production or to dailynutrient requirements, the natural comparison between the researchmodels and the practical models can help them to see the directconnections between the specific biological mechanisms and the practicalapplication of them.

One final set of reasons to continue to expand research in models hasalready been given by one much more capable than myself, so I will closethe introduction with a list of reasons for using research models quoteddirectly from Chapter 1 of Modelling Ruminant Digestion and Metabolism(Baldwin, 1995):

Objectives in research modelling:

(a) Integration of existing concepts and data in a format compatible withquantitative and dynamic analyses.

(b) Reduction of conceptual difficulties in analyses of interactions among elementsof complex systems.

(c) Evaluation of concepts and data for adequacy in both the quantitative anddynamic domains.

(d) Evaluation of alternative hypotheses for probable adequacy when currentconcepts are found to be inadequate, and identification of critical experimentsand measurements.

(e) Estimation of parameter values not directly measurable and interpretation ofnew data.

Mechanistic Modelling at the Metabolic Level 283

Throughout this chapter I will follow a philosophy and approachinitiated and developed by Lee Baldwin, quoted above, and use primarilyaggregate level pathway biochemistry, such as protein and fat synthesis,and carbohydrate, fat and amino acid oxidation. Then, we can askquestions about how ‘genetics’, as exemplified by transcription of certaingenes, including endocrine and neural control, can affect the ‘kinetics’ offlux through the pathway, and how some specific environments canattenuate or enhance the genetic drive through substrate supply andresultant hormonal response. Finally, we will present the first descriptionof a model of reproductive control by nutrient use and endocrine systems.I was asked to provide a general overview, and thus I shall, with someexamples from an existing model of metabolism in the pig (Pettigrew et al.,1992a,b). The newer reader may be interested in several other reviews andresearch papers on this topic in dairy cattle and pigs (Black et al., 1986;McNamara, 1998, 2000, 2003, 2004, 2005; McNamara and Boyd, 1998;McNamara et al., 2005). The growing knowledge from genomic researchnow allows us to expand our models of metabolic control, and thus ofefficiency of food production into more and more ‘realistic representationsof reality’.

The Example of Lactation

Lactation provides a challenge not only to the female, but to the modelleras well. Key challenges are the interaction of the complex of organsinvolved in the adaptation and sustaining of metabolism to the newphysiological state, and the range and speed of change in early lactation.One goal for the continued improvement of detail and accuracy is toimprove our quantitative understanding of control of metabolic systems.Pregnancy and early lactation are times of metabolic stress met with acoordinated response from the hormonal and neural systems (McNamara,1994). In order to manage the changes in nutrient flows andinterconversions in the animal there is a complex and redundant system ofcontrol factors, better known as hormones and neurotransmitters(McNamara, 1998; McNamara and Boyd, 1998). Adipose tissue, as anenergy storage reservoir and, as we now understand, an endocrine organ(Mohamed-Ali et al., 1998), adapts to support fetal growth and lactation(McNamara et al., 1985; McNamara and Pettigrew, 1994, 2002a,b; Parmleyand McNamara, 1996). These systems are inextricably linked and excellentreductionist experiments have identified key elements of each subsystem.However, experiments that describe equation forms and parameter valuesfor the control exerted on flux are more limited in availability, primarilybecause of the cost and complexity of conducting such experiments. Amore detailed analysis of quantifying metabolic control is given inMcNamara and Boyd (1998).

It is not always easy or affordable to do research with sufficientrepeated measures to estimate such rapidly changing fluxes, so some

284 J.P. McNamara


compromises must be made. However, even with these limitations, using amodelling approach can help us to design reasonable experiments to helpus improve. Yet another problem is in experimental focus and design.Many of our nutrition experiments are purposefully done in mid- to late-lactation to reduce the variance among animals and are usually short termdue to cost. We, as scientists, need to study the metabolic regulation duringthe lactation cycle more often and in more detail. There has been a lot ofgood new research in genetic control (Bastianelli et al., 1996; Hurley et al.,2000; Lovatto and Sauvant, 2003), but we need to understand how thesecontrols relate to metabolic flux. Also, in much nutrition research, animalsare often grouped in genetically similar units instead of designing studiesto determine the interaction between genetics (with a measure admittedlyas crude as previous production) and diet.

A final limitation to having more detailed and accurate models is(obviously) the complexity of the system itself. Frankly, this author thinksthat proper experiments are often not done because too many scientistssimply either do not appreciate the true complexity of the system, or theydo but are unwilling or unable to actually study it. In order to meet thisgoal of describing complexity, we need to focus more strongly on theendocrine and neural regulation of gluconeogenesis, lipolysis andlipogenesis, amino acid interconversions and of feed intake. An excellentway to do this is in the continued development, testing, evaluation, andchallenging with real data, of dynamic, mechanistic, metabolic models ofmetabolism. We need to change the philosophy of single-investigator, smallstudy funding priorities into one of more team approaches and integrativebiology. We need to have funding proposals and panels who canunderstand and fund whole animal integrative biology.

Brief Description of Dynamic, Mechanistic, Metabolic Models

A key characteristic of a model is how it describes change over time. Amodel that describes a process at one time, usually through an empiricalequation is static. This is true even if the time frame studied was overseveral months. A dynamic model integrates change over time. Both areuseful; however, only a dynamic model will help us truly improve ourunderstanding, first because that is reality; secondly because therequirements at one time or over a short period are always partially afunction of what has come before. Dynamic models using differentialequations over time, and continuous non-linear functions (e.g. Michaelis-Menten) can describe the turnover functions that can be ascribed either tomaintenance or to heat increment, such as ion transport, protein turnoverin the muscle and viscera, and triglyceride turnover in the adipose tissue.When one actually studies these functions, one gets an appreciation for justhow important and variable they can be. For example, a change in muscleprotein turnover of 10%, which is at least a minimum increase in lactation(Pettigrew et al., 1992a,b; Overton et al., 1998; Drackley, 1999; McNamara

and Baldwin, 2000; Phillips et al., 2003) would increase energy formaintenance by about 8.4 MJ/day (see Baldwin, 1995 for calculations andstoichiometry). Over 100 days, that is an error of 840 MJ or about 28 kg ofadipose tissue. In a lactating sow, then, we may err by 170 MJ or over 5 kgof body fat in predicting energy use.

Integrating Genetic Elements into Metabolic Models

There has been a wealth of work on genomics, metabolic control theory,flux control and the like (Roehe, 1999; Hirooka et al., 2001; Quintanillaet al., 2002). Simplistically, all kinetics is genetically controlled, eventhough many environmental, including nutritional, effects may be larger(e.g. an animal with a greater genetic drive for muscle growth mayaccrete less muscle than a genetically inferior animal if the nutritionalinputs differ sufficiently). There has been significant work done onstructural genetics and gene expression in pigs (Roehe, 1999; Hirooka etal., 2001; Quintanilla et al., 2002). There is even work beginning onbreeding for traits important for animal welfare (Kanis et al., 2005); it ispast time to start working elements of genetic control into metabolic fluxmodels.

There should be certain objectives to doing this, such as:

1. Develop a model that integrates transcription of genes coding for keymetabolic enzymes in growing, pregnant and lactating pigs to understandunderlying patterns of control.2. Develop a model relating genetic variance among lines of pigs todifferences in metabolic patterns in order to identify variation in efficiencyof food use. 3. Use models of metabolism and metabolic control to identify whichgenes would exert the majority of control over these flux rates. 4. Integrate models of structural genomics with metabolic models to identifykey patterns and sequences that are common to the most efficient animals. 5. Integrate kinetic flux models with those describing secretions andmechanisms of endocrine action to identify the quantitative importance ofkey control elements.6. Develop a model of the interactions between nutrient use patterns,endocrine secretions and actions, and downstream effects on genetranscription to improve the understanding of key response elements.

Hargrove (2004) has given some examples of modelling gene expression,which in turn regulate kinetic flux. These models may be used as teachingtools, such as described by Collins (2004), or as hypothetical models to helpdirect mechanistic research trials. We also need to find ways to connect‘pure gene level’ models of genetic expression (Jiang and Gibson, 1999a,b;Hirooka et al., 2001) with kinetic models, as the first exists to control thesecond! With agricultural animals, we have sufficient genetic records thatwe have been incorporating them into models for at least 40 years.

286 J.P. McNamara


Enzymes control the rates of chemical reactions. Key enzymes arecontrolled in turn by substrate and product concentration, allostericcontrol by other molecules (such as ATP or messengers from hormonalaction); and hormonal control of enzyme synthesis or destruction. A simplegraphic (Fig. 14.1) summarizes these well-known control elements(McNamara, 2005). Some simple examples of the types of control are givenin Table 14.1. These varied and redundant mechanisms have direct controlon flux rates through the key pathways of glucose synthesis and oxidation,and fat and protein synthesis. Sometimes control is simply exerted bydetermining the presence or absence of a process or pathway. Otherenzymes, primarily those we study in nutrition, are actively regulated inboth short term (minute-to-minute) to longer term (hours, days) to directthe use of nutrients by cells, and more pertinent to the animal, by organs.Most of these processes have several levels of control, from substrates andproducts to hormones. Substrate concentration is often the greatesteffector of flux, but in the example of lactation, a sow might be consumingall the starch she can, but not as much of that absorbed glucose will go tobody fat as it would in the non-lactating state because the hormones oflactation have altered several genetic level control points (transcription ofacetyl CoA carboxylase for one).

Thus we must model these different levels of control, followingobjectives such as those laid out by Baldwin, or those above, or others, tohelp detail the specific role of each type of regulation. Some potentialmechanisms will be confirmed as the critical initiative events or responses,

Substrate

product

enzyme

DNA transcription site *

mRNA

Aminoacids

cAMPHormone* orNutrient

Receptor*

Nucleotides

*K2

Vm,Ks*>>> Pathway >>>

End Product

Initialsubstrate(s)

<<< Pathway <<<

*K1

Fig. 14.1. Conceptual model of control of flux through a reaction, indicating types of geneticcontrol over flux. Conceptual flow of genetic mechanisms of control of flux. The asteriskindicates states (proteins, nutrients) that are genetically controlled and may have ameasurable heritability. Each state (box) and rate (arrow) can be measured to determineappropriate parameters. Large dashes indicate a mechanistic state (with components), smalldashes indicate a lower level of organization to the main objective.

288 J.P. McNamara

Table 14.1. Examples of control of enzyme-catalysed reactions.

Catalytic level: Control of enzyme activity; does not require protein synthesis orbreakdown, usually for the short term; response time in seconds, effect can be quicklyreversed or removed.

Level and type of control Controllers Example reactions

Substrate activation Glucose Glucokinase, Phosphofructokinase

Product inhibition Fructose-6-phosphate PhosphofructokinaseFatty acids Fatty acid synthetaseAcetyl CoA Acetyl CoA carboxylase

Allosteric activation and inhibitionHormonal: Insulin, glucagon, corticoids, usually via:Phosphorylation Pyruvate dehydrogenaseand dephosphorylation Hormone sensitive lipase

Metabolic: ATP, citrate, glucose, and other metabolites:Glucose oxidation PFK, FBP-aceFatty acids Ac CoA carboxlyase, FAS

Concentration level (control of enzyme presence or concentration); usually requiresprotein synthesis or breakdown; fast to slow (few hours or days; may take longer forresponse to be reversed or removed).

