Quantifying the trends expected in developing ecosystems

Ecological Modelling 112 (1998) 1–22

Quantifying the trends expected in developing ecosystems

Michael T. Mageau *, Robert Costanza, Robert E. Ulanowicz

Uni6ersity of Maryland Institute for Ecological Economics, Center for En6ironmental and Estuarine Studies, Uni6ersity of Maryland,PO Box 38, Solomons, MD 20688, USA

Received 21 November 1997; accepted 16 April 1998

Abstract

In this paper we describe an assessment of ecosystem health that is both comprehensive in that it is based on aseries of common trends associated with the process of ecological succession, and operational in that the indicescapable of quantifying these trends can be easily calculated given appropriate simulation model output or estimatesof material exchange. We developed a simulation model which generated output characteristic of an ecosystemadvancing through the various stages of succession to test the ability of a suite of systems-level information indicesto quantify these trends. Our regression analyses suggest that these indices may be able to capture the trendsassociated with ecological succession, hence the reversal of many of these trends characteristic of ecosystem responseto anthropogenic stress. We further argue that indice performance could be enhanced with the use of more dynamicmodelling techniques. In addition, we introduce a methodology for the valuation of non-marketed ecosystemcomponents which could be easily included with our assessment of ecosystem health. We conclude that this measureof ecosystem health in combination with the valuation technique may provide an informative compliment to manypast and future regional modelling projects aimed at better understanding and managing the impacts of anthropo-genic stress on our regional ecosystems. © 1998 Elsevier Science B.V. All rights reserved.

Keywords: Ascendancy; Ecosystem health; Ecosystem management; Ecological succession; Network analysis; Sustain-ability

1. Introduction

We need to arrive at a healthy balance betweenour stocks of human-made (HMC) and natural

capital (NC) if we are to continue to survive onthis planet. In the past, we have been largelyunable to quantify the effects of anthropogenicstress on our natural ecosystems with the degreeof certainty required to influence policy decisions.Popper (1990) argues that the natural world iscausally open at all scales of observation includ-ing those occupied by ecosystems, and suggests

* Corresponding author. Present address: 5815 GlenwoodStreet, Duluth, MN 55804, USA. Tel.: +1 218 5255311; fax:+1 410 3267354; e-mail: [email protected]

0304-3800/98/$ - see front matter © 1998 Elsevier Science B.V. All rights reserved.

PII S0304-3800(98)00092-1

M.T. Mageau et al. / Ecological Modelling 112 (1998) 1–222

our inability to predict ecosystem behaviour(Abrams, 1994) is due not to lack of informationregarding system dynamics, but to the fact thatthese systems are intrinsically indeterminate.Therefore, rather than continue to pursue theunattainable goal of predicting ecosystem be-haviour, we must begin to use our best currentinformation to reach consensus on predictions ofwhat factors would likely lead to the sustainabilityof ecosystem structure and function, and developpolicy in a flexible, adaptive framework capableof incorporating rather than obviating this uncer-tainty (Costanza and Ruth, 1998). Crucial to thistask is the development of a systems-level measureof ecosystem health which is comprehensive, oper-ational and capable of encompasing the uncer-tainty associated with ecosystem dynamics.

1.1. Definitions and measures of ecosystem health

Many researchers have attempted to define anddevelop operational and meaningful definitionsand indicators of ecosystem health. Leopold(1941) contributed to the practice of ‘land health’by identifying indicators of ‘land sickness’. Rap-port et al. (1985) expanded on Leopold’s originalindicators arriving at what he called ecosystemdistress syndrome (EDS). Costanza (1992) sum-marized the wide variety of proposed conceptdefinitions of ecosystem health based on EDS:Health as homeostasis; as absence of disease; asdiversity or complexity; as stability or resilience;as vigor or scope for growth; and as balancebetween system components. Karr et al. (1986)stated that a biological system can be consideredhealthy when its inherent potential is realized, itscondition is stable, its capacity for self repairwhen perturbed is preserved, and minimal exter-nal support for management is needed. Kerr andDickey (1984) suggested evaluating ecosystemhealth using the size distribution of biota. Schaef-fer and Cox (1992) stated that health is achievedwhen functional ecosystem thresholds are not ex-ceeded. Schindler (1990) provided a detailed ac-count of whole lake acidification experimentationdemonstrating a sequence of abnormal signs ofecosystem structure and function. Smol (1992)defined a healthy ecosystem as one that existed

prior to human cultural impact. Odum (1985) andUlanowicz (1986) suggested that stressed ecosys-tems are characterized by an inhibition or evenreversal of the trends associated with ecosystemdevelopment. Costanza (1992) suggested that anecosystem is healthy if it is stable and sustainablethat is if it is active, maintains its organizationand autonomy over time and is resilient to stress.Finally, there is a related body of literature thatuses the term ‘integrity’ in place of ‘health’ whenreferring to ecosystem transformations understress, and they generally consider a healthyecosystem to be pristine (Karr, 1993; Kay, 1993;Woodley et al., 1993; Westra, 1994).

Unfortunately, for each of the above definitionsof ecosystem health and integrity there are manymethods of measuring or quantifying the particu-lar symptoms of distress resulting in an inordinatenumber of ecosystem health indicators. Theserange from single species indicators (Kerr andDickey, 1984) to a composite of species (Karr,1991) to measures of biodiversity to system levelmeasures of ecosystem structure, function andorganization (Ulanowicz, 1986; Schindler, 1990;Costanza, 1992) to very broad measures which gobeyond the biophysical realm and include humanand socio-economic aspects (Rapport, 1992). Asone increases the complexity of the indicator itsrelevance increases, but the associated uncertaintyincreases as well making it more difficult to mea-sure and operationalize the concept. Costanza(1992) discussed this trade-off between ease ofmeasure and relevance (Fig. 1). Therefore, thechallenge is to develop a comprehensive definitionof ecosystem health that embodies many of theconcepts discussed above, and to identify andquantify large-scale ecosystem phenomena whichare sensitive to the effects of anthropogenic stress.

