ecopath with ecosim: methods, capabilities and limitationsecological modelling 172 (2004) 109–139...

Ecological Modelling 172 (2004) 109–139

Ecopath with Ecosim: methods, capabilities and limitations�

Villy Christensen∗, Carl J. WaltersFisheries Centre, University of British Columbia, 2204 Main Mall, Vancouver, BC, Canada V6T 1Z4

Abstract

The Ecopath with Ecosim (EwE) modeling approach combines software for ecosystem trophic mass balance analysis (Ecopath),with a dynamic modeling capability (Ecosim) for exploring past and future impacts of fishing and environmental disturbancesas well as for exploring optimal fishing policies. Ecosim models can be replicated over a spatial map grid (Ecospace) to allowexploration of policies such as marine protected areas, while accounting for spatial dispersal/advection effects.

The Ecopath approach and software has been under development for two decades, with Ecosim emerging in 1995, andEcospace in 1998, leading to an integrated and widely applied package. We present an overview of the computational aspects ofthe Ecopath, Ecosim and Ecospace modules as they are implemented in the most recent software version. The paper summarizesthe capabilities of the modeling system with respect to evaluating how fisheries and the environment impact ecosystems. Weconclude by a warning about pitfalls in the use of the software for policy exploration.© 2003 Elsevier B.V. All rights reserved.

Keywords:Ecosystem model; Fisheries management; Policy exploration; Ecopath with Ecosim

1. Introduction

The modeling approach ‘Ecopath with Ecosim’(EwE, http://www.ecopath.org) is being widely usedas a tool for analysis of exploited aquatic ecosystems,having reached 2400 registered users in 120 coun-tries, and leading to in excess of 150 publications.EwE combines software for ecosystem trophic massbalance (biomass and flow) analysis (Ecopath) with adynamic modeling capability (Ecosim) for exploringpast and future impacts of fishing and environmentaldisturbances. It has an elaborate user interface thateases a variety of data management chores and calcu-lations that are a cumbersome but necessary part of

� Manuscript PFITEC-2 (EMECS 9) for Ecological Modeling,May 2003.

∗ Corresponding author. Tel.:+1-604-822-5751;fax: +1-604-822-8934.

E-mail address:[email protected] (V. Christensen).

any endeavor to systematically examine an ecosystem,its resources, and their interactions and exploitation.

Recent versions of the software have broughtEcosim much closer to traditional single-species stockassessment, by allowing age-structured representationof particular, important populations and by allowingusers to ‘fit’ the model to data. Ecosim models can bereplicated over a spatial map grid (Ecospace) to allowexploration of policies such as marine protected ar-eas, while accounting for spatial dispersal/advectioneffects and migration.

The Ecopath approach was initiated byPolovina(1984) in the early 1980s, and has been under con-tinuous development since 1990 (Christensen andPauly, 1992), with Ecosim emerging in 1995 (Walterset al., 1997, 2000), and Ecospace in 1998 (Walterset al., 1999), leading to an integrated software pack-age, ‘Ecopath with Ecosim’. We give an overviewof the computational aspects and capabilities of theEcopath, Ecosim and Ecospace modules as they are

0304-3800/$ – see front matter © 2003 Elsevier B.V. All rights reserved.doi:10.1016/j.ecolmodel.2003.09.003

http://www.ecopath.org

110 V. Christensen, C.J. Walters / Ecological Modelling 172 (2004) 109–139

implemented in the most recent software version(EwE Version 5), along with some reflections of po-tential pitfalls related to application of the software.

2. Mass-balance modeling: Ecopath

The core routine of Ecopath is derived from theEcopath program ofPolovina (1984), and since mod-ified to make superfluous its original assumption ofsteady state. Ecopath instead bases the parameteriza-tion on an assumption of mass balance over a giventime period (usually 1 year, but see discussion belowabout seasonal modeling). In its present implemen-tation Ecopath parameterizes models based on twomaster equations, one to describe the production term(Eq. (1)), and one for the energy balance for eachgroup (Eq. (7)). A summary of symbols used for vari-ables is presented inTable 2.

2.1. Prey mortality is predator consumption

The total production ratePi for each groupi can besplit in components:

Pi = Yi + M2i × Bi + Ei + BAi + M0i × Bi (1)

where Yi is the total fishery catch rate ofi, M2i isthe instantaneous predation rate for groupi, Ei thenet migration rate (emigration− immigration), BAiis the biomass accumulation rate fori, while M0i isthe ‘other mortality’ rate fori. Pi is calculated asthe product ofBi, the biomass ofi and (P/B)i, theproduction/biomass ratio fori. The (P/B)i rate undermost conditions corresponds to the total mortalityrate,Z (seeAllen, 1971), commonly estimated as partof fishery stock assessments. The ‘other mortality’ isa catch-all rate including all mortality not elsewhereincluded, and is internally computed from

M0i = Pi × (1 − EEi)

Bi

(2)

where EEi is called the ‘ecotrophic efficiency’ ofi, andcan be described as the proportion of the productionthat is utilized in the system as described, seeEq. (6).

The predation term,M2, in Eq. (1) serves to linkpredators and prey as

M2i =n∑

j=1

Qj × DCji

Bi

(3)

where the summation is over alln predator groupsjfeeding on groupi, Qj is the total consumption ratefor groupj, and DCji is the fraction of predatorj’s dietcontributed by preyi. Qj is calculated as the productof Bj, the biomass of groupj and (Q/B)j, the con-sumption/biomass ratio for groupj.

An important implication of the equation above isthat information about predator consumption rates anddiets concerning a given prey can be used to estimatethe predation mortality term for the group, or, alterna-tively, that if the predation mortality for a given preyis known the equation can be used to estimate the con-sumption rates for one or more predators instead.

For parameterization Ecopath sets up a system with(at least in principle) as many linear equations as thereare groups in a system, and it solves the set foroneof the following parameters for each group, biomass,production/biomass ratio, consumption/biomass ratio,or ecotrophic efficiency. The other three parametersalong with following parameters must be entered forall groups, catch rate, net migration rate, biomass ac-cumulation rate, assimilation rate and diet composi-tions.

It was indicated above that Ecopath does not relyon solving a full set of linear equations, i.e. there maybe less equations than there are groups in the system.This is due to a number of algorithms included in theparameterization routine that will try to estimate itera-tively as many ‘missing’ parameters as possible beforesetting up the set of linear equations. The followingloop is carried out until no additional parameters canbe estimated:

1. The gross food conversion efficiency,gi, is esti-mated using

gi = (P/B)i

(Q/B)i(4)

while (P/B)i and (Q/B)i are attempted solved byinverting the same equation.