Enzyme destruction (increasing proteolysis and removal of enzyme)

Enzyme synthesis (increasing synthesis of enzyme, through classic transcription andtranslation mechanisms)

Insulin, glucagon, thyroid hormone, growth hormone,Prolactin, estrogen, progesterone, testosterone

GlucokinasePDH, AcCoA Carb.FAS

others may be identified to be important, but downstream, or secondary interms of quantitative control. Others may be identified as redundant,acting only when other systems are not operating. More than one controlsystem may operate on an enzyme to control flux, but the net effect ofthree such controllers does not differ from that of two or one (and any oneof the three can do the job). An example might be pyruvatedehydrogenase (PDH), which is under allosteric control by hormones andtheir second messengers, substrate, products and downstream productssuch as ATP. Yet one or all of these controllers might reduce PDH activityto negligible rates by themselves.

The enzymes of primary importance in glucose and fatty acidmetabolism are controlled at multiple levels from enzyme activation/deactivation to DNA transcription and RNA translation. Those under thestrictest control would include glucokinase, phosphofructokinase, fructose


bisphosphatase, pyruvate dehydrogenase, acetyl CoA carboxylase, fatty acidsynthetase, phosphoenylpyruvate carboxykinase and pyruvate carboxylase(Tepperman and Tepperman, 1970; Girard et al., 1997). For mammals it isthe maintenance of a relatively constant supply of blood glucose to the brainthat provides a large part of the metabolic control in the body. In addition,homeorhetic controls in different physiological states then provide furtherregulation. Certainly no nutritional model is pertinent which does notinclude some elements of these control points on flux. In turn, the state andrates of glucose use directly affect the rates of fatty acid and amino acidmetabolism. So it is important that models do an adequate job of describingthis control.

All enzymes and hormones are genetically regulated, from immediategene transcription and translation, to heritability of variations in hormoneand enzyme synthesis and secretion. Some examples may be found inGirard et al. (1997), Bosch et al. (1999) and Daniel et al. (1999). Muchgenetic variation may have its initial effect in the central nervous system orin endocrine organs such as the thyroid or pancreas, but the end effect ison flux. Years of genetic selection and growth and lactation trials in pigs,chickens and cattle have proved the point (McNamara, 2000; andMcNamara and Boyd, 1998 for examples). It is also pertinent to describethe shorter-term genetic controls such as gene transcription andtranslation in models. The objective of a model dictates (or should) themodel components. If an objective is to model metabolic flux in any onespecies of animal, allowing for description of variation among animals,then genetic control by definition must be included.

Included in genetic effects on flux would be the presence or absence ofa transcribed and translated gene for an enzyme, the number of copies(concentration) of the enzyme, as well as the enzyme catalytic ability itself.While the latter can change through various isozymes and there are somespecies differences, within a species this is not thought to be a majorcontrol point. It is the transcription of the gene and translation of themRNA that alters the concentration of an enzyme, as well as the hormonaland neural control of enzyme activity, that are the primary genetic control.For example, lipoprotein lipase activity will change under the control ofhormones of pregnancy and lactation, in both the mammary gland and theadipose tissue. In this instance, the change is in opposite directions(decreasing flux in adipose tissue and increasing flux in mammary;McNamara, 1998). This is certainly a genetic effect, and is probablyheritable. Adipose tissue enzyme activity is heritable in relation to body fatamount in agricultural animals (McNamara and Martin, 1982; Hausmanand Hausman, 1993; McNamara, 1998; McNamara and Boyd, 1998),albeit the actual causative gene or genes (whether in the adipose or due tohormonal differences) is not clearly known as yet.

Thus, a valid argument is that the initial conditions in growth,initiation of pregnancy or lactation, are genetic effects that set theoptimum for the ensuing states and rates, which of course can beattenuated or enhanced by the environment. In the example of milk

production (as most phenotypes), genetic control is a pleiotropic effect,with many genes involved, including those controlling cellulardifferentiation and senescence as well as those genes for milk protein,lactose and fat synthesis. This may be a phenotypic single trait (milkproduction), but many genes are involved. Many potential effectorsaggregate to control a few key pathways (protein synthesis, proteolysis, fatsynthesis, esterification, lipolysis, lactose synthesis, glycogen synthesis andglycogenolysis, gluconeogenesis). Thus a model may initially incorporatethe concentrations of ATP, acetyl CoA, acyl CoA, free CoA, citrate, insulin,glucagon and translation rates of the gene encoding for acetyl CoAcarboxlyase, on the flux through this enzyme.

So, back to the basic objective of a model. A model with a primaryobjective to describe the control of flux of carbon through the acetyl CoAcarboxlyase reaction would include certain pools, equation forms andparameters at a very specific chemical level. Such conceptual models havebeen constructed (Girard et al., 1997 and references therein). However, amodel with the primary objective of describing the metabolism of absorbedenergy-containing nutrients, including amino acids, related to long-termfeeding strategies in the lactation phase of the reproductive cycle of sows(Pettigrew et al., 1992a,b) would not likely have the same level of detail. Yetit would contain genetic control elements to describe the effects of geneticselection and nutrient supply on fatty acid synthesis, in adipose tissue andthe mammary gland. By aggregation of the total sum of reactions into thelipogenesis pathway, for example, we can describe the reactions at ourdesired level of biological organization with pertinent descriptions ofgenetic control.

In this type of model – pathway biochemistry, we can sum up controlof an aggregated pathway in a simple and scientifically correct fashion.Continuing to use lipogenesis as an example, kinetic flux can be describedthrough the two Michaelis-Menten parameters of maximal velocity (Vmax)and substrate sensitivity (Km), example shown in Fig. 14.2. Relevantnutritional models with an objective of describing input/outputrelationships at the organism level should be dynamic and aggregated atthe level of pathway biochemistry in each organ. That really is what theanimal does. Higher level (whole body) or lower level (individual cells,pathways, or enzymes) models are useful, but have a different objective.

This type of description can provide simple possibilities forconstruction and testing of models integrating genetic elements. Theequation below is used in Pettigrew’s model of metabolism in lactating sowsto describe glucose conversion to body fat (Pettigrew et al., 1992a):

UGlTs = vGlTs /(1 + (MGlTs/cGl)), and (14.1)

MGlTs = MAGlTs * (( cGlr/cGl)tAGlTs); (14.2)

where MGlTs is the substrate sensitivity constant for glucose, and iscontrolled by the concentration of glucose (reflecting the hormone insulin)such that as glucose concentration rises (insulin increases), the sensitivity

290 J.P. McNamara


constant becomes smaller and reaction rate would increase. Therepresentation of insulin (cGlr/cGl) is raised to a theta value that can alterthe sensitivity of the reaction.

Let us explore the genetic elements in this equation. The Vmaxrepresents the total amount of catalytic activity available, in this case, in thesum of body adipose tissue (at other levels of aggregation, this may be in aspecific organ, cell or single enzyme or receptor; Figs 14.2, 14.3). This iscontrolled genetically, inherited from the parents. The Vmax itself may bevariable, decreased by periods of energy deficit that decrease the total massof adipose tissue. The value of this parameter for a population of animalsmay be determined in studies combining direct measures of enzyme

0

1

2

3

4

5

6

7

8

9

10

1 1.8 2.6 3.4 4.2 5 5.8

Substrate Concentration

Rat

e of

Rea

ctio

n

Vm = 10, Km = 3

Vm = 15, Km = 3

Vm = 10, Km = 1

Theta = 3

V = Vmax/(1 + (Km/[S])Θ)

Fig. 14.2. Example of genetic control over substrate saturation (Michaelis-Menten) reactions.A typical example of a reaction with a maximal velocity and substrate sensitivity. In anaggregated pathway model, the Vmax is the genetic component representing total enzymeconcentration, cell number, or tissue mass or protein. The substrate sensitivity constant isalso genetically controlled and may also represent enzyme concentration. The theta value onthe (Km/[S]) function indicates sensitivity to substrate, which is also genetically controlled.This may represent sensitivity to hormonal or substrate/product allosteric control.

activity and measures of total body adipose protein content. The Kvariable, substrate sensitivity, is also inherited (but may not have a highheritability, as the catalytic sensitivity of this enzyme, as for most, is afunction of the molecule, not concentration of the molecule). Theaggregate pathway sensitivity is partly controlled by environmentalinfluences that alter insulin concentrations. The K for glucose in thisreaction reflects the availability of glucose to provide energy. The equationalso introduces the concept of ‘anabolic hormone’, or insulin, which iscalculated from (cGl/rcGl), such that as glucose concentration increasesagainst the normal or reference glucose concentration, the effect of glucoseincreases, decreasing the denominator and increasing reaction rate. Thesensitivity of insulin to glucose availability may be changed to reflectgenetic differences in insulin function if data are available to justify such achange.

The genetic elements of any metabolic reaction can be incorporatedinto flux control. In Fig. 14.2, equation forms for substrate saturation,

292 J.P. McNamara

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

Concentration of Hormone

Per

cent

bou

nd

Normal

Hi M

Lo K

Hi Theta

11.

41.

82.

22.

6 33.

43.

84.

24.

6 55.

45.

8

Fig. 14.3. Example of genetic control over hormone-receptor binding reactions. A typicalexample of a hormone-receptor reaction with a maximal binding of receptor [R] anddissociation constant [K] in response to hormone [H] concentration. The maximal binding ofhormone receptor is the genetic component, as is the dissociation constant. The hormoneconcentration is also genetic, but would be represented with another model showinghormone synthesis and degradation rates. Changing either [R] or K by genetic selection willchange hormone-receptor binding and, possibly, the end result in flux in the cell (by alteringallosteric control of the reaction given in Fig. 14.2, for example).


which includes most controlled reactions in metabolic pathways, and inFig. 14.3, per cent receptor binding for hormonal control are shown.Through these equations, genetic elements are integrated into fluxmodels. Maximal rates and substrate sensitivities are genetically inheritedand, in some cases, have a measurable heritability. Substrate sensitivity ismore a function of the molecule itself than of the number of molecules, butin an aggregate pathway, changes in substrate sensitivity can be measured(McNamara, 1998; McNamara and Baldwin, 2000). Binding maxima andsensitivity also are so controlled. We can also envision the Vmax varyingduring the life cycle or by hormones related to environmental orphysiological state. An example is available in the Pettigrew model for thecontrol of lipid storage in adipose tissue:

dQTsdt = PFaTs + PGlTs –UtsFa (14.3)

UFaTs = vFaTs / (1 + (MFaTs / CFa) + (M6FaTs / CGl)) (14.4)

UTsFa = (vTsFa / (1 + (MTsFa / Clh))) * (Qts**0.67)*(1–((QsTs/Qts)**thTsFa)) (14.5)

In Eqn 14.3, we see the accumulation of triacylglycerols (Qts) on a dailybasis as a function of synthesis from fatty acids (re-esterification, PFaTs),de novo lipogenesis (PGlTs, given in Eqn 14.1) and lipolysis (UTsFa). Wesaw how lipogenesis can be modelled to include genetic andenvironmental control in Eqns 14.1 and 14.2. The same is true for re-esterification (Eqn 14.4), which is controlled by a maximal velocity (vFaTs),and a sensitivity constant for fatty acids (MFaTs) as well as for glucose(M6FaTs). These can be considered to be defined by genetics (presence orabsence of genes; transcription of genes in adipose depots). Obviously,then the environmental control of gene transcription can also bemodelled, if we can measure the effects of nutrients or hormones on genetranscription. The control by substrate availability is self-evident.Triacylglycerol lipolysis (UTsFa, Eqn 14.5) is controlled by a maximal rate,as well as by ‘lactation hormone’ (Clh), which is a function of a basiclactation curve:

Clh = MYF *(1.0 + 4.02E – 2* (t – T2) – 7.65E – 4 * (t – T2)** 2) *(step(T2) – step(T3)) + 0.00001 (14.6)

Equation 14.5 (lipolysis) is completed by scaling to metabolic body size (astep that, in this author’s opinion, is not warranted, but it was theprevailing thought of the day). This equation is obviously simplistic andaggregated, but provides a clear and concise view of the flux. We canmodel more control as available data warrant it. Genetic control elementscan be included in simple (or complex) descriptions of flux. A theoreticalmodel describing upstream regulation (transcription control), andinclusion of other hormones (catecholamines, thyroid) can be built up fromhere.