Costanza (1992) suggested a comprehensive,multiscale, dynamic, hierarchical measure of sys-tem vigor, organization and resilience would serveas an excellent definition of ecosystem health.These concepts are embodied in the term sustain-ability which implies the systems ability to main-tain its structure (organization) and function(vigor) over time in the face of external stress(resilience). Vigor is a measure of system activity,

M.T. Mageau et al. / Ecological Modelling 112 (1998) 1–22 3

metabolism or production. Organization is a mea-sure of the number and diversity of interactionsbetween the components of a system, and re-silience refers to the ability of a system to main-tain its structure and function in the presence ofstress (Mageau et al., 1995). Costanza and Patten(1995) describe the debate surrounding the defini-tion of sustainability, and suggest that much ofthe discussion is misdirected because sustainabilityis not a definitional concept, but more one ofprediction. For example, you cannot demonstratethe sustainability of any ecosystem until after thefact, much like the fitness of an organism. Whenapplied to complex systems such as ecosystems,predictions regarding sustainable configurationsare typically highly suspect, and as such should besubjected to elaboration, discussion and debate.Maintaining the sustainability of a system’s vigor,organization and resilience embodies all the defin-itions of ecosystem health discussed above.

1.2. Trends associated with ecosystem response tostress

Fortunately for our purposes, the literaturecontains a rich history documenting robust trendsor patterns associated with the response of a widevariety of ecosystems to many different perturba-tions. These trends are specific enough to bequantified with a unique suite of indices, and yetcomprehensive enough to serve as meaningful,systems-level indicators of ecosystem response toanthropogenic stress.

Woodwell (1967) described various changes inecosystem structure and function typically associ-ated with the natural process of ecological succes-sion: (1) diversity tends to increase as new nichesare occupied; (2) competition increases efficiencyand reduces redundancy within a given nichewhile decreasing the level of competition betweenniches; (3) nutrient inventories, storage and cy-

Fig. 1. Diagram depicting the general trade-off between ease of measure and overall relevance of the index (Costanza, 1992).


cling increase; (4) the structural and functionalstability of the ecosystem increases, and the ratiosof production per unit biomass and respirationtend to decline. If, during this process of succes-sional development, one or more factors essentialto the system became exhausted or limited, theprocess of succession is halted or slowed, respec-tively. Woodwell (1967) further reasoned that ifthe system was exposed to an extreme natural oranthropogenic stress, the successional develop-ment would not only be halted but reversed.Therefore, the opposite of the trends discussedabove would indicate an ecosystem that isstressed. Woodwell (1967) tested these hypothesesby irradiating a section of climax oak/pine forest,and found the pattern from the zone receiving thehighest levels of radiation to the lowest was theexact opposite of the pattern of naturalsuccession.

Woodwell (1970) further discussed the implica-tions of his findings in the ‘irradiated forest.’ Hewas struck by the fact that changes in vegetationpatterns along the gradient of radiation exposurewere similar to those found along natural gradi-ents of increasing environmental stress such asthose associated with increasing elevation alongexposed mountain slopes, salt spray and waterstress. He also found that the species survivingintense radiation were very similar to those foundin typically stressed areas such as roadsideditches, gravel banks and places with unstablesoils. In addition, the changes in his climax forestsystem paralleled those found in association withthe oxides of sulphur radiating from Sudbury’ssmelters (Gorham and Gordon, 1960) and thereplacement of Vietnam’s extremely diverse forestcanopies with bamboo in the wake of massiveherbicide applications (Tschirley, 1969).

Odum (1985) developed a more complete list ofcertain well defined development trends to beexpected in stressed ecosystems, and provided ahistory of theoretical and empirical evidence doc-umenting their occurrence. Odum (1985) arguedthat increasing community respiration, unbal-anced P/R ratios, increasing P/B and R/B ratios,increasing dependence on external energy, andincreased export of unused primary productionare energetic trends to be expected in stressed

ecosystems. He also provided evidence of in-creased nutrient turnover, horizontal transportand loss from stressed ecosystems coupled withdecreasing internal nutrient cycling. In addition,Odum (1985) highlighted several changes in com-munity structure and function. The proportion ofR-strategists tends to increase while the size andlife-span of organisms tends to decrease. Foodchains shorten as the result of reduced energy flowto higher trophic levels, and biodiversity tends todecline along with an increase in the redundancyof parallel pathways of material exchange. Fi-nally, Odum (1985) suggested evidence of thesetrends may serve as an excellent ecosystem-levelindicator of stress.

Schindler (1990) tested Odum’s hypotheses re-garding the trends expected in stressed ecosystemsby analyzing the effects of nutrient enrichmentand acidification on whole-lake ecosystems.Schindler’s analysis supported Odum’s hypothesesto a large extent. For example, the acidified lakeswere characterized by: increased periphyton com-munity respiration, P/R ratios, nutrient export,R-strategists among zooplankton, and decreasedutilization of allochthonous inputs, vertical cy-cling of nutrients, life-spans of fishes, benthiccrustaceans, sizes of zooplankton and chirono-mids, length of food chain, species diversity andefficiency of resource use, all of which supportOdum’s hypotheses. Schindler also found no evi-dence of increasing P/B and R/B ratios, nochange in exported primary production, a de-crease in the horizontal transport of nutrients, adecrease in R-strategists among the fish, and anincrease in the average size of phytoplankton allof which apparently contradict Odum’s hypothe-ses, but the majority of these exceptions wereexplained within the confines of the paradigm. Inthe eutrophied lakes Schindler (1990) again foundgeneral support for Odum’s hypotheses, despite afew apparent, often explainable, exceptions.

The most studied, and arguably the most im-portant trend in Odum’s list is loss in biodiversity.This trend has a great deal of support from paststudies, and has several serious ramifications re-garding ecosystem structure and function. Recentwork by Tilman et al. (1996) has cast some lighton a long-standing debate regarding biodiversity


and ecosystem stability. Elton (1958) suggesteddecreased diversity would lead to decreasedecosystem stability. McNaughton (1977) pre-sented data on plant productivity in the Serengetisupporting Elton (1958) and Vitousek andHooper (1993) found the rates of many ecosystemprocesses were increasing but saturating functionsof species diversity. On the other side of thedebate, May (1973) using a simple model of multi-species competition showed population dynamicswere progressively less stable as the number ofcompeting species increased. Others (DeAngelis,1975; Gilpin, 1975; Pimm, 1979) reached similarconclusions resulting in a consensus lasting twodecades that decreased population stability wouldlead to decreased ecosystem stability.