2. TheP/B ratio is then estimated (if possible) from

Pi

Bi

= Yi + Ei + BAi +∑

j Qj × DCji

Bi × EEi(5)

This expression can be solved if both the catch,biomass and ecotrophic efficiency of groupi, andthe biomasses and consumption rates of all preda-tors on groupi are known (including groupi if

V. Christensen, C.J. Walters / Ecological Modelling 172 (2004) 109–139 111

a zero order cycle, i.e. ‘cannibalism’ exists). Thecatch, net migration and biomass accumulationrates are required input, and hence always known.

3. The EE is sought estimated from

EEi = Yi + Ei + BAi + Bi × M2iPi

(6)

where the predation mortalityM2 is estimated fromEq. (3).

4. In cases where all input parameters have beenestimated for all prey for a given predator groupit is possible to estimate both the biomass andconsumption/biomass ratio for such a predator.The details of this are described in the EwE HelpSystem, Appendix 4, Algorithm 3 (available athttp://www.ecopath.organd distributed with EwE).

5. If for a group the total predation can be estimatedit is possible to calculate the biomass for the groupas described in detail in the EwE Help System,Appendix 4, Algorithm 4.

6. In cases where for a given predatorj theP/B, B, andEE are known for all prey, and where all predationon these prey apart from that caused by predatorj is known theB or Q/B for the predator may beestimated directly.

7. In cases where for a given prey theP/B, B, EEare known, and where the only unknown predationis due to one predator for which theB or Q/B isunknown, it may be possible to estimate theB orQ/B of the prey in question.

After the loop no longer results in estimate of any‘missing’ parameters a set of linear equations is setup including the groups for which parameters are still‘missing’. The set of linear equations is then solvedusing a generalized method for matrix inversion de-scribed by (Mackay, 1981). It is usually possible toestimateP/B and EE values for groups without re-sorting to including such groups in the set of linearequations.

The loop above serves to minimize the computa-tions associated with establishing mass-balance inEcopath. The desired situation is, however, that thebiomasses, production/biomass and consumption/biomass ratios are entered for all groups and that onlythe ecotrophic efficiency is estimated, given that noprocedure exists for its field estimation. As a con-sequence, the estimated ecotrophic efficiency can be

considered an expression of model uncertainty ratherthan an ecologically meaningful term.

In some, but very rare, cases it may not be possibleto estimate the ‘missing’ parameters using the meth-ods referred to above, for instance if a feeding cycle(e.g. A eatsB eatsC eatsA), is included where thebiomasses of all groups in the cycle are unknown. Insuch cases a routine will break the cycle by removingthe link where the difference between the trophic levelof the consumer and the prey has the lowest value, typ-ically this will be where a low trophic-level consumereats high trophic-level prey (which are actually lowertrophic-level juveniles). An iterative routine will thenestimate all ‘missing’ biomasses.

The mass balance constraint implemented in the twomaster equations of Ecopath (seeEqs. (1) and (7))should not be seen as questionable assumptions butrather as filters for mutually incompatible estimates offlow. One gathers all possible information about thecomponents of an ecosystem, of their exploitation andinteraction and passes them through the ‘mass balancefilter’ of Ecopath. The result is a possible picture ofthe energetic flows, the biomasses and their utiliza-tion. The more information used in the process and themore reliable the information, the more constrainedthe outcome will be.

2.2. The energy balance of a group

After the ‘missing’ parameters have been estimatedso as to ensure mass balance between groups energybalance is ensured within each group using the fol-lowing equation:

Consumption= production+ respiration

+ unassimilated food (7)

This equation is in line withWinberg (1956), whodefined consumption as the sum of somatic and go-nadal growth, metabolic costs and waste products. Themain differences are that Winberg focused on mea-suring growth, where we focus on estimating losses,and that the Ecopath formulation does not explicitlyinclude gonadal growth. The Ecopath equation treatsthis as included in the predation term (where nearlyall gonadal products end up in any case). This may bea shortcoming, but it is one that can be remedied, andactually is in Ecosim as described below.

http://www.ecopath.org


We have chosen to perform the energy balance soas to estimate respiration from the difference betweenconsumption and the production and unassimilatedfood terms. This mainly reflects our focus on applica-tion for fisheries analysis, where respiration rarely ismeasured while the other terms are more readily avail-able. To facilitate computations we have, however, in-cluded a routine (‘alternative input’) where the energybalance can be estimated using any given combination(including ratios) of the terms in the equation above.

Ecopath can work with energy as well as with nutri-ent related currencies. If a nutrient-based currency isused in Ecopath the respiration term is excluded fromthe above equation (as nutrients are not respired), andthe unassimilated food term is estimated as the differ-ence between consumption and production.

2.3. Addressing uncertainty

A resampling routine, Ecoranger, has been includedin EwE to accept input probability distributions forthe biomasses, consumption and production rates,ecotrophic efficiencies, catch rates, and diet composi-tions. Using a Monte Carlo approach a set of randominput variables is drawn from user-selected frequencydistributions and the resulting model is evaluatedbased on user-defined criteria, and physiological andmass balance constraints. The results include proba-bility distributions for the estimated parameters alongwith distributions of parameters in the accepted modelrealizations.

The Ecoranger routine can provide probability dis-tributions for transformation of the input variables.The derived probability distributions are likely to benarrower than the original distributions indicating thatwe have gained information in the process of check-ing for mass balance constraints, and eliminatingparameter combinations that violate thermodynamicconstraints. The information that is gained comesfrom evaluation of structural relationships as imple-mented in the Ecopath model, contrary to standardBayesian approaches, which rely on data sampling.Combining such structural information from Ecopathwith prior probabilities (the original probability dis-tributions) corresponds to combining data with priorsto derive the posterior distributions in the Bayesiansense. A procedure implementing such an approachusing a ‘sampling–importance–resampling’ scheme

(McAllister et al., 1994) is included in the Ecor-anger module of EwE making it straightforward toderive what may be called ‘Bayes marginal posteriordistributions’ (Walters, 1996).

2.3.1. Categorizing data sourcesThe Ecoranger module has been available for sev-

eral years but only a few examples of its use havebeen published, and so far none has fully exploited itsBayesian capabilities. A major reason for this is thatit was a very data intensive task to describe the proba-bility distributions for all input parameters (includingthe diet compositions matrices). To facilitate this taskand to make the process more transparent we have im-plemented a ‘pedigree’ (Funtowicz and Ravetz, 1990)routine that serves a dual purpose by describing dataorigin, and by assigning confidence intervals to databased on their origin (Pauly et al., 2000).

