APPLICATIONS OF ALLOMETRIC PRINCIPLES IN ANIMAL NUTRITION RESEARCH

Dr. Aderao Ganesh N.M.V.Sc Scholar

OUTLINE Definition Body weight and BMR Genesis of surface law

Theoretical validity Quarter power scaling – Validity

Derivation of quarter power scaling Body weight and DMI, Retention time. Body weight and Gestation period Bergmann’s Rule Jarman Bell Principle Conclusion

INTRODUCTION

Isometry:- Isometric scaling is governed by the square-

cube law. An cube which doubles in length isometrically will

find that the surface area available to it will increase fourfold, while its volume and Weight will increase by a factor of eight.

CONT… Isometry:

Linear scaling: Y = a BM1.0

log Y = log a + 1.0 log BM.

DEFINITION Allometry is the study of the relationship of body size

to shape, anatomy, physiology and finally behaviour.

First outlined by Otto Snell in 1892 & Huxley,1932.

Allometric scaling is any change that deviates from Isometry.

Christopher G. (1996)

CONT.. Allometry is often expressed in terms of a

scaling exponent based on body Weight.

The Allometric relationship between the two measured quantities is often expressed as a power law: Y = kXa or

in a logarithmic form: log Y = log k + a log X

where, a is the scaling exponent of the law.

ALLOMETRIC RELATIONSHIP:BODY WEIGHT & BMR

BMR = kBM¾ Cal/day . Surface law* (Negative Allometry).

Basal Metabolic rate per unit surface area of large and small animals is the same or is independent of body size (body Weight).

B ∝ M¾ B - Metabolic rate M - body mass b ≈ ¾ - Metabolic exponent

*(Rubner 1883)

CONT..

This means that larger-bodied species (e.g., elephants) have lower Weight specific metabolic rates and lower heart rates, as compared with smaller-bodied species (e.g., mice).

This straight line is known as the “mouse to elephant curve”.

Brody et al. (1945)

CONT..

GENESIS OF SURFACE LAW Size effect is all pervasive, but it influences

different variables in different ways.

Volume (V = Mass (M) ) of an object = M L3

Surface area (A) of an object = A L2

We can rearrange this as: L M1/3 A1/2 A M2/3(Surface area = BW2/3).

CONT.. Kleiber (1932) found that:

BMR = BW2/3

So, exponent value of 0.73 was used, but afterwards for convenience of mathematical calculations exponent value of ¾ was adopted

Eventually it was observed that the exponent value ¾ used was correct.

In the years following Kleiber (1932), Benedict (1938) & Brody (1945) : both studied and proved that an exponent of ¾ is correct.

THEORETICAL VALIDITY OF THE SURFACE LAW

1. Rate of heat transfer. For a given difference between internal

temperature and surface temperature, the rate of heat transfer is proportional to the surface area (when the specific insulation for large and small bodies is the same). Kleiber. (1932)

2. Internal surface. Would be valid only if the size of cells were

proportional to animal size. if, in other words, elephants were made up of the same number of cells as mice (Not supported by histology).

3. Mean intensity of the blood current. The cross section area of the aorta BW2/3 ,

that consequently the intensity of the blood current BW2/3, which is a measure for body surface. Hoesslin. (1888)

4. Active protoplasm. The chemical composition of animals changes

systematically with body size, so that the surface law can be understood on the basis of chemical composition.

5. Inherent requirement of oxygen consumption per unit weight.

In vivo the metabolic rate of the tissues is checked by the influence of the CNS regulators, mainly the nervous and endocrine systems.

Grafe et al., (1925)

The theories that relate the surface law to rate of heat transfer and to the hemodynamics have most value for the interpretation of the surface law.

QUARTER POWER SCALING - VALIDITY

Life:Complex, self-sustaining, Reproducing structures

Need to service high numbers of microscopic units with :

In a highly efficient way

Energy, Metabolites & Information

Natural selection evolved networks to solve this: Animal circulatory systems. Plant vascular systems. Insect tracheal tubes.

These networks have to fulfil certain properties. There exist certain constraints...

Constraints on biological networks: (1) The organism's whole volume has to be

supplied → space filling, Fractal-like branching pattern. (2) The network's final branch is a size-invariant

unit → cappilaries, leaves, mitochondria, chloroplasts. (3) The energy to distribute resources is

minimized → evolution towards optimal state.