Tilman et al. (1996) provided evidence from 12years of experimentation with 207 grassland plotsexposed to the stress of extreme drought that bothsides of the debate were correct, and only theassumption that less species stability would leadto less ecosystem stability was in error. Tilman etal. (1996) found that year to year variability intotal community biomass was lower in high diver-sity plots, and the change in community biomassresulting from the stress of drought was nega-tively correlated with diversity. Finally, in addi-tion to resistance, they found the plots with ahigher species diversity recovered more quickly aswell (resilience). He also found year to year vari-ability in species abundance was not stabilized bybiodiversity suggesting that biodiversity stabilizescommunity and ecosystem processes, but not pop-ulation processes. He concluded the differencebetween species and community biomass resultedfrom inter-specific competition when stress nega-tively impacts some species others are allowed toproliferate maintaining ecosystem function whileincreasing variability in species abundance.

In addition, the literature documents evidenceof a positive relationship between biodiversity andproductivity. Naeem (1994) looked at the rivet(Ehrlich and Ehrlich, 1981) versus the redundancy(Walker, 1992) hypotheses which mark the ex-tremes along a continuum of belief regarding thecontribution of individual species to ecosystemfunction. They worked with three different levelsof biodiversity and found system production was

highest in the most diverse system, and that pro-duction levels varied less than in the less diversesystems. Tilman and Downing (1994) found thestress of drought resulted in less production de-cline in more diverse plots, and that the morediverse stands recovered quicker. Tilman et al.(1996) presented evidence supporting both thediversity-productivity and the diversity-sustain-ability hypotheses. They found more diverse plotswere able to achieve higher productivity, andargued this was because more variety in the strat-egy of nutrient use by more diverse plant commu-nities allows for more efficient use of nutrientsleading to more production. They also reportedevidence supporting the diversity-sustainabilityhypothesis by finding less nutrient leaching in themore diverse plots, and arguing that biodiversitytightens nutrient cycles leading to more sustain-able soil fertility.

Finally, there are more specific aspects of diver-sity that contribute unequally to ecosystem func-tion. Walker (1995) argues that species diversityand functional diversity are important, but thediversity of species within each functional guild ismost crucial to maintaining ecosystem function.Therefore, he suggests that when protecting biodi-versity one should ensure functional diversity byprotecting those species associated with functionalguilds containing relatively few species. As Schin-dler (1990) and Tilman et al. (1996) noticedecosystem function can be maintained despite lossof species diversity until the final species repre-senting functional guilds begin to disappear. Of-ten it is not enough to maintain high speciesdiversity, but we must be careful to ensure highdiversity within each particular guild to maintainoverall system function in the face of externalstress.

1.3. Quantifying the trends expected in stressedecosystems

Ulanowicz (1986, 1997) describes six networkanalysis, systems-level information indices whichmay be capable of quantifying the changes inecosystem structure and function associated withthe process of succession. They include: (1) totalsystem throughput (TST); (2) average mutual in-


formation (I); (3) system uncertainty (H); (4)system ascendancy (A); (5) development capacity(C) and (6) system overhead (L). These indicesstem from a unique and controversial backgroundinvolving causality in natural phenomenon(Ulanowicz, 1997). For example, Popper (1990)argued that we live in a world of ‘propensities’which characterize the probability of the occur-rence of any event given the situation in which theevent occurred. According to Popper, the vastmajority of events can be characterized by condi-tional probabilities with intermediate values (be-tween 0 and 1). It is extremely rare to find anevent characterized by a conditional probabilityof 1 (pure deterministic force) or of 0 (purelyrandom chance of occurring). Ulanowicz (1997)argues the universe is causally open at all scalesincluding ecosystems, and although many eventsmay tend to happen with high probabilities thereis no fundamental determinism underlying ecosys-tem behaviour. He stresses that any setback inscientific progress due to acknowledging chance atthe ecosystem scale could be more than offset bynew discoveries emanating from a new perspec-tive, and offers quantum physics as an example.In short, chance is part of any ecosystem transac-tion, and the conditional probability of any eventin an ecosystem can be calculated as well as thechanges in these probability assignments concur-rent with changes in ecosystem structure andfunction, and it is these changes in probabilityassignments that drive the behaviour of Ulanow-icz’s (1986) indices.

Ulanowicz (1986) identifies mutualism or auto-catalysis between system components, connectedby cyclic flow, as the underlying phenomenoninfluencing the changes in ecosystem structure andfunction measured by the indices. In autocatalysisan increase in the activity of any componentincreases the activity of all other members in thecycle and ultimately itself, resulting in configura-tions that are growth enhancing via positive feed-back. These autocatalytic configurations alsoexert selection pressure on their members. If amore efficient species enters the cycle, its influenceon the cycle will be positively reinforced, or if thespecies is less efficient, negative reinforcement willdecrease its role. In addition, as the autocatalytic

cycle increases it’s activity it absorbs resourcesfrom its surroundings. Therefore, as ecosystemsundergo the process of succession in the absenceof stress, autocatalysis increases the amount ofmaterial being transported throughout the systemand the efficiency by which its members exchangematerial and energy. Finally, different membersmay come and go, but the fundamental structureof the autocatalytic cycle remains making the loopindependent of its constituents. Therefore,Ulanowicz argues that autocatalysis streamlinesthe topology of interconnections in a manner thatfavours those transfers that more effectively en-gage in autocatalysis at the expense of those thatdo not, resulting in networks that tend to becomedominated by a few intense interconnecting flows.