The pedigree routine allows the user to mark thedata origin using a pre-defined table for each typeof input parameters. An example pertaining to bothproduction/biomass and consumption/biomass ratiosis given inTable 1. The Ecoranger module can sub-sequently pick up the confidence intervals from thepedigree tables and use these as prior probability dis-tributions for all input data.

The pedigree index values inTable 1are also used tocalculate an overall pedigree index for a given model.

Table 1Options included in EwE for definition of ‘pedigree’ for consumerproduction/biomass and consumption/biomass ratios in Ecopath

Option Index CI (%)

Estimated by Ecopath (other model) 0.0 ±80Guesstimate 0.1 ±70From other model 0.2 ±60Empirical relationship 0.5 ±50Similar group/species, similar system 0.6 ±40Similar group/species, same system 0.7 ±30Same group/species, similar system 0.8 ±20Same group/species, same system 1.0 ±10

Similar option tables are implemented for biomasses, catches, anddiets. For each group in an ecosystem one of these options is usedto define the pedigree of the input parameter. The index value isused for calculation of a pedigree index. The confidence intervals(CI) are used to describe parameter uncertainty in the balancedecosystem model using the Ecoranger, auto mass balance, andEcosim modules. Index values and confidence intervals are defaultsthat can be changed by users.


Table 2List of symbols used

Symbol Description Unit

B Biomass t km−2

BAi Biomass accumulation rate t km−2 per yearc Per biomass food intake, same asQ/B Per yearDCji Fraction of predatorj’s diet contributed by preyiE The net migration rate (emigration− immigration), orei × Bi − Ii t km−2 per yeare Emigration rate per unit biomass t km−2 per yearEE Ecotrophic efficiencyF Instantaneous fishing mortality rate Per yearg Gross food conversion efficiency, estimated as theP/Q ratioI Immigration rate t km−2 per yeari Index used for prey groups (all consumer groups can be prey as well as predators)j Index used for predator groupsK von Bertalanffy curvature parameter Per yearM0 Instantaneous ‘other mortality’ rate Per yearM2 Instantaneous predation rate Per yearn Number of living groups in the modelP Total production rate t km−2 per yearP/B Production/biomass ratio Per yearQ Total consumption rate, calculated as the product ofB and Q/B t km−2 per yearQ/B Consumption/biomass ratio Per yearSS Summed squared residualsvij Vulnerabilities (rescaled to range [1,ω])Y Total fishery catch rate t km−2 per yearZ Total mortality rate, equivalent to the production/biomass ratio Per year

Omits symbols that are used in only one section. Many symbols will have an index (or indices) referring to a group.

The index values for input data scale from 0 for datathat is not rooted in local data up to a value of 1 fordata that are fully rooted in local data. Based on theindividual index value an overall ‘pedigree index’,τ,is calculated as the average of the individual pedigreevalue based on

τ =n∑i=1

τi,p

n(8)

whereτi,p is the pedigree index value for groupi andinput parameterp for each of then living groups in theecosystem;p can represent eitherB, P/B, Q/B, Yor thediet composition, DC. To scale based on the numberof living groups in the system, an overall measure offit, t∗ is calculated (using an equation based on howthe t-value for a regression is calculated) as

t∗ = τ ×√n − 2√1 − τ2

(9)

This measure of fit is seen to describe how wellrooted a given model is in local data. It addresses an

often-aired concern of to which degree ‘models feedon models’, i.e. whether models are based on datafrom other models, which again are based on datafrom other models, etc. Work is presently in progressto describe the pedigree indices for all publishedEcopath models where we have access to the modeldescriptions (in excess of 140 cases; Lyne Morisette,Fisheries Centre, UBC, personal communication).

2.4. Automated mass-balance

Getting hold of and entering input parameters foran Ecopath model is only the start of the modelingprocess, ensuring mass-balance is the next major step.Previously this had to be done by manually adjust-ing biomasses, mortality rates, diets, etc., searchingfor data inconsistencies and gradually obtaining abalanced model. An iterative method for obtainingmass-balance has, however, been added to EwE, of-fering a well defined, reproducible, approach, whilealso allowing exploration of alternative solutionsbased on parameter confidence intervals. Background,


implementation and computational aspects of theauto-mass balance routine are described byKavanaghet al. (2004).

The auto-balancing routine uses the pedigree rou-tine described above to obtain confidence intervals,which in turn constrains how far the routine can per-turb parameters from their original values as part of thebalancing. While seeking to obtain a balanced model(i.e. EEi ≤ 1 for all groupsi) with minimal changes toinput parameters, especially for well-known parame-ters (with narrow confidence intervals), which are al-lowed less adjustment than parameters with wide con-fidence intervals.

At each iteration step, the model is perturbed byadjusting the biomass and diet components affectinggroups with EE> 1. Model perturbation may be per-formed in three different ways:

(1) Random lookup of parameters within confidenceinterval (no memory of current state) similar to theEcoranger approach discussed above, except forchanging only parameters affecting unbalancedgroups;

(2) Random steps in the neighborhood of the currentstate;

(3) Gradient descent method using the first derivativeof EE with respect to the parameter to be per-turbed.

The approach allows for user-defined specification ofthe cost function as well as of the decision logic, whichincludes a simulated annealing method. Also, a MonteCarlo approach allows for quantification of sensitivityto starting conditions and perturbations.

2.5. Particle size distributions

Based on growth and mortality information (see in-put data) the particle size distribution (PSD;Sheldonet al., 1972) for a model can be calculated. A rou-tine for this is included in EwE, where for each livinggroup the following steps are conducted:

The time spent in each of a user-defined number ofweight class is calculated starting at time 0, using

t = ln[1 − (Wt/W∞)−b]

−K+ t0 (10)

where Wt is the lower limit of the weight interval,W∞ is the asymptotic weight,b the exponent in the

length-weight relationship,K the curvature parameterof the von Bertalanffy Growth Function (VBGF), andt0 is the usually negative ‘age’ at which the weight isestimated to be zero in the VBGF. Once the time spentto reach each weight class limit is calculated, the timespent in each weight class is calculated by subtraction.

The survival is calculated as

Nt = Nt−�t × e−Z×�t = Nt−dt × e−Z×�t (11)

whereNt is the number alive at timet, Nt−�t the num-ber alive at the previous time step,�t before, andZis the total mortality rate, equivalent to the produc-tion/biomass ratio for the group;

The biomass contribution for the group to eachweight class is calculated as

Bt = Nt × Wt × �t (12)

whereBt is the biomass contribution,�t is the time thegroups spends to grow through the given weight class(t), and the rest as explained above.Bt is scaled overall weight classes so as to sum up to the total biomassof the group. The system PSD is calculated, finally, bysumming up over all groups within each weight class.