Lipolysis is controlled by catecholamine binding to beta-adrenergicreceptors. There are data in cell systems or cell free systems on binding

kinetics of this system, and there are data in adipose tissue on the responseof cAMP and lipolysis to concentrations of catecholamines (McNamara etal., 1992; McNeel and Mersmann, 1999 and references therein).Expanding on Eqn 14.5 may yield:

UTsFa = (vTsFa/(1 + (MTsFa /Clh)))* (Qts**0.67)*(1�((QsTs/Qts)**thTsFa)) (14.6)

VTsFa = v1TsFa*(cAMP/rcAMP) (14.7)

cAMP = KcAMP*[B2RecNE] (14.8)

[B2RecNE] = MB2Rec /(1 +(Kd/[NE]θ)) (14.9)

such that the maximal velocity of lipolysis (VTsFa; let us say this representstotal active hormone sensitive lipase) is a function of cAMP concentration(cAMP) in relation to a reference concentration (rcAMP); cAMP con-centration is a function of per cent beta-2-adrenergic receptor bound([B2RecNE]); and bound receptor is in turn a function of maximal binding(MB2Rec), dissociation constant (Kd) and norepinephrine concentration([NE]θ), raised to a power (sigmoidal function, as in Fig. 14.3). Furtherhomeorhetic control (Bauman and Vernon, 1993; McNamara and Boyd,1998) on the beta-adrenergic response may be exerted by lactationalhormone to increase per cent bound during lactation:

MB2Rec = MB2Rec * (Chl/rCHl) (14.10)

This treatment is basically the same as that proposed in the cow model ofBaldwin (Baldwin, 1995; Baldwin et al., 1987a,b,c), but with more points ofcontrol exerted on the final pathway flux, as in reality. A point to note isthat in fact in any given condition (nutritional status, day of lactation), theactual pathway flux described in the new model may be exactly the same asin the old model, but with a fuller description of control.

Another example of descriptions of control within this model of flux isthat of glucose utilization. It is glucose around which the major regulatoryprocesses of the body have evolved. The brain and central nervous systemrequire glucose. Although the mass amount of glucose required by thebrain is small compared to that used by the mammary gland or otherorgans, the regulatory mechanisms invoked as glucose availability changeshas a major affect on metabolic rates in other organs. Recent work in miceshows that altering glucose use by food restriction, or by gene insertion forproteins such as the insulin dependent glucose transporter (GLUT4) resultin changes in transcription of thousands of genes (Fu et al., 2004).

Carbohydrate in the body which is metabolized for energy (or to makefat or lactose) eventually is converted to triose phosphates or glucose, or isused through the same metabolic pathways so, for simplicities sake we canaggregate a lot of this. So changes in glucose concentration or pool size(Gl) in the body are summed as:

dQGldt = PAaGl + PAbGl + PPaGl + P6TsFa – UGlTs – U6FaTm – U6FaTs – UGlCd – UGlGc – U6GlTs – UGlLm – UglTm (14.11)

294 J.P. McNamara


We sum the uptake of glucose, gluconeogenesis from amino acids (PAaGl),absorbed glucose (PAbGl), glycerol from lipolysis (P6TsFa), and subtractthe use of glucose for milk and body fat synthesis (UGlTm, UGlTs); use forglycerol in TAG (U6FaTm, U6FaTs), oxidation to carbon dioxide (UGlCd),glycogen (UGlGc), lactose (Lm). In this summative equation, all geneticeffects are included in the equations describing each pathway asexemplified above (Fig. 14.4).

The use of glucose has several dozen if not hundreds of possible controlpoints throughout the body. This ‘obvious statement’ quite often getsforgotten for its simple obviousness, resulting in interpretation of researchresults far beyond their true importance. For example, one might study theeffect of glucose use in muscle, and discover a novel pathway or regulatorypoint and a ‘big deal’ is made of that. That is fine. However, quite often wedo not then make the connection that the glucose use in the muscle affectsand is affected by every single other use of glucose in the body. For example, thespecific process in the muscle may, in fact, have a major effect on glucosedynamics, or might in fact be so overwhelmed or attenuated by otherprocesses in other organs that the true physiological significance is minor.This becomes truly obvious only when we start to construct models thatmust make the connection. An example is that one animal or set of animalswill have genetically controlled different maxima for gluconeogenesis thanothers, and this definitely will affect their glucose and amino acid use.

Thus, glucose used is a function of the genetic maxima and substratesensitivity, and this is enhanced or attenuated by environment. It isdifficult, perhaps, conceptually as well as quantitatively, to determine theexact mechanism of this genetic control. It is known that the total numberof udder cells is a correlate to milk production, but certainly does notaccount for the majority of genetic variance. Flux control is exerted inlarge part by the number of proteins translated (enzyme concentration, ormaximal velocity). Other anatomical or physiological factors also come intoplay. A greater vascularity increases the maximal substrate supply. This iscertainly inherited, but may be difficult to assign a parameter value to.Genetic responses in other tissues to the hormones of lactation also affectsubstrate supply.

The Modelling Process: Experimentation, Hypothesis Setting andImprovement

Unfortunately, this particular model has been relatively ignored byscientists studying lactational biology of the pig, and I think that ignorancehas limited our progress in this area. There is a lot of biology we still donot know about the pig, including metabolic regulation in the mammarygland, muscle and adipose tissue. There are many reasons why morenutritionists or those studying metabolic control do not work in moreintegrated approaches; however, the advances in genomic knowledge andcontrol of gene transcription are starting to reverse the trend. As we learn

296 J.P. McNamara

0

0.002

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0.01

0.012

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0.016

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Day of Lactation

Sim

ulat

ed b

lood

glu

cose

con

cent

ratio

n, M

0

0.1

0.2

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Day of Lactation

Glu

cone

ogen

esis

, mol

es a

min

o ac

id /d

Fig. 14.4. Simulations of glucose use in a model of metabolism in the sow. (a) Shows theconcentrations of blood glucose during lactation and (b) shows rates of gluconeogenesisfrom amino acids. The different lines indicate alterations in either intake or in demand bymammary gland (McNamara and Pettigrew, 2002a,b). This demonstrates the behaviour andsensitivity of the model. Further work will then link glucose concentrations and downstreamendocrine signals to reproductive functions (Fig. 14.6).


more about the genome and regulation of transcription, we are comingback to why we started to study it in the first place: to learn more aboutcontrol of metabolism, nutrient use and practical farm animal efficiency.

Our laboratory conducted a number of challenges of this model overthe last 13 years to help refine it and learn more about metabolicregulation. They are too extensive to describe here, but they focused on afew key areas: how do energy intake and energy demand (milk productiondriven by litter size) alter use of nutrients in the non-mammary tissues(McNamara and Pettigrew, 2002a,b)? How do our direct estimates ofparameters of maximal velocity and substrate sensitivity for lipidmetabolism in the adipose tissue match those first proposed in the modeland, if they do not, would altering them in the model improve per-formance (Parmley et al., 1996)? What parameters can easily be identifiedand linked to genetic control, and how then do we go about getting betterestimates of their values (McNamara, 1998; McNamara and Boyd, 1998)?

During lactation, the increase in feed intake and in milk synthesiscauses major increases in metabolic rate in the liver (Pettigrew et al.,1992a,b; Reynolds et al., 2003). These processes all require an increase inenergy need (usually categorized into increased heat increment in NetEnergy schemes). In the most recent version of the sow model, ATP use ison demand for the metabolic reactions that occur (McNamara andPettigrew, 2002a,b) and the increase in demand in turn requires increasedoxidation (irreversible loss) of a mixture of glucose and fatty acids. If, forexample, there are systematic errors in the model parameters which setthe rate of muscle protein turnover and metabolic rates in the liver (ratesthat have genetic components) such that these energetic costs are too low,then the error will actually show up in an over-accumulation of fat in themodel sow.

The utility of modelling has been recently demonstrated with such anexample in the cow model of Baldwin (1995). Others and I have beenworking with this model, challenging its performance with experimentaldata and refining the model as we go (McNamara and Baldwin, 2000;McNamara, 2005; Hanigan et al., 2005). One result obtained in allsituations: the model cow accumulated too much fat. Many measurementswere made to determine possible reasons for this error, and much novelinformation on regulatory biology was found. Yet, recently, it has beenproposed that in fact the yield of ATP from electron transport is likelylower than the three ATP/NADH2 and two ATP/FADH2 incorporated intothe model. If these figures are in fact 2.5 and 1.5, then the demand forATP is not met as efficiently as we thought. In fact, changing theseparameter values in the model thus increased the obligatory oxidation ofglucose and fatty acids and then fed back on the uses of glucose, acetateand fatty acid and the over-accumulation of fat was primarily repaired(McNamara, 2005). This is an example of the modelling approach workingin a research programme: a properly constructed model founded inproper biological knowledge can help to point out specific errors in ourknowledge that otherwise would be quite hard to uncover.

Using this information, we easily went back to test the effects in the sowmodel described herein. We had known that this model also over-predicted the accumulation of body fat on low-fat, but not high-fat diets(McNamara and Pettigrew, 2002a,b), and wondered whether correctingthe ATP yield could prevent this in the sow model. Fig. 14.5 shows that theanswer is ‘It depends’. Reducing the ATP yield by 16% corrected the erroron the low fat diet, but then did not describe enough fat on the high fatdiet. This indicates that there are other errors remaining. Certainly someof these are related to the parameters for glucose use and body fatsynthesis, which are genetically regulated. Construction of more refinedmodels including genetic regulation will help us define and correct furthererrors.