TST is the most straight forward of the sixindices. It is simply a measure of the sum total ofall the inputs, outputs and materials being trans-ferred between components within the system atany given point in time. AMI is a measure of theinformation we have regarding the network ofmaterial exchange within the system. If materialfrom any particular component in the system hadan equal chance of flowing to any of the potentialrecipients then we would have no informationregarding the flow network, however, if all mate-rial from a particular component was transferredto only one of the potential recipients, we wouldhave complete information regarding the flowstructure. These extreme information values neveroccur in ecosystems, but, Ulanowicz (1986) hy-pothesizes that AMI increases with ecosystem suc-cession as autocatalytic competition streamlinesthe network of material exchange. A is simply theproduct of AMI and TST. Ulanowicz (1980) hy-pothesized that A increases with successionalecosystem development as autocatalysis increasesboth TST and AMI.

System uncertainty (H), or Shannon’s diversityof individual flows, represents the total numberand diversity of flows in a system given someamount of TST. It is a measure of the totaluncertainty embodied in any given configurationof flows. C is simply the product of TST and H.C increases as the number and diversity of flowsH in a system increases due to the increases insystem diversity and TST associated with succes-


sion. TST is limited by the amount of input incombination with the second law of thermody-namics. H increases as a given amount of TST ispartitioned among a greater number of exchangepathways associated with an increase in diversity.But, as the diversity increases, the smallest unitsare more likely to succumb to chance perturba-tion, hence the flow diversity H cannot increaseforever. Therefore, C is limited by the limits onTST and H.

Overhead (L) is the difference between capacityand ascendancy (C−A). Ulanowicz (1980) hy-pothesized that as ecosystems undergo the processof developmental succession, A approaches C atthe expense of L. At first, both A and C willincrease with succession, but ultimately C will belimited. However, A can continue to increase atthe expense of L. A certain level of L is crucial tothe maintenance of ecosystem structure and func-tion, hence there are limits to this trade-off of Afor L. Ulanowicz (1997) partitions L into fourcategories: inputs, exports, dissipations and path-way redundancy, and describes the factors whichconstrain their magnitude.

The contribution of input overhead to totaloverhead decreases as a given magnitude of inputis partitioned into ever fewer recipient categories.A trade-off develops between the benefits of con-centrating input in the most efficient input path-ways, and the vulnerability of relying extensivelyon too few input pathways. A decrease in thefraction of input to TST also leads to a decreasein the contribution of input overhead to totaloverhead. Dissipation overhead decreases with thefraction of respiration to TST, and as the distri-bution of respiration among system componentsbecomes more equitable. Overhead on useableexports decreases with the utilized proportion ofthese exports, and the contribution they make tofurther increases in TST. Finally, overhead result-ing from pathway redundancy decreases as thenetwork of material exchanges becomes stream-lined by the process of autocatalysis. A trade-offdevelops between the increasing efficiency result-ing from a network of exchanges dominated byonly the most efficient transfers, and the vulnera-bility resulting from the rigidity of such a flowconfiguration.

In summary, Ulanowicz (1986) offers the fol-lowing description of ecological succession rela-tive to his indices. In the early stages of ecologicalsuccession C, A and L increase due to the dra-matic increase in TST associated with the pulse ofgrowth provided by abundant resources. In thelater stages of succession, resource limitation ini-tiates the replacement of r-selected species by themore specialized and efficient k-selected species.This shift in species composition leads to higherlevels of species and functional diversity increas-ing TST by allowing the system to better utilizelimiting resources, and more efficiently transferbiomass to higher trophic levels. In addition, thisshift in species composition triggers an increase inH as new flow pathways continue to evolve whilenew niches are exploited. AMI also increases asthe flow network is streamlined to favour only themost efficient material transfers within each nicheor functional guild. This competition within eachniche leads to a decrease in overhead as redun-dant flow pathways are eliminated and mortality,export and respiration rates decrease. At somepoint the species occupying the most fragile ofniches are eliminated by chance perturbation de-pending on the frequency and severity of naturalor anthropogenic stress. This phenomenon pro-vides an upper bound to the potential for in-creases in H, and the laws of thermodynamicsprovide an upper bound on TST resulting in anupper bound on C. At these later stages of ecolog-ical succession TST, H and C essentially level off,but AMI can continue to increase relative to H,hence, A relative to C at the expense of L. A willcontinue to increase at the expense of L with Cremaining essentially constant until the networkof exchanges becomes to brittle or vulnerable toany change in external conditions. Each systemdevelops an optimal balance between A and Ldepending on the variability of its external envi-ronment. Therefore, the indices taken in combina-tion may be capable of quantifying the trendsassociated with the process of ecological succes-sion, and the reversal of these trends apparent inecosystems subjected to anthropogenic stress.

In this paper we test the ability of Ulanowicz(1986) indices to quantify trends expected instressed ecosystems using output from a general


Fig. 2. A general diagram depicting the interactions between the major trophic levels in the general ecosystem model.

ecosystem model capable of depicting a range ofbehaviour typical of various stages of ecologicalsuccession. The resulting correlations support ourhypotheses regarding indice response to succes-sional trends suggesting the indices may be usedto measure the response of any particular ecosys-tem to stress provided it is characterized by anappropriate, well-calibrated simulation model, ordata directly characterizing material exchangesbetween system components.

2. Materials and methods

2.1. Model de6elopment

We constructed a simple pelagic ecosystemmodel in STELLA to test the ability of Ulanowicz(1986) system-level, information indices to quan-tify the trends described above. There were fivemajor living components in the model represent-ing four trophic levels, and two nonliving storagesof nutrients and organic matter (DOM) (Fig. 2).Each trophic level contained several different spe-cies with differing degrees of functional specializa-tion (Fig. 3). The ‘A’ species in each trophic levelrepresented generalists (also the ‘B’ species in theprotozoan and carnivore trophic levels), and the‘B, C, D and E’ species in each trophic level repre-sented specialists. In addition, the various modelcoefficients were adjusted to assign the generalistspecies growth kinetics typical of R-strategists(high growth rates, high nutrient Ks values, highrespiration rates etc…), and the same was donewith the specialists to make their growth kinetics

typical of k-selected species (low growth rates,low nutrient Ks values etc…). Therefore, when thesystem was dominated by the ‘A’ species it exhib-ited behaviour typical of an early successionecosystem, and when the system was dominatedby the ‘B/C/D/E’ species it exhibited behaviourtypical of a late successional ecosystem.