2.6. Ecosystem ‘health’

The health status of a patient can often be capturedwith a single parameter, the temperature. Many havetried to find an index with similar ability to describethe health of an ecosystem to avoid the insurmount-able task associated with bottom-up approach sum-ming up the health of all ecosystem components, buta clear candidate has not appeared. The effort has ledto development and description of a variety of systemindicators, typically though with a given researcherexploring only one or a few of the potential indicatorsand on one or a few systems only.

We have sought to include a selection of ecosystemindicators in EwE using the criteria that the indicatorscan be estimated based on information included or po-tentially includable in EwE, typically based on quan-tified descriptions of food webs. In doing so we havefacilitated straightforward calculation of the indices,opening for a comparison of their properties throughapplication to a variety of the models described usingEcopath.

One area of research where we have used thisapproach relates to ecosystem maturity, a perceived


descriptor of ecosystem ‘health’.Odum (1969, 1971)described how ecosystems in a non-deterministic waydevelop over time. We can assume an undisturbedecosystem to be maturesensuOdum. Implications ofthis include that in a more mature system all nichesshould tend to be filled; that a larger part of theenergy flows should be through detritus-based foodwebs; that primary production should be more effi-ciently utilized; that the total system biomass/energythroughput ratio should be higher, etc.

When ecosystems are disturbed, notably by fishing,we expect their maturity to decrease. This was indi-cated by the findings ofChristensen (1995a), who useda series of indicators to rank a large number of ecosys-tem representations after maturity, and concluded thatthe ranking obtained was in agreement with the ex-pected state of maturity. The study included severalecosystems for which the maturity state could be com-pared before and after a disturbance, and the findingswere in all cases in agreement with disturbances lead-ing to a reduction in maturity.Christensen and Pauly(1998)modeled the recent and the unfished state fortwo marine ecosystems, and for both systems con-cluded that the indices of ecosystem maturity for thefished and unfished states in all cases were in agree-ments with Odum’s theory.

While these studies cannot be seen as providingdefinitive answers, they do indicate that it is feasible touse a composite of ecosystem indices to describe thestate of a given system and how it may have changedover time. We intend to explore this further, and toinclude a number of additional measures of ecosystem‘health’ in EwE.

The selection of ecosystem indicators referred toabove is included in EwE as part of a series of networkanalyses. In overview form (see references below andthe EwE Help system for more detailed descriptions)the following routines are among those included:

• Cycling index: fraction of an ecosystem’s through-put that is recycled (Finn, 1976).

• Predatory cycling index: corresponds to the cyclingindex but computed with cycles involving detritusgroups excluded.

• Cycles and pathways: a routine presents the numer-ous cycles and pathways that are defined by thefood web representing an ecosystem based on anapproach suggested byUlanowicz (1986).

• Connectance index: defined for a given food webas the ratio of the number of actual links to thenumber of possible links. Feeding on detritus (bydetritivores) is included in the count, but the oppo-site links (i.e. detritus ‘feeding’ on other groups) aredisregarded.

• System omnivory index: defined as the averageomnivory index of all consumers weighted by thelogarithm of each consumer’s food intake. The log-arithms are used as weighting factors because it canbe expected that the intake rates are approximatelylog normally distributed. The system omnivory in-dex is a measure of how the feeding interactions aredistributed between trophic levels. An omnivoryindex is also calculated for each consumer group,and it here is a measure of the variance of thetrophic level estimate for the group.

• Trophic level decomposition: aggregates the systeminto discrete trophic levelssensuLindeman basedon an approach suggested byUlanowicz (1995). Theroutine reverses the routine for calculation of frac-tional trophic levels.

• Trophic transfer efficiencies: calculated for a giventrophic level as the ratio between the sum of theexports plus the flow that is transferred from onetrophic level to the next, and the throughput on thetrophic level. The transfer efficiencies are used forconstruction of trophic pyramids, and others.

• Primary production required (PPR): to estimate thePPR (Christensen and Pauly, 1993) to sustain thecatches and the consumption by the trophic groupsin an ecosystem the following procedure is used.All cycles are removed from the diet compositions,and all pathways in the flow network are identifiedusing the method suggested byUlanowicz (1995).For each pathway the flows are then raised to pri-mary production equivalents using the product ofthe catch, the consumption/production ratio of eachpath element times the proportion the next elementof the path contributes to the diet of the given pathelement.

• Mixed trophic impact (MTI): Leontief (1951)devel-oped a method for input–output analysis to assessthe direct and indirect interactions in the economyof the USA, using what has since been called the‘Leontief matrix’. A modified input–output analy-sis based on the procedure described byUlanowiczand Puccia (1990)is implemented in EwE. The MTI


describes how any group (including fishing fleets)impacts all other groups in an ecosystem trophically.It includes both direct and indirect impact, i.e. bothpredatory and competitive interactions.

The MTI for living groups is calculated by con-structing ann × n matrix, where thej, ith elementrepresenting the interaction between the impactinggroup j and the impacted groupi is

MTI ji = DCji − FCij (13)

where DCji is the diet composition term expressinghow muchi contributes to the diet ofj, and FCij is ahost composition term giving the proportion of thepredation onj that is due toi as a predator. Whencalculating the host compositions the fishing fleetsare included as ‘predators’.

For each fishing fleet a ‘diet composition’ is cal-culated representing how much each group con-tributes to the catches, while the host compositionterm as mentioned above includes both predationand catches. The matrix is inversed using a standardmatrix inversion routine.

• Ascendency: EwE includes a number of indices re-lated to the ascendency measure described in detailby Ulanowicz (1986). Ascendency is seen as a mea-sure of ecosystem growth and development.