A question that can now be asked is: ‘Can we select for, or by othermeans change, the genetic control of body fat synthesis to improveefficiency of milk synthesis (without reducing the health of the cow)?’Complex mechanistic dynamic models, integrating ‘genetics’ into ‘kinetics’,can help us to predict the potential outcomes of such decisions. Thesesimple examples given here just touch on the complexity of geneticchanges for ‘practical traits’ at the organism level. It is one thing to do a‘knockout’ to determine what happens if a protein is not made. But it is a

298 J.P. McNamara

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Bod

y F

at, k

g

LoFnorm

HiFnorm

LoFHiPO

HiFHiPO

Hi F Obs = 29.4

Lo F Obs = 26.3

Fig. 14.5. Effect of altering ATP yield on use of body fat in lactation of sows. If the currentnewest estimates of ATP yield from NADH2 and FADH2 of 2.5 and 1.5 are correct, this willhelp explain the over-prediction of body fat. The sow model over-predicts the accumulation ofbody fat in situations of high fat intake. However, the error does not seem to be in thestoichiometry of the adipose tissue equations (McNamara and Pettigrew, 2002b). If instead,the original older estimates of ATP yield were too high, then less glucose and fat would beoxidized to supply the ATP demand, and more body fat would accumulate. An example ofhow a properly constructed model can help to point out errors in knowledge, which can thenbe corrected.


different problem to describe and predict what may happen due to morepractical genetic changes. That is our charge, however.

Differences in milk production, body fat and body protein are geneticand inherited. Rates of amino acid, fatty acid and glucose use in the majororgans are also genetically controlled. Empirical applied data (feed intake,litter growth) can be collected and compared to a ‘theoretical’ model to asksuch questions as: ‘What would we expect the range of milk production tobe if this number were used as the Vmax for lactose synthesis (or bodyprotein synthesis)?’ Here again, our quantitative knowledge ofbiochemistry allows us to ask such questions. What factors control genetranscription in the mammary gland? Conceptual and quantitative modelswill be of great assistance here to codify our knowledge and set hypotheses.

How About a Model of Reproduction?

In 1992, Pettigrew et al. (1992a) wrote:

The mechanisms connecting the diet to reproductive performance arepresently unknown but may include variations in voluntary feed intake,digestion, absorption, metabolism of absorbed nutrients, and endocrine effects.Clear understanding and manipulation of this connection to optimize long-term sow herd performance requires ability to track, systematically andquantitatively, dietary effects through the various processes to reproductiveperformance. The objective of the present work is to begin to develop therequired systematic, quantitative understanding of that connection.

In the 12 years since that article was published, a large body of work hasbeen done on the control of reproduction in sows, and even more in dairycattle. Yet no one, to my knowledge, has published a true mechanisticmodel of nutrient metabolism and reproduction. At the same time, severalcompanies are promising great results in reproductive improvement withvarious nutritional products or management. So, if the results are sopredictable, why don’t we have a model? It should have been easy! I havealluded to several of the political, scientific and monetary reasons in theparagraphs above. Those won’t be solved here or soon. Thus, I would liketo present the possibility of the beginnings of such a model, to continue thework proposed by my colleagues long ago.

We know growth and ovulation of viable eggs is under the regulationof follicle stimulating hormone (FSH) and luteinizing hormone (LH).Further, much is understood about the relationship of glucose flux toovulation, effects of fats and IGF on the ovary, and potential negativeeffects of ammonia or urea on the uterine environment (Garcia-Bojalil etal., 1998; Staples et al., 1990; Mattos et al., 2002; Westwood et al., 2002;Farmer and Palin, 2005). A flow diagram connecting the essential elementsof the Pettigrew sow model and Baldwin cow model with reproduction isproposed in Fig. 14.6. Examples of equations necessary to describe part ofthe system may include control of FSH and LH secretion and degradation,and their effects on follicular development and ovulation.

dLH = secLH – degLH (14.12)

secLH = pLH * kGlLH * kLpLH * kEsLH (14.13)

Deg LH = KdegLH * [LH] (14.14)

sFSH = pFSH * kGlFSH *kPGFSH – KEsFSH (14.15)

Deg FSH = KdFSH * [FSH] (14.16)

V RFoll to DevFoll = VReDe * (KfollFSH * [FSH]) (14.17)

V DevFoll to Domfoll = VDvDo * (KfollFSH * [FSH]) (14.18)

Equation 14.12 shows the change in LH as a function of secretion anddegradation, secLH (Eqn 14.13) is a function of synthesis, glucose,luteinizing hormone releasing hormone and oestrogen. Degradation ofLH (Eqn 14.14) is some constant (but it does not have to be a constant), thesame is true for FSH (Eqns 14.15 and 14.16). Eqns 14.17 and 14.18describe the development of developing follicles from resting follicles andon to dominant follicles. I would contend that there is enough data in theliterature to begin to construct these equation forms and parameter values.Further data would need to be found or collected to relate glucose

300 J.P. McNamara

Hypothalamus

Pituitary

FSH LH

Developingfollicles

OvulatedEgg(s)

ImplantationFetus(es)

Glucose

LeptinOestrogen

CorpusLuteum

Progesterone

Fatty Acids

AminoAcids

NH3

DominantFollicle

IGF1

BodyProtein

Adipose

(CLA)

Fig. 14.6. Description of a model of nutrient control of reproduction in the sow. Flux rates ofseveral nutrients, and secondary hormonal responses, have direct effects on folliculardevelopment, ovulation and uterine environment. Why do we not yet have a mechanisticmodel of nutrient/reproduction interactions, given the wealth of information we have? Here ispresented a flow diagram of one such model. Equation forms will need to be derived andparameters estimated. The model then becomes a framework for identifying inadequacies inour knowledge.


concentrations to these functions, and on to all the equations depicted inthe flow diagram of Fig. 14.6. From there we can begin more specificexperiments into both applied models and models of genetic (genomic,transcriptional, translational) control of these processes. Why not?

Summary and Implications

When one stands on the shoulders of giants, one is humbled and gratefulthat the horizon is closer in view. While the objective of eventuallyunderstanding everything that happens in an animal may be far beyondthe horizon, progress is being made and our true purpose of feeding theworld efficiently throughout many geographical areas and for manycenturies is becoming closer. A quantitative and systems approach is theonly way to continue upon this path. Reductionistic research, especiallyinto the true functionality of the genome and physiological control ofmetabolism will be essential to improvement. In addition, continued effortsin simple, economical and effective chemical methodology for definingfeedstuffs is a must. But over-riding all, is the integration of knowledge,data, and concepts, into an organized representation of reality: a modelthat will achieve our goal. Research can help us overcome politics andother human frailties with a system that can ensure adequate foodsupply for all. That is our ultimate goal, and societal, industrial andgovernmental support for the modelling approach to research is critical toachieve it.

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Pettigrew, J.E., Gill, M., France, J. and Close, W.H. (1992b) Evaluation of amathematical model of lactating sow metabolism. Journal of Animal Science 70,3762–3773.

Phillips, G.J., Citron, T.L., Sage, J.S., Cummins, K.A., Cecava, M.J. and McNamara,J.P. (2003) Adaptations in body muscle and fat in transition dairy cattle feddiffering amounts of protein and methionine hydroxy analog. Journal of DairyScience 86, 3634–3647.

Quintanilla, R., Milan, D. and Bidanel, J.P. (2002) A further look at quantitativetrait loci affecting growth and fatness in a cross between Meishan and LargeWhite pig populations. Genetic Selection and Evolution 34, 193–210.

Reynolds, C.K., Aikman, P.C., Lupoli, B., Humphries, D.J. and Beever, D.E. (2003)Splanchnic metabolism of dairy cows during the transition from late gestationthrough early lactation. Journal of Dairy Science 86, 1201–1217.

Roehe, R. (1999) Genetic determination of individual birth weight and itsassociation with sow productivity traits using Bayesian analyses. Journal ofAnimal Science 77, 330–343.

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Tepperman, J.and Tepperman, H.M. (1970) Gluconeogenesis, lipogenesis and theSherringtonian metaphor. Federation Proceedings 20, 1284–1293.

Westwood, T., Lean, I.J. and Garvin, J.K. (2002) Factors influencing fertility ofHolstein dairy cows: a multivariate description. Journal of Dairy Science 85,3225–3237.

15 The Place of Models in the NewTechnologies of ProductionSystems

D.M. GREEN1 AND D.J. PARSONS2

1University of Oxford, Department of Zoology, South Parks Road, Oxford,OX1 3PS, UK; 2Cranfield University, Silsoe, Bedford, MK45 4HS, [email protected]

Introduction

The problem

Farmers aim to produce livestock within the tight targets imposed on themby their customers (increasingly, supermarkets) and to do so at a profit.Both the consumer and the government, however, are increasingly beinginfluenced by concerns other than price alone, including issues such asenvironmental damage and pollution, human and animal health andanimal welfare (Fox and Sachs, 2003). The role of science and technologyin agriculture is to enable the farmer both to increase profit and to addressthe further concerns of the consumer.

Integrated management systems

Most parts of the animal production process have been subject toautomation. Equipment is available to monitor the animals, to feed them,and to control their environment. Integrated management systems (IMS)represent an attempt not only to combine these various subsystems butalso to delegate control of them to an automatic controller (Frost, 2001).The potential benefits of IMS are multiple (Whittemore et al., 2001a).Precise control, while freeing staff time, will allow precise formulationand rationing of the diet to improve economic and environmentalefficiency of livestock production, with a product of high quality giving ahigh margin, while also addressing health, welfare and environmentalconcerns.


At the core of an IMS lies a model, which provides two benefits. First, itallows forward predictions to be made of the impact of managementdecisions: the best course of action can then be automatically determinedby the system. Secondly, IMS involves considerable automated monitoringof livestock and its environment therefore the model provides a powerfuldiagnostic tool to detect when livestock performance deviates from thatexpected and to alert the stockperson to the potential problem.

There are few examples in the literature of fully functioning IMSsystems, but various authors have made steps in this direction. Of these,automated feeding and weighing systems will be discussed below.Halachmi et al. (1998) discuss an automatic feeding system for cows, whichallows a substantial collection of data, but this is not integrated with amodel or control system. Pietersma et al. (2001) developed a decisionsupport system to analyse lactation data for cattle and to examineindividual performance, but again without a model or control system.Many models of pig and poultry nutrition exist, ranging in scope fromthose describing the nutrition of a single animal up to those describing thewhole farm and its economy. But aside from the examples describedbelow, these models have not yet been integrated into on-line livestockproduction systems.

The general approach shared by the IMS systems described below isthat of model-based predictive control (IMS Pigs1; IMS Poultry2; Aerts et al.,2003a,b). This is a two-stage process: first, continuously collected data arefed back into an adaptive (growth) model; second, forward predictions ofthis model are used to identify the management regime required to satisfythe control objectives. How the various components of a generic IMSsystem interact is shown in Fig. 15.1. The goal of IMS is to produce asystem that is entirely on-line and operates in real-time without humanintervention (in normal operation: problems would require interventionwhen detected). The systems currently in development achieve this tovarying degrees.