The relative dominance of any particular pro-ducer or bacterial species depended largely ontheir growth rates, respiration rates and theirabilities to utilize available supplies of nutrientand DOM, respectively (Fig. 4). The relative dom-inance of species in higher trophic levels dependedlargely on their feeding efficiencies, respirationrates, mortality rates and the species distributionat the producer and bacterial trophic levels (Fig.4). However, there were also important ‘topdown’ feedbacks which depended on the feedingrates and efficiencies of the species present in thehigher trophic levels. The net result of this dy-namic tension between ‘bottom up’ and ‘topdown’ feedback mechanisms was model outputcharacteristic of an ecosystem advancing throughthe various stages of ecological succession.

Finally, nutrients entered the system via exter-nal input and internal recycling which was directlyproportional to DOM regeneration, and exitedthe system via export and producer uptake (Fig.5). DOM entered the system via external input,excretion and mortality from the living compo-nents within the system, and exited the system viaexport and regeneration depending on bacterialingestion in combination with species specific re-generation efficiencies (Fig. 5). The rate of exter-nal input and export of nutrients and DOM washeld constant throughout the entire simulation.


2.2. Indice calculation

We calculated Ulanowicz (1986) system levelinformation indices within the STELLA model, sowe could track these values over the course of anysimulation. Ulanowicz (1986) describes the calcu-lation of the network analysis based, systems levelinformation indices in detail, so we provide only abrief summary in this paper. Of the three networkmeasures TST was the most straight forward tocalculate. In our ecosystem model TST was mea-sured as the sum of all material being transferredfrom donor compartment ‘i ’ to receipient ‘j ’ overall flow pathways in any particular time step (Eq.(1)).

TST=% Tij (1)

AMI=% Tij�log(Tij�TST/Tj�Ti) (2)

H=% Tij/TST�log(Tij/TST) (3)

A=TST�AMI (4)

C=TST�H (5)

L=C−A or =TST�(H−AMI) (6)

AMI and H represented the sum of each uniqueindividual compartment’s information and uncer-tainty values, and were calculated within the sim-ulation model using Eqs. (2) and (3), respectively.Where Ti is the sum of all material leaving the ithcomponent, and Tj is the sum of all materialentering the jth component. Ascendancy is simplythe product of TST and AMI, and capacity is theproduct of TST and H (Eqs. (4) and (5)). We havechosen this particular form of ascendancy in placeof the more comprehensive biomass-inclusive ver-sion because it has a definitive upper bound whichallows the calculation of corresponding overheadvalues (Ulanowicz, 1997). Finally, overhead is thedifference between C and A, or the differencebetween H and AMI scaled by TST, and wascalculated using Eq. (6).

Fig. 3. The complete network of living components in the general ecosystem model. The various levels of specialization are depictedas well.


Fig. 4. The conceptual diagram and growth equation for a primary producer which is representative of the bacterial species as well,and a protozoan which is representative of all species in higher trophic levels.

2.3. Hypotheses and regression analyses

We formulated several hypotheses regarding theresponse of the indices to the trends discussedabove, and tested them by regressing the ratio ofthe biomass representing the sum of species ‘A’biomasses (and the ‘B’ species in the protozoanand carnivore trophic levels) to the total systembiomass with TST, AMI, H, A, C and L. Ourhypotheses were divided into those regarding en-

ergetics, nutrient dynamics and community struc-ture. With regards to energetic trends, dominanceby species ‘A’ in each trophic level, given theirgrowth kinetics, should have lead to increasedrespiration rates, export rates, P/B and R/B ra-tios. These energetic trends should have lead to arelative increase in overhead at the expense ofascendancy for any given value of TST. There-fore, we hypothesized a positive correlation be-tween overhead and dominance by species ‘A’,


ascendancy and species ‘A’ resulting from a de-crease in TST and a relative increase in overhead.Finally, from a community structure perspective,dominance by the ‘A’ species should have lead toa relative increase in r-selected species dynamics,and a decrease in the diversity of functional guildsparticipating in the system. We hypothesized thatthese trends would lead to a decrease in capacity,ascendancy and overhead, and to a relative in-crease in overhead at the expense of ascendancy.

and a negative correlation between ascendancy anddominance by species ‘A’. From a nutrient per-spective, the ‘A’ species were characterized by lowKs values, and were ingested less efficiently byhigher trophic levels. In addition, a percentage ofeach were lost from the system. These characteris-tics should have lead to a decrease in the efficiencyby which nutrients are cycled within the system,and a loss of nutrients from the system. Therefore,we hypothesized a negative correlation between

Fig. 5. The conceptual diagram of the nutrient and dissolved/particulate organic matter components indicating the major inputs andoutputs to and from these components.


Overall, dominance by members of the ‘A’ spe-cies should have produced behaviour characteris-tic of early successional ecosystems which shouldhave lead to increases in overhead at the expenseof ascendancy for any given capacity and TST.Whereas, an increase in dominance by membersof the B, C, D, and E species should have pro-duced behavior characteristic of late successionalecosystems which should have lead to relativeincreases in ascendancy at the expense of over-head for any given capacity and TST. In addition,dominance by the more efficient species B, C, Dand E should lead to an overall increase in TST,AMI and H, and drive corresponding increases inascendancy, capacity and perhaps overhead de-pending on the relative influence of TST.

3. Results

3.1. Component biomass 6alues

Fig. 6 depicts the carbon biomass of each sys-tem component over the course of the entiresimulated successional event. Supplies of availablenutrient and DOM declined to limiting levels bythe midpoint of the simulation, and remained atthose levels for the duration. The primary pro-ducer and decomposer components displayed sim-ilar behaviour. The total biomass of eachcomponent category increased throughout the en-tire simulation while species B and C essentiallyreplaced species ‘A’ by the midpoint of the simu-lation. The protozoans and herbivores exhibitedthe same basic pattern including an increase intotal biomass throughout the entire simulationalong with a replacement of the generalist speciesby the specialists around the midpoint of thesimulation. Finally, carnivore biomass also in-creased throughout the entire simulation, how-ever, the C, D and E species were unable tocompletely replace the A and B species as they didin the other trophic levels.