3. Time-dynamic simulation: Ecosim

The basics of Ecosim are described in detail byWalters et al. (1997, 2000), and will only be given acursory treatment here, omitting details that have beenpreviously published, focusing instead in describingmore recent additions to the modeling approach. Inoverview, Ecosim consists of biomass dynamics ex-pressed through a series of coupled differential equa-tions. The equations are derived from the Ecopath mas-ter Eq. (1), and take the form

dBi

dt= gi

∑j

Qji −∑j

Qij + Ii

− (M0i + Fi + ei) × Bi (14)

where dBi/dt represents the growth rate during thetime interval dt of group i in terms of its biomass,Bi, gi is the net growth efficiency,Eq. (4), M0i thenon-predation (‘other’) natural mortality rate esti-

Fig. 1. Simulation of flow between available (Vi) and unavailable(Bi − Vi) prey biomass in Ecosim.ai is the predator search ratefor prey i, v is the exchange rate between the vulnerable andun-vulnerable state. Fast equilibrium between the two prey statesimplies Vi = vBi/(2v + aBj). Based onWalters et al. (1997).

mated from the ecotrophic efficiency,Fi is fishingmortality rate,ei is emigration rate,Ii is immigrationrate (assumed constant over time, and hence inde-pendent of events in the ecosystem modeled), andei × Bi − Ii is the net migration rate ofEq. (1). Thetwo summations estimates consumption rates, the firstexpressing the total consumption by groupi, and thesecond the predation by all predators on the samegroup i. The consumption rates,Qji , are calculatedbased on the ‘foraging arena’ concept, whereBi’s aredivided into vulnerable and invulnerable components(Walters et al., 1997, Fig. 1), and it is the transfer rate(vij ) between these two components that determines ifcontrol is top-down (i.e. Lotka–Volterra), bottom-up(i.e. donor-driven), or of an intermediate type. Theset of differential equations is solved in Ecosim usingan Adams–Basforth integration routine (default) or aRunge–Kutta fourth-order routine.

Detritus flows are for each detritus group and foreach time step estimated from the amount of detritusimported, transferred from other detritus groups, andproduced by ecosystem groups (from unassimilatedfood plus contribution from dead organisms) less theamount of detritus eaten by living groups, transferredto other detritus groups and the export of detritus.

3.1. Predicting consumption

Ecosim bases the crucial assumption for predictionof consumption rates on a simple Lotka–Volterra or‘mass-action’ assumption, modified to consider ‘for-aging arena’ properties. Following this, prey can bein states that are or are not vulnerable to predation,


for instance by hiding (e.g. in crevices of coral reefsor inside a school), when not feeding, and only be-ing subject to predation when having left their shelterto feed (Fig. 1). In the original Ecosim formulations(Walters et al., 1997, 2000) the consumption rate fora given predator feeding on a prey was thus predictedfrom the effective search rate for predator–prey spe-cific interactions, base vulnerabilities expressing therate with which prey move between being vulnerableand not vulnerable, prey biomass, predator abundance(numbers for split pool groups as discussed later, andbiomasses for other groups).

The model as implemented implies that ‘top-downversus bottom-up’ control is in fact a continuum,where low v’s implies bottom-up and highv’stop-down control. The input vulnerability rates (υij ) inEwE are scaled to range from 0 to 1, with 0.3 serving asdefault for mixed control, and 0 implying bottom-up,1 implying top-down control. The actual vulnerabili-ties (vij ) used in the computations are rescaled fromthe enteredυij ’s as:vij = exp[2× (exp(υij ) − 1)].

As a consequence of user requests for adding newfacilities the equation for describing consumption hasgradually grown to the following, more elaborate ex-pression:

Qij =aij × vij × Bi × Bj × Ti × Tj

×Sij × Mij/Dj

vij + vij × Ti × Mij + aij × Mij

×Bj × Sij × Tj/Dj

(15)

whereaij is the rate of effective search fori by j, Tirepresents prey relative feeding time,Tj the predatorrelative feeding time,Sij the user-defined seasonal orlong term forcing effects,Mij the mediation forcingeffects, andDj represents effects of handling time asa limit to consumption rate:

Dj = hj × Tj

1 + ∑k akj × Bk × Tk × Mkj

(16)

wherehj is the predator handling time. The feedingtime factors, allocation of food for growth and re-cruitment, fecundity constraints, etc. are discussed byWalters et al. (1997, 2000). The consumptionEq. (15)above includes terms to describe forcing functions andmediation effects. These are described in more detailbelow.

3.1.1. Forcing functionsThe impact of physical or other environmental fac-

tors on ecosystem groupings may be modeled usingforcing functions are of two types:

• seasonal, which may be applied to biomass produc-tion or to egg production (for groups with onto-genetic representation) occurring within a year andrepeated in all years of the run; and

• longer term, which may be applied to modify theQ/B ratio of the consumer groups, to represent, forinstance, decadal regime shifts, and to force con-taminant contributions (seeSection 3.4) below.

3.1.2. MediationIt is not uncommon for some third type of organism

to affect the feeding rate of one type of organism onanother. At least two types of effects are possible:

• Facilitation: The third organism type behaves insome way that makes prey more available to apredator when the third organism is more abundant.For example, pelagic piscivores like tuna may drivesmaller fishes to the surface making them moreaccessible for birds. This is a concern for modelingmarine mammals and bird dynamics, especiallyin areas where fishing has reduced abundances oftunas and billfishes.

• Protection: The third organism provides protectionfor a prey type when the third organism is moreabundant. For example, juvenile fishes may usecorals, macrophytes, and/or sponges for protectionfrom predators, and fishing may directly impactthese ‘cover’ types, making the juvenile fishesaccessible for predation.

3.2. Life history handling

Ecosim offers to ways to handle life history dy-namics, through splitting groups in adult and juvenilecomponents, and through a recently added facility formodeling of multiple life stages.

3.2.1. Adult-juvenile splitTo better represent ontogenetic shifts in Ecosim

groups can be split in juvenile and adult components,Ecosim applies a Deriso–Schnute delay-differencemodel (Deriso, 1980; Schnute, 1987) to keep track ofthe number that recruits from juvenile to adult stages,


and the number at age/size in the adult groups. Theimplementation and computational aspects of this aredescribed byWalters et al. (2000).

The delay-difference representation of populationage and size structure permits explicit representationof changes in growth, mortality, and recruitment pro-cesses with changing feeding conditions. It also makesit straightforward to include: (1) changes in how foodintake is allocated between growth and reproductionas food conditions varies; (2) changes in vulnerabilityto predation associated with changes in feeding be-havior as prey densities vary; and (3) recruitment con-straints related to juvenile size and fecundity. Theseaspects will be described further below.

3.2.2. Multiple stanza representationsEwE users can create a set of biomass groups rep-

resenting life history stages or stanzas for species thathave complex trophic ontogeny. Mortality rates anddiet composition are assumed to be similar for indi-viduals within each stanza. The procedure requiresbaseline estimates of total mortality rate,Z and dietcomposition for each stanza, but biomass,Q/B, andbiomass accumulation, BA for one ‘leading’ stanzaonly.

For Ecopath mass balance calculations, the totalmortality rateZ entered for each stanza-group is usedto replace the EcopathP/B for that group. Further, theB and Q/B for all stanza-groups besides the leading(entry) stanza are calculated before entry to Ecopath,using the assumptions that:

(1) body growth for the species as a whole follows avon Bertalanffy growth curve with weight propor-tional to the length-cubed;

(2) the species population as a whole has had rela-tively stable mortality and relative recruitment ratefor at least a few years, and so has reached a sta-ble age–size distribution.