IMS brings together many of the subjects that have been discussedelsewhere in this book. Different approaches can be used to model feedintake, nutrient and energy usage, growth and feed intake: approachesfrom detailed modelling at the metabolic level (e.g. Green andWhittemore, 2003) through to data-based ‘black box’ approaches (e.g.Aerts et al., 2003a,b). Regardless of the approach used, in practice noanimal will ever perform exactly as predicted by a model, due toconsequences of the social, disease and thermal environment (seeWellock et al., Chapter 4, this volume) and genetic effects. Theseunknown parameters must be estimated from the data before the modelcan be used for accurate prediction. Identifying these parameters is aform of model inversion problem (see Doeschl-Wilson et al., Chapter 9,this volume).

This chapter addresses the components and concepts of IMS systems.First, the various pressures and objectives of IMS are addressed, then theequipment and data sources available on the farm. The models themselves

306 D.M. Green and D.J. Parsons

are then discussed: modelling strategies used for IMS, methods foroptimizing models in response to the collected data, and how modelpredictions can be used to make control decisions. Finally, some IMSsystems already developed and in development are discussed, beforeconsidering likely future developments.

Market Forces and Control Objectives

The IMS approach is adaptable for a variety of objectives, either alone orin combination. These can be categorized as follows:

1. Economic objectives. In most cases, the primary objectives of producerswill be to maximize profit. The best course of action here may be to rearlivestock as quickly as possible, although this is not necessarily the case. Forexample, faster growth might be at the expense of meat quality, and if thisadversely affects the price achieved then slower growth may be desired. Afull model of not only growth and nutrition, but also of economics at thefarm level, will be of benefit here in choosing the optimal strategy. Themarket may impose constraints on the farmer: animals at or below a givenfatness may be required, or delivery of animals of a specified size at aspecified date. Multiple routes to profit may exist which an IMS systemcould identify: e.g. either, on the one hand, high levels of production with

Models in the New Technologies of Production Systems 307

Fig. 15.1. Flowchart showing design of an abstract integrated management system.

Previousstatus

Predictstatus now

Predictfuture status

Diet andenvironment

Amend dietand environment

Futurecontrol targets

Run model

Run model

Measurestatus now

Diet andenvironment

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low margin per animal sold or, on the other, a lower level of production ofmeat of higher value.2. Environmental objectives. In England, over 70% of nitrates and 40% ofphosphates in water are derived from agricultural land (DEFRA, 2002).The increasing concern within the EU has led to the designation of nitratevulnerable zones and legislation to minimize nitrogen emissions. IMS willbe able to assist here as emissions targets, along with production targets,can be embedded in the systems. A typical target might be to minimizenitrogen emissions per animal produced. A model is required to solve thisproblem: feed excess dietary protein and growth will be fast, but wastefulof nitrogen; feed too little dietary protein and growth will be slow, with theanimal contributing to pollution over a longer timescale.3. Health and welfare objectives. It is not anticipated that automatedsystems will ever replace the experienced stockperson. However, wheretime is limited, the IMS system will provide a useful extra tool to alert thestockperson to health and welfare issues. Indeed, where animals arecontinuously monitored in terms of growth rate and feed intake, an IMSsystem may alert the farmer to a problem before any clinical signs appear.For example, an animal with low intake and with both low predicted andlow observed growth would be categorized as suffering from low appetite.Alternatively, an animal with normal intake and normal predicted growth,but low observed growth (i.e. a high feed conversion ratio) would bedesignated a sick animal.

Multiple objectives. The optimum for control is much more difficult todetermine where there are multiple control objectives. A discussion of thecomplexities of multiple criteria decision making is beyond the scope of thischapter. It may, however, be simpler to consider additional objectives asconstraints on the system; this may be appropriate where, for example, thereare government-imposed limits on emissions associated with production.

The IMS systems IMS Pigs and IMS Poultry and that of Aerts et al.(2003a,b) were not equipped with full economic models of production,having specific growth targets already set, in order to test the ability ofcontrol to achieve such targets. For the poultry systems, the target wasweight at a particular age; for pigs, as well as growth rate or final size, anadditional objective was specified: level of fatness at the end of the trial.This is an important target in a species where payment by theslaughterhouse may be based on carcass quality.

Equipment

An important step towards integrated management systems has been thegrowth in sensor systems to measure performance and related data (Frostet al., 1997), and in particular, a growth in affordable sensor systems.Without a commercially viable means of collecting data with sufficientfrequency, accuracy, and at a suitable level (individual, pen, etc.), the


affordability of modern computer systems is of little benefit. For bothsensor systems and control systems (environmental controllers, feeders,etc.), there are the following considerations.

1. Cost. The necessity for equipment to be affordable has already beenmentioned. This applies not only to installation costs but also to operatingcosts in terms of both money and personnel time.2. Maintenance. Maintenance requirements must be low, especially wherea large number of pieces of equipment are installed. Devices with movingparts tend to become clogged with dust and require cleaning andrecalibration. Devices at ground level will be soiled and require cleaning.In the case of pigs, there is the likelihood that any novel object withinreach will attract their special attention.3. Invasiveness. Equipment must be non-invasive, and not causedeleterious change to animal behaviour. Any requirement for frequentmaintenance will, of course, lead to more animal disturbance. Addressingboth of these last two points, a device that can operate remotely from theanimal is of more benefit than one in contact with the animal.

All of the above criteria are satisfied by the recently developed ‘VisualImage Analysis’ (VIA) system (Marchant et al., 1999; Schofield et al., 1999),which is commercially available [Osborne (Europe) Ltd]. This novel systemallows for measurement of the plan-view area of an (indoor housed) pig, byvideo camera mounted overhead. These cameras are inexpensivecompared with computer hardware and software costs, easy to install andcalibrate, and easy to maintain, since maintenance extends only to lenscleaning, there being no moving parts. A number of cameras can share onecomputer. If pigs are fitted with radio-frequency transponders, thenindividual pigs can be measured; without these, estimates of pen-averagepig weight can be obtained.

A series of images is continuously collected while an animal is in view.From these area and length measurements (Fig. 15.2), live weight can bedetermined with accuracy similar to that of weigh scales (White et al.,2004), and there is tantalizing evidence showing that other useful indicesof pig shape and size, correlated with composition and conformation, canbe measured too (Doeschl et al., 2004; Doeschl-Wilson et al., 2005). Liveweight itself is, in effect, a proxy for ‘amount of meat’: the potential ofVIA is that it may measure this directly, rather than doing so via liveweight.

VIA offers promise as a means of monitoring size for animals with aclear, relatively invariable outline; similar approaches have been used forfish (Tillett et al., 2000), and work is also in progress to determine thethree-dimensional shape of live pigs (Wu et al., 2004). However, thisrequires camera equipment that is unlikely to become affordable forcommercial use and the placement of cameras at pig level is alsoproblematic. Fur and feathers provide more of a challenge for VIA systemsbecause the animals can present more variety of apparent sizes to thecamera. Nevertheless, progress has been made on using the VIA approach


for poultry (de Wet et al., 2003). VIA analysis of pigs from alternativeviewing angles (side and rear views) is also currently under investigation.Such data may provide measurement of condition, which is particularlyimportant for sows (Schofield, 2004): but note again the concern overcamera placement.

Automatic (conventional) weighing systems have long been availablefor both pigs and poultry. For example, Williams et al. (1996) report on theeffectiveness of weighing pigs through automatic forelegs-only weighingplatforms associated with feeders. For pigs, electronic tagging allowscollection of weight data for individual animals, whereas for poultry,average weights of the birds visiting the weigher are obtained.

Pig fatness is generally determined by backfat depth at the P2 site (inthe UK). Though such measurements would be valuable input into IMSsystems for pigs, providing an added dimension of data for modeladaptation, its manual measurement can cause distress and is labourintensive. Ultrasonic P2 measurement remains currently the most practicalmeans of easily determining carcass composition, amongst a field includingultrasound (Newcom et al., 2002) and alternatives such as CT scanning(Kolstad, 2001) and MRI (Mitchell et al., 2001), whose use is restricted toresearch.

Feeding equipment is at once both a potential sensor and a controller.Systems exist for controlling and measuring feed intake and blend for bothpigs and poultry (Filmer, 2001; Ellis and Hyun, 2005), though whetherfeeding other than ad libitum is possible will depend upon housingconditions.


Fig. 15.2. Screenshot from a running VIA system showing identification of three body regions.

Models and Model Adaptation

Modelling strategies

Modelling represents an attempt to abstract important elements of reality,in order to study the behaviour of a system and make predictions. Anysuch model, however, cannot describe every detail of the system.Depending upon how much a priori information is encompassed by themodel, two extremes of modelling approach exist: empirical andmechanistic. The empirical model abstracts from the observables. This is asimple approach, requiring few assumptions as to the nature of the system,though data must be collected in order to build the model. Such modelsare generally quick to compute, and so can be used in time-criticalsituations. However, they cannot safely be used to make predictions outsidethe range of data that they were built from.

At the other end of the scale are mechanistic models. These models aremore complex, based on more assumptions regarding the underlyingsystem and then tested against the observables. They are slower tocompute. However, their predictive power is greater and not so limited bythe range of data already collected, though model predictions must alwaysbe used with caution, and more so with highly complex models. They canalso be used predictively early in a trial, where an empirical model couldnot, as insufficient data would be collected up to that point.

A second modelling distinction can be made between stochastic anddeterministic models: deterministic models always give the same resultseach time the model is run; stochastic models give a range of likely outputsfrom each set of inputs. Deterministic models are quick to run andrepeatable, but only stochastic models give the user not only a prediction,but also a level of confidence in that prediction. Stochastic models areuseful where it is necessary to model populations of animals: the variationin weight around the mean at the end of a trial may be of as much interestas agreement between the mean and the target weight. For example, thevalue of carcasses might be considerably reduced above a certain level offatness. In this case, targeting just under this level of fatness will beacceptable where the variation in fatness is predicted to be small, butunacceptable where large.

The literature concerning pig and poultry growth and nutritionmodels is extensive, and a full review of the different approaches used isbeyond the scope of this chapter. It is necessary, however, to draw attentionto those models, and their sources, that have been used in thedevelopment of the IMS systems exampled here. In modelling the growingpig (IMS Pigs), Green and Whittemore (2003, 2005) used a detailedmechanistic approach, considering the growth and nutrient use of pigswith different genetic merit and in social, thermal, and diseaseenvironments with different levels of challenge. The justification for thisapproach was largely drawn from the reviews of Whittemore et al.(2001b,c,d). A mechanistic approach was chosen in order to allow the IMS


system to make control decisions at the beginning of the trials, before datahad been collected.

The IMS Poultry programme (Frost et al., 2003; Stacey et al., 2004) usesa semi-mechanistic model of poultry growth: a compromise between acomplex, slow, mechanistic model, with extensive a priori assumptionsconcerning growth built in, and a quick-running empirical model, whichwould be of limited use early in a trial. This model was built from theprinciples established by Emmans (1981, 1987, 1989, 1994), Emmans andFisher (1986) and Hancock et al. (1995). Also for poultry, Aerts et al.(2003a) chose an empirical approach, and used a recursive linearregression relationship to relate cumulative feed intake to mass, using alimited number of past measurements to predict future weight; they founda time-window of 5 days to give good forward prediction (Aerts et al.,2003b).