3.2. Network information indices

Fig. 7 depicts the response of the systems-level,network, information indices to the component

biomass results described above. Capacity (C)and its two components overhead (L) and ascen-dancy (A) increased throughout the first half ofthe simulation, and then levelled off in the secondhalf. Average mutual information (AMI) also in-creased in the first half of the simulation and thenlevelled off in the second. System uncertainty (H)increased rapidly at the start of the simulation,double-peaked and then declined by the midpointremaining constant for the latter half. Finally,total systems throughput (TST) increasedthroughout the entire simulation, but at a slowerrate in the latter half.

Fig. 8 illustrates the response of overhead andits five components per unit TST to the simulatedresults described above. This total weighted over-head index declined throughout the entire simula-tion, but at a more rapid rate in the first half. Thefive components of overhead also declinedthroughout the entire simulation, but at differingrates. The weighted measures of export and inputoverhead declined at the fastest rate, DOM andrespiration overhead components declined at anintermediate rate, and the overhead attributed tointernal transfers declined at the slowest rate.

3.3. Regressions: biomass ratios 6ersus indices

Fig. 9 illustrates the relationship between thevarious network indices and the ratio of r-selectedspecies biomass to total system biomass (BR).There was a strong negative correlation betweenC, A, AMI and TST (R2=0.94, 0.97, 0.96, 0.96,respectively) and the BR. L was also negativelycorrelated with the BR, but the correlation wasnot as strong (R2=0.88). However, the overallL/TST measure was positively correlated with theBR (R2=0.91). Finally, there was no correlationbetween the BR and H (R2=0.02).

4. Discussion

4.1. Simulated successional changes in speciescomposition

We attempted to create an ecosystem modelcapable of simulating the general process of eco-


Fig. 6. The biomass value in carbon of each of the main system components throughout the entire simulated ecological successionevent. Each graph depicts all the species within a given trophic level. (A) Nutrients and DOM; (B) primary producers; (C) bacteria;(D) protozoans; (E) herbivores; (F) carnivores.

logical succession discussed above (Woodwell,1967; Odum, 1985; Rapport et al., 1985; Tilmanet al., 1996). In our model the relative supply ofNutrient and DOM influenced the species com-position and relative biomass of the primaryproducer and decomposer trophic levels respec-tively (Fig. 6A,B,C). The r-selected species in

these trophic levels had much higher growth rateand half-saturation parameters than their k-se-lected counterparts. Therefore, their initial rapidgrowth caused the decline in nutrient and DOMwhich ultimately led to a shift in species compo-sition in favour of the more efficient (lower half-saturation parameters) k-selected species. This in


turn influenced the species composition and relativebiomass of species representing the higher trophiclevels. In general, as the levels of DOM and nutrient

declined throughout our simulated version of eco-logical succession the k-selected species replacedthe r-selected ones at the lowest trophic levels

Fig. 7. Indice values throughout the entire simulated ecological succession event. Information is measured in units of ‘bits’, and TSTin units of carbon.


Fig. 8. The value of total system overhead (A) and its five components (B) divided by TST over the entire simulated ecologicalsuccession event. Units are in bits/carbon.

leading to similar species compositional shifts atsuccessively higher trophic levels (Fig. 6D, E, F).

Due to the differing characteristics of our sim-ulated r and k-selected species the above compo-sitional shifts led to the following changes insystem characteristics: (1) higher biomass valueswithin each trophic level as species with moreefficient growth kinetics better incorporated lim-iting resources, and more efficiently transferredtheir biomass to successively higher trophic lev-els; (2) increased TST as higher biomass valuesled to more material transfer between compo-nents; (3) a more streamlined flow network as

increasing dominance by specialist species de-creased the redundancy of pathways of internalmaterial transfer; (4) decreased community respi-ration and export of unused primary productionper unit biomass; (5) increased diversity of bothspecies and pathways of material transfer be-tween them as specialists occupied more nichesthan their generalist counterparts. Each of thesesystem characteristics are, of course, representa-tive of the trends associated with ecological suc-cession. The remaining question is how do thenetwork indices respond to these system dynam-ics?


4.2. Indice response to simulated successionaltrends

In general the system-level, information indicesresponded to our simulated ecological successionevent as hypothesized indicating that they mayserve as a useful measure of the trends associatedwith ecological succession, hence, the arrestmentor reversal of these trends associated with anth-ropogenic stress. Ascendancy (A) increased

throughout the simulation due to increases in itstwo components AMI and TST (Fig. 7A, B, D).The rate of increase in A, AMI and TST wasgreatest in the first half of the simulation corre-sponding to the gradual replacement of r-selectedspecies by the more efficient and specialized k-se-lected species within each trophic level. Thegreater efficiency of the k-selected species led tohigher levels of TST, and their specialization(fewer pathways of material exchange per species)

Fig. 9. A phase-plane plot of the relationship between the Biomass Ulanowicz (1986) network, information indices. (A) Capacity;(B) ascendancy; (C) overhead; (D) uncertainty (E) average mutual information; (F) total system throughput.


led to higher values of AMI. After the midpointof the simulation the rate of increase in AMI wasnear zero, whereas TST and A continued to in-crease, but at a much slower rate. Steady co-dom-inance by the limited number of k-selected speciesin the second half of the simulation likely con-strained any further rise in AMI, and the gradualincrease in TST as the result of slowly increasingbiomass fueled the slight rise in A.