Under the stable age distribution assumption, therelative number of agea animals is given byla/

∑la,

where the sum is over all ages, andla is the populationgrowth rate-corrected survivorship:

la = e−∑aZa−a×BA/B (17)

where the sum ofZ’s is over all ages up toa, andthe BA/B term represents effect on the numbers atage of the population growth rate. Further, the relative

biomass of animals in stanzas should be

bs =∑as,max

a=as,minla × wa∑amax

a=1 la × wa

(18)

wherewa = [1 − exp(−K × a)]3 is the von Berta-lanffy prediction of relative body weight at agea, s,min ands, max are the youngest and oldest age foranimals in stanzas, and amax is the oldest age in-cluded overall. Knowing the biomass for one leadingstanza, and thebs for each stanzas, the biomasses forthe other stanzas can be calculated by first calculatingpopulation biomassB = Bleadings/bleadings, then set-ting Bs = bs ×B for the other stanzas.Q/B estimatesfor non-leading stanzas are calculated with a similarapproach. This assumes that the feeding rates varywith age as the 2/3 power of body weight (a ‘hidden’assumption in the von Bertalanffy growth model).This method for ‘extending’ biomass andQ/B esti-mates over stanzas avoids a problem encountered in‘split-group’ EwE representations, where users couldenter juvenile biomasses and feeding rates quite in-consistent with the adult biomasses and feeding ratesthat they had entered. The internal calculations ofsurvivorship and biomass are done in monthly agesteps, so as to allow finer resolution than 1 year inthe stanza biomass and mortality structure (e.g. lar-val and juvenile stanzas that last only one or a fewmonths).

The stanza age–size distribution information (la,wa) is used to initialize a fully age–size structuredsimulation for the multi-stanza populations. That is,for each monthly time step in Ecosim, numbers atmonthly agesNa,t and body weightswa,t are updatedfor ages up to the 90% maximum body weight age(older, slow growing animals are accounted for inan ‘accumulator’ age group). The body growthwa,t

calculations are parameterized so as to follow vonBertalanffy growth curves, with growth rates depen-dent on body size and (size- and time-varying) foodconsumption rates. Fecundity is assumed propor-tional to body weight above a weight at maturity, andsize-numbers-dependent monthly egg production isused to predict changes in recruitment rates of age 0fish. Compensatory juvenile mortality is representedthrough changes inZ for juvenile stanzas associatedwith changes in foraging time and predator abun-dances, as in split-group calculations.


In Ecospace (see below), it is not practical to dy-namically update the full multi-stanza age structuresfor every spatial cell due to computer time and memorylimits. The multi-stanza dynamics are retained, but thepopulation numbers at age are assumed to remain closeto equilibrium (changes in numbers at age associatedwith changes in mortality rates, foraging times, etc. areassumed to ‘immediately’ move the numbers-at-agecomposition to a new equilibrium). We have foundthat this moving-equilibrium representation of popu-lation numbers generally gives results quite close tothose obtained when full age–size accounting is donedynamically, provided feeding and mortality rates donot change too rapidly. This is similar to the generalfinding with Ecospace that time predictions of overallabundance change are quite similar to those obtainedwith Ecosim, even though the ‘dynamic’ calculationin Ecospace is really just a stepwise movement towardpredicted spatial equilibrium values for all variables.

3.3. Nutrient recycling and limitation

Ecosim uses a simple strategy to represent nutri-ent cycling and potential nutrient limitation of pri-mary production rates. It is assumed that the system atany instant in time has a total nutrient concentration,NT, which is partitioned between nutrient ‘bound’ inbiomass versus free in the environment (accessible toplants for nutrient uptake). That is,T is represented asthe sum:

NT =∑i

ηi × Bi + Nf (19)

whereηi is (fixed) nutrient content per unit of poolibiomass, andNf is free nutrient concentration. Thenassuming that NT varies as

dNT

dt= I − v × NT (20)

whereI is total inflow rate to the system from all nu-trient loading sources, andv is total loss rate fromthe system due to all loss agents (volume exchange,sedimentation, export in harvests, etc.), and thatv isrelatively large, NT is approximated in Ecosim bythe (possibly moving) equilibrium value NT= I/v.Changes in nutrient loading can be simulated by as-signing a time forcing function number to NT, in whichcase NT is calculated as NT= ft × NT0, where NT0

is the Ecopath base estimate of NT, andft is a timemultiplier (ft = 1 implies Ecopath base value of NT).Under the moving equilibrium assumption, changes inft can be viewed as caused by either changes in inputrate I or nutrient loss ratev. The Ecopath base esti-mate NT0 of total nutrient is entered by specifying thebase free nutrient proportionpf = Nf /NT0 on entry toEcosim, from which we can calculate NT0 as simply

NT0 =∑

i ηi × Bi

1 − pf(21)

Primary production rates for producer poolsj arelinked to free nutrient concentration during each simu-lation through assumed Michaelis–Menten uptake re-lationships of the form

(P

B

)j

= (P/B)max,j × Nf

Kj + Nf(22)

3.4. Predicting movement and accumulation oftracers in food webs

Ecosim flow rates along with auxiliary informationabout factors such as isotope decay rate and physicalexchange rates can be used to predict changes in con-centrations of chemicals (e.g. organic contaminantsand isotope tracers) that passively follow the biomassflows. The dynamic equations for such passive flowdiffer from biomass flow rate equations, and are gener-ally linear dynamical equations with time-varying ratecoefficients that depend on the biomass flow rates.

A routine, Ecotracer, has been implemented tomodel such movement and accumulation of contam-inants and tracers in food webs allowing simulationof one tracer or contaminant type while the biomassdynamics equations in Ecosim are being solved inparallel. Tracer molecules are assumed to be eitherin the ‘environment’ (typically the water), or in thebiota at any moment. Molecules are assumed toflow between pools at instantaneous rates equal tothe probabilities of being ‘sampled’ as part of thebiomass flow. The routine also allows for direct flowsfrom the environment into pools, representing directuptake or absorption of the tracer material, and fordifferential decomposition/decay/export rates by pooland from the environmental pool. Schematically, theflow of tracer molecules through any biomass pool


Fig. 2. Representation of the flow of tracer molecules through abiomass pool.

is represented by the components shown below (seealsoFig. 2).