Model adaptation

Environmental, health, and genetic effects will mean that at run time, themodel will produce output that deviates to a greater or lesser degree fromthe observed data. Therefore, the model is continuously updated byreparameterization from these data. Model parameterization can beconsidered as a function minimization problem, where the function to beminimized is a loss function describing the poorness of fit of the model;minimization by least squares or negative log-likelihood are the two mainapproaches here. Strategies of function minimization are many and varied(Press et al., 1992), and which is the most appropriate depends upon thenature of the model response surface (in however many dimensions thereare parameters to be optimized). The surface can have single or multipleminima, be continuous or discontinuous, differentiable or nondifferentiable(Fig. 15.3). The most simple and foolproof method is the grid search (in onedimension, linear search): this method searches through the whole ofparameter space, with a given precision, to find the minimum value.However, such a brute force approach requires an extraordinarily largeamount of processing time, especially where the number of dimensions(model parameters) is not small.

Several more ‘intelligent’ approaches exist, which can be dividedgenerally into methods that only require evaluation of the model/function,and those that in addition require evaluation of the gradient (Press et al.,1992). The latter methods are less appropriate for models where outputshows plateaux and discontinuities; such output is possibly more likelyencountered with complex mechanistic models. Gradient-followingapproaches include the Newton-Raphson and quasi-Newton methods (Gill etal., 1981), as well as the Marquardt-Levenberg algorithm (Marquardt, 1963).The revised simplex method (Nelder and Mead, 1965) does not requirecalculation of gradients, but does follow the descent of the model responsesurface and so can become trapped at local minima. The methods of


simulated annealing (Kirkpatrick et al., 1983) and genetic algorithms (Holland,1975; Goldberg, 1989) both have the benefit of being able to escape fromlocal minima. However, they tend to take longer to compute. These twomethods are stochastic, in that a different solution will be obtained eachtime the algorithm is run. The amount of variation in the parametersobtained in repeated runs will provide some estimate of the parametererror. A comparison of the different methods of function minimization isshown in Table 15.1.

IMS Poultry fitted a single parameter to their model of broiler growthat run time using a linear search algorithm. This had the advantage ofalways finding the minimum, and yet at an acceptable speed. With a largernumber of model parameters fitted (two), IMS Pigs used a variant of the


Fig. 15.3. Smooth and unsmooth model response surfaces.

Input variable

Out

put v

aria

ble

Table 15.1. Comparison of methods of function minimization or optimization.

Risk of Can fit Inherently Number of local non-linear bounded Stochastic parameters minima functions Speed

Linear/grid search yes no low low yes lowQuasi-Newton/Newton-Raphson/ no no medium high yes highMarquardt-LevenburgRevised simplex no no medium high yes highSimplex (linear yes no medium low no high

programming)Genetic algorithm yes yes high medium yes mediumSimulated annealing no yes high medium yes medium

revised simplex approach, amending the method to include thespecification of sensible constraints on the model parameters (Parsons,1992). For this particular problem, with a small but not singular number ofparameters, and a complex model response surface, it was found to bemore robust than the quasi-Newton approach, and faster than the geneticalgorithm, offering a compromise between high speed and high robustness(Parsons et al., 2004).

Parameter selection for model adaptation

For data-based, empirical modelling approaches, model building and modelparameterization can be equivalent. The model itself may be as simple as aset of linear equations, though other strategies, such as the use of neuralnetworks, have been proposed. The interpretation of these models,however, can become difficult: though externally simple, they can beinternally very complex, and as such not easily understandable. For thisreason, such approaches have been described as ‘black box’ models. Thedangers of using predictions from these models outside the range of thedata collected are greater: this is essentially a problem of model over-fitting.The more transparent approach used by Aerts et al. (2003a,b) to modelgrowth response, also empirical, was conceptually more easy to understand,and more robust. These authors used recursive linear regression to describethe relationship between growth and cumulative feed intake.

The problem of model over-fitting is not limited to empirical models;the same issue arises when fitting the parameters of a mechanistic model.Where too many parameters are fitted, parameter estimates can becomecorrelated. The model will fit the current data set well; but modelpredictions can be unstable outside the possibly narrow range of data usedfor parameterization, producing biologically unfeasible output. Underthese conditions, it is as well to combine the correlated parameters into asingle parameter and fit this new parameter.

In the IMS Poultry project (Frost et al., 2003; Stacey et al., 2004), asingle parameter was chosen for adaptation. This parameter controlled thecombined efficiencies of utilization of protein and energy; this was foundmore robust than fitting the two efficiencies simultaneously as twoparameters. The growth model of Aerts et al. (2003a,b) and IMS Pigs bothfitted two parameters. In the former case, these represented the slope andintercepts of the simple linear model. In the latter, mechanistic model, anumber of parameters were available and were considered. Twoparameters existed controlling maximum rate of protein retention and twocontrolling efficiency of energy and protein use (both genetic and diseaseeffects) (Green and Whittemore, 2005). However, a good fit was found,without generating biologically unreasonable model output, by fitting onefrom each pair. Since weight data from the VIA system was available forindividually identified pigs, model parameterization in IMS Pigs wascarried out on the individual animals.


Stacey et al. (2004) draw attention to the question of how much data itis necessary to collect before model adaptation should be performed.Though this period depends critically on the confidence level used, acertain minimal period must elapse before statistically significant changesin animal state can be detected. Kearney et al. (2004), on automaticweighing of cattle, recommend collection of data for up to 2 months inorder to quantify growth rate. Stacey et al. (2004) decided upon a period of14 days for growing chickens; this was chosen as a compromise betweenbeing able to respond correctly and promptly to differences in animalgrowth rate, and responding falsely to measurement errors. For pigs,White et al. (2004) noted that for platform weighers, a period of 4–13 daysis required before changes in pig state can be detected with 95%confidence; and for VIA systems, 8–10 days. Precisely quantifying growthrate would take longer. Aerts et al. (2003a,b) chose a window of 5 days ofcollected data on which to base forward predictions.

In the IMS Poultry, IMS Pigs and Aerts et al. (2003a,b) growth models, asingle dimension of data, live weight, was available for model optimization.With VIA (White et al., 2004) or with automatic fat depth measurements(Frost et al., 2004), there is the potential of extra dimensions of data infuture systems. In this case, there will be greater potential to include moreparameters and preserve model robustness.

Control

Controllable elements

Whittemore (1998) draws attention to four aspects of the productionprocess that are subject to control.

1. The feed intake ration.2. The feed intake blend, particularly with respect to the ratio of energy toamino acids.3. The choice of the point of slaughter.4. The choice of breed, its lean:fat ratio, composition, and conformation.

These aspects are as applicable for poultry as they are for pigs. To thesecan be added:

5. The social environment of the animal; group size, mixing and lighting.6. The thermal environment; temperature, floor materials, humidity,ventilation, etc.

Objectives

An adapted model, once generated, can be used to make forward pre-dictions. The difference between these forward predictions of productionoutputs and their control objectives can be minimized by adjusting the


aforementioned controllable elements in a manner parallel to fitting amodel to collected data. Many of the same principles discussed for modeladaptation apply here. Control objectives can be implemented in a numberof ways, as follows:

1. Single-point targets. Here, the target for control is a single point at theend of the trial. The control system can devise any route in order to reachthis goal. This is simple to implement but has drawbacks. The system may‘select’ a route that demands growth performance at the limit of what ispossible for an average animal. This may constitute a welfare problem, andshould the performance demanded exceed that possible for an individualdiffering from the population average, control may fail to achieve the target.2. Trajectories. The problems of single-point targets for growth can beavoided by setting a trajectory for the animals to grow along through thewhole trial period. This approach was used for poultry projects by bothIMS Poultry and Aerts et al. (2003a,b). IMS Pigs used both trajectory andend-point approaches, as the control software was adapted for either. Theweighting of deviations of predicted growth from this trajectory need not,however, be equal through the whole trajectory: it might, for example, beweighted more heavily at the end, to ensure that early forward predictionsare not constrained to give a good fit to the target trajectory at the expenseof achieving the final target weight. In effect, this is a compromise betweenend-point and trajectory approaches.3. Integrals. Both of the above methods are similar in that the system isattempting to steer towards a target at a particular time. They differ in thatthe latter method specifies more the route to be taken towards this target.In contrast, there are objectives for which the value is summed over thewhole period of production. The value at a particular time is not ofinterest, only its summation over time. Production costs or nitrogenemission targets are likely to fall into this category.4. Constraints. Some production outputs, such as nitrogen output, arebest considered as constraints on the system, rather than as absolutetargets. It may be, for example, that nitrogen output below a particularlevel is acceptable, not that a particular level is desired. This distinction isone that can be made for single-point targets, trajectories, and integralsalike.

Control algorithms and control variable selection

The number of control variables subject to optimization during control islikely to be larger than the number of parameters fitted during modeladaptation. Moreover, each control variable can be regarded separately foreach period modelled during the remainder of the trial, giving apotentially large number of dimensions for optimization. The algorithmsavailable to fit model predictions to control targets are the same as thoseavailable to fit model predictions to previously collected data and the sameprinciples apply in choosing the best method.


In the IMS Poultry project, both control of feed intake and control offeed blend (varying dietary protein content between two extremes) werepossible. With each control variable able to be specified for each day of thetrial, the dimensions of the problem were at least 30. With this largenumber of dimensions, a genetic algorithm (Holland, 1975; Goldberg,1989) was found to be robust, and operated at an acceptable speed (Staceyet al., 2004). The system of Aerts et al. (2003a,b), also studying poultry,considered control by restricted feed intake alone. These authors fitted asingle control variable – the amount of food to be fed in the succeeding 24hours – to follow a defined target trajectory for growth.

Rationing of feed was not possible in the IMS Pigs study. But here, pigswere housed in relatively small groups of 12 and the feed blend could bevaried at the individual feeder level (again, dietary protein content variedbetween two extremes). This control variable was divided into four controlperiods, as tests showed that little improvement in control would be gainedby using shorter periods (Parsons et al., 2004). The number of dimensionshere being considerably smaller than in Stacey et al. (2004), the revisedsimplex algorithm was found to be suitable for optimization, as was alsoused for model adaptation in this study.

In the case of blending feed as a control variable, both the IMS Pigsand IMS Poultry projects considered not the blend itself, but the rate ofchange of the blend, constrained within narrow bounds. This preventedlarge step changes or quick changes in the blend of the diets, which mightbe poorly tolerated.