Capacity (C) increased throughout the simula-tion in a manner similar to that of TST. However,at the midpoint of the simulation there was aslight decline in capacity which corresponded withthe noticeable decline in uncertainty (H) followingits double peak (Fig. 7A, C, D). Uncertainty is ameasure of the diversity of material exchangepathways, and increases as a given amount ofTST is more equally partitioned into ever morepathways (Ulanowicz, 1986). The double peaks inuncertainty corresponded to the period in thesimulation when all species existed as the special-ists were slowly replacing the generalists. It was atthis unique point in the simulation when thenumber of pathways of material exchange perunit system throughput was at its peak. H thenlevelled off after a steep decline corresponding tothe point when the generalist k-selected speciescompletely out competed their r-selected counter-parts and dominated for the remainder of thesimulation. Therefore, the behaviour of capacitywas largely the result of TST, but the slightdecline at the midpoint of the simulation, and thedecreased slope in the second half of the simula-tion was attributed to declines in H.

Overhead (L) also increased throughout thesimulation in a manner similar to TST. However,L showed a slight peak at the midpoint of thesimulation followed by a gradual decline in thethird quarter, and then a gradual increase in thefourth. L is measured as the difference between Cand A, or as TST(H−AMI) (Ulanowicz, 1986).Because AMI was nearly constant for the entiresecond half of the simulation the behaviour of Lwas largely determined by the rate of increase inTST and decline in H. In the third quarter of thesimulation the rapid decline in H overcame theslight increase in TST resulting in the slight de-cline in L. In the fourth quarter of the simulation

H levelled off and the slight increase in L wasattributable to the slight increase in TST.

This behaviour in L was inconsistent with ourhypotheses. According to theory (Ulanowicz,1986) overhead should decrease with ecologicalsuccession as A approaches C, or AMI ap-proaches H. These phenomena occur as the moreefficient specialists tend to dominate the food webresulting in a greater diversity of flow pathways,but fewer connections per node, less mortality,less respiration and export per unit biomass, andinputs which are partitioned into fewer compo-nents. L increased throughout the simulation be-cause of the dominant influence of TST. However,L/TST declined throughout the simulation in amanner more consistent with our hypotheses (Fig.8A). In addition, each of the five components ofoverhead also declined throughout the simulationwhen corrected for the dominant influence of TST(Fig. 8B). Further evidence supporting our hy-potheses comes from the fact that AMI ap-proaches H in the second half of the simulation asAMI remains constant while H declines, and thisleads to a slight convergence in the A and Lcurves as A makes up a larger proportion of C(Fig. 7A, B, C).

Finally, as a more empirical measure of theability of the network indices to quantify thetrends associated with ecological succession weplotted and quantified the relationship betweeneach indice and the ratio of the biomass of ther-selected species with the total system biomass(BR) (Fig. 9). A low BR indicates dominance byk-selected species and represents a system in thelater stages of ecological succession. Whereas ahigher BR indicates dominance by r-selected spe-cies characteristic of an early successional ecosys-tem. Therefore, the strong negative correlationbetween the BR and A, C, AMI, and TST sup-ported our hypotheses based on the theory behindthe network indices. We hypothesized that over-head would be positively correlated with the BR,but as explained earlier a negative correlationresulted due to the dominant effects of TST.However, the fact that the correlation was weakerthan that of A, C, AMI and TST lends somesupport to our initial hypotheses. In addition,there was a strong positive correlation between


Fig. 10. (A) A phase-plane plot of the relationship between the value of total system overhead per unit TST and the biomass ratio;(B–F) the relationship between each of the five components of overhead per unit TST and the biomass ratio.

the BR and the overhead values per unit TST (Fig.10A, B).

4.3. Limitations of simulation modelling

Overall, the behaviour of the suite of networkindices in relation to our simulated ecologicalsuccession event was largely consistent withUlanowicz (1986) theory of indice response to

ecosystem development. In the first half of oursimulated ecological succession event we witnesseda dramatic increase in TST, A, C, and L as avail-able resources were quickly utilized. In addition,the BR declined as the k-selected species replacedtheir r-selected counterparts leading to the dra-matic increase in AMI. Finally, H peaked when allspecies in the system were equally represented atthe midpoint of the r to k-selected dominance shift.


In the second half of our ecological successionevent TST, C, and A continue to increase slightlywhile AMI, H and L essentially level off. Thecontinued increase in TST, C and A are consistentwith our hypotheses, however we also suspectedAMI would continue to increase while H re-mained fairly constant and L declined. In hind-sight these apparent contradictions can beattributed to limitations imposed by our simula-tion model that would likely be absent in naturalsystems. For example, in our model the maximumnumber of species in each trophic level was eitherthree, four or five. This resulted in a cap on thevalue of H, and the peaks in H corresponding tothe points in the simulation when all species wereco-dominant. Beyond this point as the k-selectedspecies attained clear dominance biodiversity andH actually declined from their co-dominancepeaks. In a natural system as diversity increaseswith succession H would likely continue to in-crease well beyond the levels representing therelatively early successional co-dominance of rand k-selected species. This suggests that deter-mining the appropriate levels of aggregation maybe crucial to the success of using simulation mod-els in combination with the network indices tomeasure the health of any given ecosystem.

Another problem with our simulated successionevent was that TST tended to dominate the moreinteresting contributions of AMI and H through-out the entire simulation. In the later stages ofsuccession changes in AMI and H should domi-nate the relatively small changes in TST. Theproblem is that ecosystem simulation models aretypically rigid in structure, and offer only a me-chanical description of ecosystem dynamics. Oncethe original framework of a model is set, thevalues representing the component biomasses andtheir interconnecting flows can vary dramatically,but new components or pathways of mediumexchange between them (changes in network to-pology) often cannot arise, nor can previous onesdisappear.

Ulanowicz (1986) indices are sensitive to bothchanges in the relative magnitude of mediumtransferred within a static network topology, andchanges in the actual topology itself. In our simu-lation model, the network topology was fixed, so

our indices were only responding to the first ofthese two factors, and TST tended to dominatethe more subtle effects of AMI and H. In naturalsystems, of course, the topology of food webs arenot fixed. A simulation model capable of captur-ing each of these factors would lead to far morevariability in the measures of AMI and H, henceA, C and L. Jorgensen (1986, 1988a,b, 1992) de-scribes a new generation of structurally dynamicsimulation models based on goal functions whichevaluate the unique parameter set that optimizesthe function at each particular time step, andwhich may be capable of depicting the interestingchanges in network topology often missed bymore traditional modelling approaches. It is cru-cial to develop these more dynamic simulationmodels capable of simulating changes in networktopology if Ulanowicz (1986) indices are to beused to measure the hindrance or reversal of thetrends associated with ecological succession.