In the rate equation for time changes in contaminantconcentration in pooli, these components are repre-sented as follows:

(1) Uptake from food: Cj ×GCi ×Qji/Bj, whereCj:concentration in foodj; GCi: proportion of foodassimilated by typei organisms;Qji : biomass flowrate fromj to i, Bj: biomass of foodj;

(2) Direct uptake from environment: ui × Bi × C0,where ui: parameter representing uptake perbiomass per unit time and per unit environmentalconcentration;Bi: biomass in pooli; C0: environ-mental concentration;

(3) Concentration in immigrating organisms: ci × Ii,where ci: a parameter giving tracer per unitbiomass in immigrating biomass;Ii: biomass ofpool i immigrants per time;

(4) Predation: Ci × Qij/Bi;(5) Detritus: Ci×M0i+(1−GCi)×

∑j Cj×Qji/Bj,

whereM0i: non-predation mortality rate of typei(per year);

(6) Emigration: ei×Ci, whereei: emigration rate (peryear);

(7) Metabolism: di × Ci, where di is the summedmetabolism and decay rate for the material whilein pool i.

3.5. Fleet and effort dynamics

Ecosim users can specify temporal changes in fish-ing fleet sizes and fishing effort in three ways: (1)by sketching temporal patterns of effort in the modelrun interface; (2) by entering annual patterns via ref-erence files along with historical ecological responsedata; and (3) by treating dynamics of fleet sizes andresulting fishing effort as unregulated, and subject to

fisher investment and operating decisions (‘bionomic’dynamics, fishers as dynamic predators).

When the fleet/effort response option is invoked,Ecosim replaces all previously entered time patternsfor fishing efforts and fishing rates with simulatedvalues generated as each simulation proceeds. Thefleet/effort dynamics simulation model uses two timescales of fisher response: (1) a short time response offishing effort to potential income from fishing, withinthe constraints imposed by current fleet size, and(2) a longer time investment/deprecation ‘populationdynamics’ for capital capacity to fish (fleet size, vesselcharacteristics). These response scales are representedby two ‘state variables’ for each gear typeg: Eg,t isthe current amount of active, searching gear (scaledto 1.0 at the Ecopath base fishing mortality rates),andKg,t is the fleet effort capacity (Eg,t < Kg,t). Ateach time step, a mean income per effort indexIg,t iscalculated asIg,t = ∑

i qg,i × Bi × Pg,i, where i isthe ecological species or biomass group,qg,i is thecatchability coefficient (possibly dependent onBi)for speciesi by gearg, andPg,i is the market priceobtained per biomass ofi by gearg fishers. Also,mean fleet profit rates PRg,t for fishing are calculated,equal to(Ig,t − cg) × Eg,t , wherecg is the cost of aunit of fishing effort for gearg. For each time step,the ‘fast’ effort response for the next (monthly) timestep is predicted by a sigmoid function of income pereffort and current fleet capacity:

Eg,t+1 = Kg,t × Ipg,t

Ip

hg + Ipg,t

(23)

Here,Ihg andp are fleet-specific response parameters,where the income level needed for half of the maxi-mum effort is Ihg and p represents a ‘heterogeneity’parameter for fishers: highp values imply all fishers‘see’ income opportunity similarly, while lowp valuesimply fishers initiate their effort over a wide range ofmean incomes, as shown inFig. 3.

3.6. Compensatory mechanisms

Sustaining fisheries yield when fishing reducesstock size depends on the existence of compensatoryimprovements in per capita recruitment, growth,and/or natural mortality rates. Ecosim allows a va-riety of specific hypotheses about compensatory


Fig. 3. Effort response relationship describing the statistical be-havior of a fleet of fishers that have heterogeneous fishing abili-ties and perceptions of the current income level needed to attracttheir participation. The slope of the plot represents the amount ofadditional fishing effort expected for each increment in mean in-come; it is steepest at the mean income level where the majorityof fishers see the possibility of just breaking even by going out.

mechanisms, and these mechanisms broadly fall intwo categories:

• direct—changes caused over short time scales (ofthe order of 1 year) by changes in behavior of or-ganisms, whether or not there is an ecosystem-scalechange due to fishing; and

• indirect—changes over longer time scales due toecosystem-scale responses such as increased preydensities and/or reduced predator densities.

Usually we find the direct effects to be most im-portant in explaining historical response data. Herewe describe how to generate alternative models or hy-potheses about direct compensatory responses; thesehypotheses fall in three obvious categories: recruit-ment, growth, and natural mortality.

3.6.1. Compensatory recruitment (models with splitpools/multiple stanza only)

Compensatory recruitment effects are usually ex-pressed as a flat or dome-shaped relationship betweennumbers of juveniles recruiting to the adult pool ver-sus parental abundance (stock-recruit relation). Thereare two main ways to create such effects in Ecosim:

(a) non-zero feeding time adjustment for the juvenilepool combined with fixed time in juvenile stageand high EE, or high proportion of the ‘other’mortality (the mortality not accounted for) beingsensitive to changes in predator feeding time;

(b) zero feeding time adjustment combined with vari-able time in juvenile stage.

Mechanism (a) represents density-dependentchanges in juvenile mortality rate associated withchanges in feeding time and predation risk, while(b) represents density-dependent changes in juve-nile growth rate and hence total time spent exposedto high predation rates over the juvenile life stage.Other, generally weaker compensatory responses canalso be caused by changes in adult energy allocationto reproduction. For mechanisms (a) and (b), it isusually also important that the vulnerabilities of preyto the juvenile group also be relatively low.

3.6.2. Compensatory growthCompensatory growth rate responses are modeled

by setting the feeding time adjustment rate to zero, sothat simulatedQ/B is allowed to vary with a group’sbiomass (non-zero feeding time adjustment results insimulated organisms trying to maintain Ecopath baseQ/B by varying relative feeding time). Net produc-tion is assumed proportional (growth efficiency) toQ/B, whether or not this production is due to recruit-ment (for groups where ontogenetic changes are mod-eled) or growth. TheQ/B increase with decreasingpool biomass is enhanced by lowering vulnerability ofprey to the pool. In the extreme as vulnerability ap-proaches zero (donor or bottom-up control), total foodconsumption rateQ approaches a constant (Ecopathbase consumption), soQ/B becomes inversely propor-tional toB.

3.6.3. Compensatory natural mortalityCompensatory changes in natural mortality rate (M)

can be simulated by combining two effects: non-zerofeeding time adjustment, and either high EE from Eco-path or high proportion of ‘other’ mortality being sen-sitive to changes in predator feeding time. With thesesettings, especially when vulnerabilities of prey to agroup are low, decreases in biomass lead to reducedfeeding time, which leads to proportional reduction innatural mortality rate.