Modelling feed intake

The accurate prediction of ad libitum feed intake can be considered thebane of growth modelling. For pigs, food intake in a commercialenvironment differs substantially from that in experimental conditions andthere are marked differences between genotypes, premises, andmanagement practices (Whittemore et al., 2001b). Mechanistic models areinformative in predicting the qualitative effects of a change of environment(social, disease or thermal) or diet (Wellock et al., 2003a,b; Whittemore etal., 2003); however, some authors have considered feed intake as being bestobtained by observation (Schinckel and de Lange, 1996) and therefore bestspecified as a model input (Green and Whittemore, 2003). Where feed isrationed below the likely ad libitum intake (and refusals can be assumedlow) as may be the case for individually housed sows, this is reasonable.Elsewhere however, it is necessary to predict ad libitum intake fromobservations.

For both the IMS Pigs and IMS Poultry projects, the experimental set-up included measurements of feed consumption. Feed intake data frompreceding trials were used to predict ad libitum feed intake for animals of aspecified size for entry into the growth models. However, allowance wasmade for individual deviation from the assumed feed intake for short


periods. Where an animal was eating more than an average amount, forthe purposes of future prediction (and therefore control) this behaviourwas expected to continue for a period, after which average feed intake wasthen assumed. The problem of feed intake prediction was not an issue forthe growth model of Aerts et al. (2003a,b), who fed specific feed rations togroups of chickens subject to control.

IMS Systems in Practice

By way of an example showing the interaction of the many components ofIMS systems described above, we will now turn to two systems that havebeen developed. The first of these, IMS Pigs, is in development; thesecond, IMS Poultry, forms a completed research project now incommercial use (available as PIMS from David Filmer Ltd).

Integrated management systems for pigs

The IMS Pigs project investigated the performance of a novel system forpig production and pollution control (Green et al., 2004; Parsons et al.,2004). This system is work in development and not all components areonline and fully automated. Nevertheless, the scientific proof of principlehas been shown. The main data stream for IMS Pigs was a VIA system(Marchant et al., 1999; Schofield et al., 1999) which provided automatic liveweight estimates on a daily basis for individual animals. It wascomplemented with manual P2 backfat measurements and manualmeasurements of live weight. Feeding was ad libitum but the crude proteincontent of the feed was varied between 13 and 19% on a per-pen basis(manually, at the instruction of the IMS controller). Each of the 12 penshoused 12 pigs during each trial, pairs of pens sharing one of sixcontrolled-environment rooms at ADAS Terrington, Norfolk, UK.

A revised simplex method (Nelder and Mead, 1965) was used to fit twoparameters of a mechanistic model of pig growth (Green and Whittemore,2003, 2005) to the data collected from the VIA system. In effect, oneparameter specified the efficiency of growth and the other defined thepartitioning of dietary nutrients between protein and lipid deposition.Weekly forward predictions from the fitted models were used to determinethe crude protein content to be blended for each pen in order to bestsatisfy the control objectives. Fitting of model output to the controlobjectives was also carried out using the revised simplex approach.

In the trials, two sets of objective targets were specified: targets forweight gain (50 or 60 kg gain during the growth period) and for P2backfat depth at the slaughter point (12 or 16 mm). Results from one ofthe trials are shown in Table 15.2. Model fit was good before optimization,with the means of the final observed and predicted weights differing byonly 6 kg. Optimization reduced this to less than 1 kg, even where


optimization was performed only on the early part of the collected data.This shows the optimized models to have good predictive power.

Control of fat depth was partially successful. The lower target wasachieved with good accuracy, but the pigs set the higher target ended thetrial 2–2.5 mm thinner than specified. However, reference pigs fed only onthe low protein diet were similarly below target, showing that achievementof this target was beyond the capability of the system. Weight gain controlwas achieved within 3 kg of the targets on three of the four pens. Thefourth pen finished below target by nearly 6 kg. This was unavoidablebecause these pigs, although on target until the penultimate week of thetrial, then showed an unexplained reduction in growth rate. Where suchchanges, possibly caused by a sub-clinical illness, occur early in the trial,there is time for the IMS system to take corrective action. In this case,there was no time remaining on trial for such a severe departure from thetarget to be corrected. Nevertheless, for healthy pigs, this study providesproof of principle of control of pig weight through control of diet on adlibitum feeding. If rationed feeding is implemented, greater control of bothweight and fatness can be expected.

Integrated management systems for poultry

The IMS Poultry project uses, as does the IMS Pigs project, the IMSstructure shown in Fig. 15.1 (Frost et al., 2003; Stacey et al., 2004).Compared with the individual animals studied in IMS Pigs the commercial-sized scale here was much larger: each of the eight houses on the trial farmheld 30,000–40,000 birds. Mean live weight for each house was providedby automatic ‘Flockman’ weigher systems (http://www.flockman.com), aswith IMS Pigs providing daily weight data. Again, as with IMS Pigs, themain controller was diet blend: the birds were usually fed ad libitum, butthe composition of the food was varied to give a range of protein content.Rationed feed intake was, however, available in some trials.


Table 15.2. Growth targets in IMS Pigs. Growth targets for each pen,with mean final deviation from targets. Standard errors are shown inbrackets.

Target Deviation

Weight gain (kg) (approximate) 50 2.1 (2.4)50 2.3 (0.9)60 –5.8 (1.5)60 2.0 (2.4)

Final P2 backfat depth (mm) 12 –0.9 (0.53)12 0.2 (0.60)16 –2.1 (0.72)16 –2.4 (0.68)

http://www.flockman.com

As with IMS Pigs, a mechanistic model of growth and nutrition wasused, albeit one that was simpler and faster to compute. Only a singlemodel variable was fitted to the data, specifying efficiency of use ofnutrients, and so the robust linear search algorithm was used for modelparameterization, since the more complex algorithms were unnecessarywith a one-dimensional problem. For control, a genetic algorithm(Holland, 1975) was used, their being many more dimensions in theoptimization, of the order of 30.

The control targets comprised a target weight trajectory, with controldecisions being made by the IMS system thrice weekly. Model output, asfound with the IMS Pigs model, was good, but varied from house to house.This is of course expected, and is why the model adaptation mechanism isimplemented; following model adaptation, error between the model andactual weights was reduced from approximately 108 g to approximately29 g. The IMS system provided a precision of control equal to thatachieved by human managers. Stacey et al. (2004) comment that, withcontrol of not only feed blend but also feed ration, even betterperformance of the system will be found.

Future Prospects

Further progress in IMS systems for pigs and poultry are to some extentdetermined by the development of sensor systems. For sows, someprogress has been made in the development of VIA systems (Schofield,2004). However, the changes during pregnancy in the sow are smallcompared with those of the growing pig, being more a matter of shapethan size, and this provides more of a challenge for the VIA system(Doeschl-Wilson et al., 2005). Side-view VIA is more appropriate forevaluating the sow, but needs more awkward placement of cameras thanthe overhead placement used for viewing the growing pig. Amongst otheruses for VIA is the potential to track animal movements (Tillett et al.,1997), thereby providing a measure of activity and its concomitant energyusage.

Another data source that may prove useful in IMS is sound.Vocalizations are known to be an indicator of welfare in both pigs andpoultry (Manteuffel et al., 2004) and progress has been made inrecognition of vocalization types with neural networks (Chedad et al.,2001). For reviews of recent developments in the detection of chemicalsrelating to health and welfare, nuisance, or pollution see Persaud (2001)and Frost et al. (1997).

The IMS systems described above are all indoor systems. IMS outdoorswill provide more obstacles. VIA systems would have to be more robustand contend with more varied lighting conditions than are found indoors.Modelling of the thermal environment and its effects on energy use wouldbe considerably more difficult than in the controlled conditions of indoorhousing.


Conclusions

Integrated management systems represent an exciting new use of models,operating in real time as part of livestock production systems to provide abasis for management decisions to be made by automatic control systems.Their use relies on the provision of continuous data streams from automaticsensor systems, which are growing in affordability and reliability. Thecommercial development of such systems is just beginning, but trial studiesshow that their performance compares favourably with that of humanmanagers. It is hoped that IMS will provide benefits to the producer, to theconsumer, to the welfare of livestock, and to the environment.

Acknowledgements

With thanks to Andrea Doeschl-Wilson and Istvan Kiss.

Endnotes

1. Integrated Management Systems for pig nutrition control and pollution reduction.LINK Sustainable Livestock Production programme funded project; UKDepartment of Environment, Food, and Rural Affairs (formerly MAFF)http://www.defra.gov.uk/science/Link/Agriculture/SLP/Key references: Parsons et al. (2004); Green and Whittemore (2003,2005); White et al. (2004).

2. Integrated management systems to enhance efficiency and pollution control inpoultry production. As above.Key references: Frost et al. (2003); Stacey et al. (2004).

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Index

325

ability to cope 65acclimation state 215adipose tissue

control of lipid storage in 293energy storage tissue 284enzyme activity 289see also fat

age at first egg, mean, prediction of236–237, 255

air quality 38, 82–84air velocity (and speed) 34, 54, 190–191,

198–200, 213, 215, 221algebraic model inversion 167,

169–177, 185sources of error 174

allometriccoefficients 24relationships 24, 49, 80

amino acidscoefficients 30deaminated 29, 145, 148, 152first-limiting 25, 46, 49, 57, 125–126feed intake 29 immune response 71, 126, 128–135,

138–139limiting 2,25, 31, 33optimum content 91–93profiles 29–30 ratio with energy 46, 77ratio with protein 46response 79, 132utilization of limiting 2

anabolic hormone 292anabolism 156–157animal

behavioural changes 36–37breeding strategies 64description 24, 46, 48disease and health 39, 41, 117, 136health 39–42, 117–118, 129–136,

305, 320homeothermic 188–192thermal environment 210–214, 306

appendages, bare 190–194, 203appetite 32, 56–57, 71, 308artificial neural networks 98, 103, 105ash deposition 261ATP cost 152–153ATP synthesis 149–152, 158ATP yield 158, 298automated feeding and weighing

systems 306, 310

backfat 56, 153, 171–180, 310, 318–319

basal metabolic rate 153between-animal variation 63–64, 66, 71behavioural freedom 215bimodal distribution 237, 243, 256biological responses, accuracy of

defining 22birds in transit 218

bodycomposition 15, 35, 49, 95,

154–156, 171, 178–179maintenance 169, 261–262reserves 26, 154temperature 37–38, 189, 193, 202,

212, 216–222, 244see also carcass

boundary layer 191–203breast meat yield 78, 80breeding values, estimated (EBV) 108,

163broiler

behaviour 82feeding programmes 77–82, 85,

91–94bulk constraint 31–32, 38

calorimetry, indirect 145carbon dioxide balance 211carcass

composition 77, 80, 310protein 157quality 308value 311

catalytic activity 291chance constrained programming 109chaos theory 99, 101circadian rhythm 229–230, 238–241,

255coccidiosis 16compensatory responses 26, 34controllable elements in production 315control algorithms 316–317control objectives 306–308, 315–318

constraints 316integrals 316single-point targets 316trajectories 316

cost–benefit analysis 84costs

feed 77processing and transport 77

decision analysis 111decision support system 306degree of maturity 25, 275diet

composition 81, 171least cost 14, 78

digestible energy 45–46, 143, 172digestion 15, 28, 49Discomfort Index 197disease

and performance 39–41, 71challenge 23, 38clinical 127intestinal 16, 30susceptibility 71

diseased growing pigs 117

economic objectives 307effective energy 28, 43–44, 147, 153efficiency of utilization of protein (ep)