DERIVATION OF QUARTER POWER SCALING

Fractal-like structures in nature (here: circulatory system):

N branching from aorta (level 0) to capillaries (level N).

Blood transports oxygen, nutrients, etc. for metabolism:

B ∝ M3/4

3 = dimensionality of space 4 = 3 + 1 = increase in dimensionality due to fractal-

like space filling

CONT.. If B ∝ Ma (a will be determined later) then Q0 ∝ Ma

CONT.. Capillary is an invariant unit (i.e. Qc is equal

for all mammals). Number of capillaries must scale in same

way as the metabolic rate

N M3/4 But : Total no of Cells: Ncells M(linear).

Number of cells fed by capillaries increases as M¼ (efficiency increases with size)

CONT.. How do radii and length of tubes scale through

the network

Recall : terminal branches of the network are invariant type.

Network must be conventional self similar fractal

Number of branches increase in proportion (Nk = nk) as their size geometrically increases from level 0 to N

CONT.. Nc = number of generations of branches scales

only logarithmically with size:

A whale is 107. times heavier than a mouse but has only about 70% more branching from aorta to capillary.

CONT..

CONT.. The sum of cross sectional areas of daughter

branches equals that of parent.

Cross sectional area of parent branch Number of daughter

branches (branching ratio)

Cross sectional area of each branch

CONT.. Recall: If B α Ma → Nc =nN α M

If Vb α M and Vc α M0

a = - ln n / ln(γβ2)

With γ = n-1/3 (space filling) β = n-1/2 (area -preserving)

a = ¾ (independent of n)

Overview of further scaling laws

West and Brown (2005)

Physiological variables Scaling Exponent Heart beat rate -¼ Period of heart rate ¼ Life span ¼ Diameter of tree trunks ¾ Diameter of aorta ¾ Brain mass ¾ Metabolic rate ¾

RECENT THEORETICAL VALIDITY OF THE SURFACE LAW

Recent attention has focused on theoretical explanations for this quarter-power scaling based on the geometry of nutrient supply networks (West et al., 1997; Banavar et al., 2002; Bejan, 2000)

Three-quarter power scaling of mammalian BMR is a central paradigm of comparative physiology that has been accepted for over 70 years and remains in widespread use.

Recent studies proves that the three quarter power scaling is biologically and mathematically correct.

(West et al., 1997)

Allometric relationship: Body Weight and DMI,

Retention Time & Particle Matter

ALLOMETRIC RELATIONSHIP: BODY WEIGHT AND GESTATION PERIOD,

METHANE PRODUCTION We can predict that animals with a shorter

gestation period should be particularly “successful” (e.g. in terms of species diversity & higher fecundity due to shorter gestation period)

Clauss et al. (2013)

BERGMANN’S RULE An ecologic principle stating that body

Weight increases with colder climate. This is so because if less surface area (More

Body Mass) is there then heat losses will be less than the the animals with more surface area (which is needed in colder environment).

JARMAN-BELL PRINCIPLE Differences in Allometric relationships within

animal groups can explain species diversification and Niche differentiation along a Weight gradient.

One of the prominent example of such an argument : the “Jarman-Bell Principle” 1.Larger herbivore eat Low Quality Food. 2.this is because they have a digestive

advantage due to their Larger Digestive Tract.

CONT.. The daily energy and protein requirements of

mammals= BM0.75

For this reason, small-bodied species require more energy and protein d-1per unit body Weight.

The high metabolism of small-bodied species can be sustained only on highly digestible forage.

Small-bodied ungulates require a forage of relatively low fiber content and high protein content.

The difference between gut capacity and food intake increases with body weight.

Digesta retention scales to body weight.

CONT.. Therefore more gut capacity per unit food

intake with increasing body Weight is available.

Also, Retention time is scaling with body Weight which is advantageous for digestive physiology by efficient utilization of the available poor quality forage.

Scaling coefficient - 0.16(0.12-0.19)

Clauss et al., 2013

CONT..

Crude fiber Ingestion and Digestion scales with body Weight allometerically.

Methane production in digestive tract due to digestion scales allometrically

Clauss et al., 2013

CONCLUSION Surface area of animal do not gives the

accurate estimate of heat transfer that occurs from body.

Quarter power Allometric scaling is characteristic of all organisms wherein the model predicts structural and functional properties of vertebrate cardiovascular and respiratory system.

It is the most pervasive theme of biological science that accurately predicts spatial and temporal niche of organisms varying in body size.