Christensen (1995) used Odum (1969) list ofsuccessional attributes to develop and index ofecosystem maturity, and examined the correlationbetween his maturity index and many of Ulanow-icz (1986) indices using 41 steady-state models ofaquatic ecosystems. Christensen found that over-head was positively correlated with his index ofsystem maturity. This is in agreement with ourfindings discussed above, although counter toUlanowicz (1980) hypothesis. As described above,we suggest that the dominating effects of increas-ing TST along with ecological succession or matu-rity relative to the more subtle effects of AMI andH typical of topologically rigid simulation modeloutput may explain this apparent positive correla-tion. In fact, Costanza suggests replacing TSTwith net system throughput (NST) which wouldsimultaneously avoid the problems associatedwith the dominant effects of TST over H andAMI, and make the analysis independent of scaleor the level of system aggregation.

Christensen also found that relative ascendancy(A/C) was negatively correlated with his maturityindex, which is directly opposed to Ulanowicz(1980) hypothesis, and our report of ascendancyincreasing along with the process of ecologicalsuccession. The measure of A/C can be reduced toAMI/H. Ulanowicz (1980) hypothesized that at


some point in the later stages of ecological succes-sion the value of H will no longer increase aschance perturbations effectively trim further in-creases in diversity. However, AMI can continueto increase despite the relatively constant value ofH as a greater proportion of material flows alongthe most efficient transfer pathways. Prior to thispoint in the later stages of ecological successionboth AMI and H are hypothesized to increase,and it is possible that H may increase faster thanAMI as organization lags behind increasing flowdiversity. Therefore, the negative correlation be-tween A/C and maturity may be attributed to thefact that none of the systems analyzed by Chris-tensen (1995) had advanced beyond this criticalpoint in maturity, or the simulation models repre-senting these systems were simply unable to cap-ture the subtle changes in network topology thatwould drive the hypothesized relation betweenmaturity and A/C.

4.4. Valuation of non-marketed ecosystemproducts and ser6ices

The ecological economic literature describesmany techniques aimed at the valuation of non-market ecosystem products and services. Thesetechniques range from the strictly biophysical ap-proaches such as embodied energy (Costanza,1980) to a variety of contingent valuation ap-proaches based primarily on the cognitive deci-sions or preferences of human beings. Each ofthese methods have their strengths and weak-nesses based on their relative abilities to capturethe biophysical and preference components ofvalue, and the degree of uncertainty their esti-mates contain.

Ulanowicz (1997) describes a robust valuationtechnique based on a modified version of ascen-dancy which incorporates component biomassvalues. In this approach, the contribution of eachcomponent to the overall system ascendancy rep-resents the value of the stocks stored there in thecontext of the functioning of the entire ecosystem.Therefore, the ascendancy characterizing a partic-ular component in the system represents the rela-tive value of that component as a member of thefunctioning ecosystem. The ascendancy for each

component can be easily calculated along with theindices described above, and can be converted toa monetary value given some ratio of dollars/as-cendancy. This ratio can be determined from acomponent in the system with a defined marketvalue (i.e. salmon or lumber). This ascendancybased valuation technique is extremely inclusiveand easy to calculate, but it provides only aconservative estimate of value relative to somemarketable ecosystem product.

One must obtain a comprehensive estimate ofthe value of the entire ecosystem in question foruse in place of the value of a single species toovercome the problem of overly conservative indi-vidual component value estimates (Costanza etal., 1997). A better estimate of overall ecosystemvalue, hence individual component values, couldbe obtained by summing the known market valuesof the many products and services the systemprovides, and including a conservative estimate ofany additional instrumental and intrinsic value.This estimate of overall system, hence individualcomponent value would be no more arbitrary thatany other valuation technique currently offered,and would be more comprehensive than onebased on only the value of a single species. Inregards to overall system valuation, the sametrade-off (between precision and comprehensive-ness) characterizing the various measures ofecosystem health appears to arise. Perhaps, inaddition to developing an ecological economicmodel, a group of individuals with a vested inter-est in the particular system could arrive at aconsensus regarding the optimal balance betweenprecision and comprehensiveness while estimatingthe value of their particular ecosystem (Costanzaand Ruth, 1998). Finally, given the uncertaintyembodied in any estimate of overall ecosystemvalue, it may be extremely useful to consider themost likely consequences of such an estimate onthe health of the ecosystem when making a valua-tion decision. The valuation procedure suggestedhere would provide such immediate feedback, andthe opportunity to factor the likely consequencesof any particular estimate on the health of theecosystem into the decision making process.


5. Conclusion

We feel the ecosystem health assessment de-scribed in this paper is both comprehensive in thatit is based on the system-wide trends expected instressed ecosystems, and operational in that theindices can be calculated given output from ap-propriate simulation models. Our general simula-tion model successfully depicted many of thetrends characteristic of ecological succession(Odum, 1969), and, in many cases, Ulanowicz(1986) indices responded to these trends as hy-pothesized. The apparent discrepancies were likelyattributed to limitations inherent in typical simu-lation models such as limited diversity due toaggregation, and the dampening effects of rigidnetwork topology on the variation of H and AMIrelative to TST. We suggest these indices may beused to quantify the trends associated with eco-logical succession, hence the reversal of thesetrends associated with anthropogenic ecosystemstress. Finally, an ascendancy based valuationmethodology can be included as part of the analy-sis making it possible to not only quantify thehealth of a particular ecosystem, but to estimatethe economic value of its individual componentsas well. We conclude that this assessment ofecosystem health in combination with the ascen-dancy based valuation technique may provide aninformative compliment to many past and futureregional modelling projects concerned with betterunderstanding and managing the impacts of an-thropogenic stress on our natural ecosystems.

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