31, 43, 262effect of temperature on 124

eggdouble-yolked 231, 236, 242,

245–246, 255–257soft-shelled 242, 246–247, 255weight, predicting 230, 249–252,

255–256empiricism 4,10energy

balance 37, 145, 214content, optimizing 2cost 148–153, 172

of physical activity 154dietary 2,31, 55, 172gross 143, 172insufficient supply 267losses 3,143

faecal 144urinary and gaseous 145, 146

maintenance 28, 37, 40, 59,151–154, 166, 275

metabolizable 29, 119–122, 143,145, 261

partitioning 155systems 143, 145, 147–148, 157

classical 147digestible 143effective 28, 43–44, 147, 153metabolizable 143net 143

transactions, stoichiometry of 148environment

macro- and micro- 189spatial and temporal variation 188thermal 35, 37, 48, 56, 210–218,

306, 315, 320

326 Index

environmental factorsair velocity 4, 54, 190–191, 198–200,

213, 215, 221ambient temperature 35, 43, 48, 54,

170, 213, 220see also temperature

environmental stressors 54–70, 117,163, 210, 214

environmental objectives 308exposure to pathogens 71, 126–127,

129, 136

faecal energy losses 144fasting heat production (FHP) 28, 146,

282fat

content 26deposition 26, 33–34, 37growth 25–27, 32, 35reserves 26synthesis 284, 287, 290, 298see also carcass; lipid

fatness, inherent 24fatty acids 18–19, 144, 149–151,

288–293, 297, 299feather

coat 90, 190, 193density score 85growth, rate of 81, 85, 88–90total score 85

feathering ratemultiplier 88non-linear effect on variation 91

feedcosts 77formulation 78, 83, 99, 108–110pelleted 84variation in chemical and physical

nature 84see also feeding

feedingad libitum 44–45, 117, 125, 310,

317–319choice 46costs 77–78, 92–94restricted 170, 317see also feed

feed intakeconstrained 31, 89desired 28

fibre (crude) 27, 31, 144–147floor type 54follicle maturation 230–235follicular hierarchy 238, 245, 255foods

energy limiting 119, 120–123protein-adequate 121protein limiting 122, 125

fractal analysis 212fractional anabolic and catabolic rates

156fuzzy logic 98–100, 211

geneticalgorithms 103, 107, 313–314, 317factors 273parameters 62, 64, 70, 81, 85,

87–94, 183, 266–277potential 23, 67, 79, 163, 166, 178,

185gluconeogenesis 10, 150, 285, 290, 295glucose 18–19, 144, 148–152, 287–303growth

ash 27compensatory 26, 34fat (lipid) 25–27, 32–35, 178feather 81, 88homoeorhetic and homoeostatic

control 156–157, 289, 294moisture 27parameters 25, 65, 68potential rate of 23, 25, 31, 165, 169protein 24–29, 38, 39, 49, 80–83,

91, 130, 165, 266gut capacity 23, 33, 43, 49

healthstatus 22–23, 27–28, 39–42, 49and welfare objectives 308

heatexchange 188, 190–193, 205,

212–216, 219, 222 conduction 191, 215convection 82, 191, 192, 215radiation 191physiology of 188

increment of feeding 8,146–147,150–152, 158, 285, 297

production 145stress 85, 197, 212, 215, 221

Index 327

heat loss 35–38, 212, 215evaporative (latent) 35–36,

192–194, 202–204, 206from Dumbo 212sensible (non-evaporative) 36–37,

191, 193, 204, 215, 228heritability 70, 85, 165, 179, 181, 287,

292–293hierarchy of organizational levels 8homeostatic and homeorhetic controls

156homeothermic animals 188–192housing 45, 210–211, 215, 310, 320hypothermia 212, 221–222

ideal protein 130–133, 170intake 118–119, 125, 131requirement 30–31, 128

immune response 71, 126–139 acquired 126, 129, 135variation in 71

immunity 126–135maintenance of 129rate of acquiring 135

infectious 17, 54, 71environment 54stressors 71

initial weight 88innate immunity and repair 127–128integrated control systems 211integrated management systems (IMS)

305–308, 318–321internal cycle length 237–241,

253–254isothermal net radiation 190–204

Kalman filter 103–108

lactating sow 18, 286, 290lactation 19, 108, 284–298lactation curve 108, 293lactose 17–19, 290, 294–295

synthesis 19, 290, 299laying hen 2,79–80, 92, 104, 111, 257

see also egglinear programming (LP) 2,12, 77, 99,

108–110, 313linear search algorithm 313, 320

lipid:protein ratio at maturity (LPRm)24–26, 43–48, 85, 88–92

lipiddeposition 46, 147–156, 166, 172,

261, 270, 275–278growth 26, 34, 178metabolism 151, 297protein ratio, minimum 27, 118,

155, 171, 174, 272lipogenesis 151, 285, 290, 293lipolysis 285, 290, 293–295lipoproteins 289litter size 297liver 145, 150, 297livestock houses 211logistic growth curve 230

maintenanceactivity component 28, 37, 40–41,

59–63, 154, 320requirement 119, 169, 272, 309

amino acids 125disease/immunity 39, 127, 129energy 38, 40–41, 155

support costs 153mammary gland 18, 289–290,

294–296, 299marginal response in PR on energy

limiting foodseffect of genotype 121effect of liveweight 120effect of temperature 121

mature body protein (Pm) 24–25, 266,277

maximum lipid in gain 88meat quality 22, 307–308metabolic body size 293metabolism 148, 150–154, 276,

282–299metabolisable energy (ME)

content 29, 121, 145intake 119, 120requirement for maintenance 119,

261system 143

milk 18production 295–299synthesis 17–19, 290, 295–298

minerals 84, 104

328 Index

modelapplication of 2,10, 14, 22, 79, 98,

165, 263Bristol–Reading 237deterministic 14, 99, 171, 209, 260,

311dynamic 14, 101, 169, 202, 209,

212, 285, 298economic 2,308empirical 4,9–10, 15, 20, 97–103,

163, 230, 282, 311–314examples 1inversion 165

by optimization 167laying henlinear multiple regression 12metabolic flux 286, 289mixture 104Reading 79sow 297–299stochastic 64, 79, 97–101, 109, 168,

178, 212, 230, 236, 311teleonomic 9thermal balance 212see also requirement response

modellingprogress in 19physiological response 217

mortality 83, 218, 222

neutral detergent fibre (NDF) 144nitrogen

balance techniques 145excretion 145, 147retention 29, 147see also protein

nursery pigs 43, 44nutrient

absorption 10content, variation in 83–84, 109density 33, 43, 77–78partitioning 15, 23, 126, 130requirements 3,22, 71, 109, 118,

257, 283specifications 2utilization 10, 79, 297, 306, 311

nutritional status 294objective function 13–14, 78, 184, 210operations research 12, 103–108, 110

optimizationalgorithm 176criteria in model inversion 176pig production strategies 64

optimum (optimal)amino acid content in feed 77–92feeding programme 77–82, 93nutrient density 77production environment 212thermal micro-environment

210–213, 216ovarian follicle 229, 232oviposition time 240–243, 255–256ovulation

internal 236, 244–245, 254–257rate 230, 234–243, 254–256

ovulatory cycle 229–235, 240–241, 254

partitioningnutrients 23, 155, 318of nutrients during disease 126of scarce food resources 117

immune pigs 129naïve pigs 129

pathogenchallenge 117, 126–136virulence of 129

phase-shift 241photoperiodic control 230piglets 46, 51pigs per pen 62pollution control 318populations 71, 79, 92, 126, 311

correlated distributions 85Predicted Mean Vote (PMV) 214prime sequence length 238, 253–254programming

chance constrained 99, 109–110compromise 14goal 14, 110linear 2,12, 77, 83, 99, 108–110parametric 14quadratic 110separable 14

proteindeaminated 29, 145, 148, 152deposition rate 25, 152, 261

maximum 265losses

endogenous gut 29integument 29, 30maintenance protein 30

Index 329

protein continuedsynthesis 152–153, 287–290turnover 29, 152, 154, 178, 285, 297see also carcass, feedstuff, nitrogen

quadratic programming 110, 209

radiation increment 198, 199, 203radio-telemetric systems 217rate of maturing (B) 24, 25, 39, 80, 81rate:state formalism 12, 14, 16, 19reductionist approach 100regression analysis 103–105reproductive performance 210, 299respiratory tract 204response

curvilinear-plateau, of population66

homeostatic 217immune 71, 126–139linear-plateau 66mean population 65of a system 9,15to an LH surge 232to environmental constraints 38to light 257to stressors 65–72

revised simplex algorithm 312–317Richards function 266

sensitivity analysis 88, 174sensor systems 308–309, 320–321sequence length, mean 253–254, 256simulation, stochastic 76social environment 23, 38, 49, 62, 64,

71, 315social dominance 64social stressors 54–72

ability to cope, genetic differences54, 61–72, 133–134, 165

effect on performance 56–57feeder space allowance 54, 59,

70–71group size 54–75, 315mixing 54, 58, 60–71space allowance 54, 57–71

starch 121, 144, 146–151state, current 23, 25, 63, 81, 156stoichiometry 145, 147–153, 158–159,

286, 298stocking density 23, 38–39, 81–82

stresscold 215, 221–222effect on performance 55, 61heat 212–215, 220, 224in group housing 38

subclinical infection 117, 127substrate sensitivity 290–297sugars 144, 146support costs for maintenance 153surface wetting 221synthesis

milk fat and lactose 17systems approach 159, 301

temperatureApparent Equivalent (AET)

197–198, 201–202, 218deep body 212, 218–222effective 35, 37, 197–200, 204–205,

214, 216humidity index 216standard operating 216

thermalbalance models 212comfort 213–223hygrometric index 197resistance 190–203

thermoregulation 82, 178, 189193–194transport

animal 215, 217, 221–223environment 215, 217feed 77–78, 83–84nutrient 152–153, 246, 285, 294,

297

ultrasound 310urea

excretion 145, 148synthesis 152, 153

uric acid 145uterus 246

variationbetween-animal 63–71, 154, 166chemical and physical nature of feed

84feed composition 76, 83–84genetic 62–62, 76126, 261–262,

275, 278, 289

330 Index

immune response 71non-linear effect, feathering rate 91spatial and temporal, of environment

188within-house 76within-population 166

ventilation 35, 82, 211, 215, 222–223,315

Visual Image Analysis (VIA) system309

vocalizations as indicator of welfare 320

water deposition 261water-holding capacity 32, 58, 60

weaning, post 40wind chill factor 197welfare 55, 64, 67–69, 210, 217–223,

305, 308, 316, 320breeding for improved, in pigs 69,

286

yolkdouble 231, 236, 242, 245–246,

255–257resorption 243weight

and age 236, 250, 256prediction 249, 255

Index 331

Documents

Mechanistic Modelling in Pig and Poultry Production