3.6.4. Compensation in recruitmentThe ‘split pool’ representation of juvenile and adult

biomasses was originally included in Ecosim to allowrepresentation of trophic ontogeny (differential dietsfor juveniles and adults). To implement this represen-tation it was necessary to include population numbersand age structure, at least for juveniles, so as to prevent


‘impossible’ dynamics such as elimination of juvenilebiomass by competition/predation or fishing withoutattendant impact on adult abundance (graduation fromjuvenile to adult pools cannot be well represented justas a biomass ‘flow’).

When we elected to include age structure dynamics,we in effect created a requirement for model users tothink carefully about the dynamics of compensatoryprocesses that have traditionally been studied interms of the ‘stock-recruitment’ concept and relation-ships. To credibly describe the dynamics of split-poolpopulations, Ecosim parameters for split pools usu-ally need to be set so as to produce an ‘emergent’stock-recruitment relationship that is at least quali-tatively similar to the many, many relationships forwhich we now have empirical data (see data sum-mary in http://www.mscs.dal.ca/∼myers/data.html).In most cases, these relationships are ‘flat’ over awide range of spawning stock size, implying theremust generally be strong compensatory increase injuvenile survival rate as spawning stock declines (oth-erwise less eggs would mean less recruits on average,no matter how variable the survival rate might be).

Ecosim can generate direct (as opposed to justpredator–prey) compensatory changes in juvenile re-cruitment via at least three alternative mechanisms orhypotheses:

1. simple density-dependence in juvenile productionrate by adults, due to changes in adult feeding ratesand fecundity (not a likely mechanism);

2. changes in duration of the juvenile stage and hencein total time exposed to relatively high predationrisk;

3. changes in juvenile foraging time (and hence ex-posure to predation risk) with changes in juvenilefeeding rates.

For all of these mechanisms, compensatory effects areincreased (recruitment relationship flat over a widerrange of adult stock size, steeper slope of recruitmentcurve near the origin) by

1. limiting availability of prey to juveniles by forcingjuveniles to use small ‘foraging arenas’ for feeding;

2. make effective time exposed to predation whilefeeding drop directly with decreasing juvenileabundance (simulates possibility that when juve-niles are less abundant, remaining ones may be

able to forage ‘safely’ only in refuge sites with-out exposing themselves to predation risk). Thisoption should be used only if field natural historyobservation indicates that the juveniles do in factrestrict their distribution to safe habitats when atvery low abundance.

3.7. Parameter sensitivity

Ecosim does not include complete formal sensitivityanalyses to test the effect of all input parameters. Thereare, however, a number of routines that can be used toexamine various aspects of the model sensitivity, andwe expect that additional routines will be added.

Ecosim runs can be repeated as Monte Carlo sim-ulations with initial Ecopath biomass estimates cho-sen from normal distributions centered on the initialinput estimates (with confidence intervals that can bebased on the model pedigree, as discussed above).Each Monte Carlo simulation trial begins by select-ing at least one random biomass combination andre-balancing the Ecopath model; the random selectionis repeated until a balanced model is found—a pro-cess is similar to the Ecoranger method for analysis ofuncertainty for Ecopath parameters described above.Then the resulting balanced Ecopath model is used toinitialize an Ecosim run.

The results can be shown as simple ‘bands ofuncertainty’ giving indications for how sensitiveEcosim results are to input parameter quality. Strongdivergence in biomass time patterns among simula-tion trials under this option is usually associated withchanges in fishing mortality rate estimates.

If time series data have been included in the analysis(see below) it is possible to retain the best fitting es-timates, i.e. the parameters which minimize the sumsof squared residuals (SS) between model and observa-tions. This approach (technically known as a ‘Matyassearch’ technique) is useful in parameter estimationand optimization problems where the parameters beingvaried can result in non-feasible solutions (constraintviolations) but where the feasible parameter valuesare not readily predicted from constraint equations.Non-feasible solutions commonly arise when Ecopathbiomasses are changed so as to violate mass balance(e.g. to values that would imply EE> 1.0). In fact, wecannot use other nonlinear estimation procedures tosearch for better initial (Ecopath) biomass estimates as

http://www.mscs.dal.ca/~myers/data.html


we do for some Ecosim parameters, since these proce-dures generally rely upon there being smooth changein the SS criterion with changes in the parameters.Such procedures use the gradient in SS to decide stepsin the parameter estimates, and good steps cannot beefficiently estimated when any step can unpredictablyresult in violation of mass balance constraints.

While there has been no comprehensive study pub-lished of Ecosim parameter sensitivity, our preliminaryexperience indicates that simulations are very sensitiveto the ‘behavioral exchange rate’, or ‘vulnerability’.This parameter expresses the exchange rate betweenthe prey being in vulnerable and non-vulnerable states(Fig. 1). It is generated by a multitude of processes,e.g. physical mixing, movement of organisms betweenresting/hiding and active feeding states, dispersal (vul-nerability to predators while moving), growth into andout of vulnerable size range, and behavioral reactionsto growth in body parasite loads.

The vulnerability parameter is not subject to directmeasurement. There are, however, other ways of esti-mating it:

1. Sensitivity analysis (see the section below);2. Fitting to time series data (see the section below);3. Two model comparisons, build Ecopath models for

a system covering two different time periods, anduse a routine included in Ecosim to search for vul-nerability parameter settings that with the given ex-ploitation rates will make it possible to move fromthe first to the second model state;

4. Estimate biomass depletion relative to the Ecopathbase biomasses (Bunfished/B0);

5. Estimate maximum fishing mortality relate to nat-ural mortality (Fmax/M).

It is possible and indeed recommended to use all ofthese methods to obtain estimates for the vulnerabilityparameters.

Ecosim simulations are very sensitive to variationsin primary productivity, see, e.g.Martell et al. (2002),therefore a variety of tools have been added for com-paring simulations with series data as described inmore detail below.

3.8. Fitting Ecosim to time series data

Based on time series ‘reference’ biomass data, andon total mortality of various pools over a particu-

lar historical period, along with estimates of changesin fishing impacts over that period Ecosim estimatesa statistical measure of goodness-of-fit to these dataeach time Ecosim is run. This goodness-of-fit mea-sure is a weighted sum of squared deviations (SS) oflog biomasses from log predicted biomasses, scaledin the case of relative abundance data (y) by the max-imum likelihood estimate of the relative abundancescaling factor (q) in the equationy = q × B, whereB is the absolute abundance. The reference data se-ries can be assigned a relative weight expressing howvariable or reliable that type of data is compared tothe other reference time series. Based on the time se-ries three types of analyses with the SS measure areavailable:

1. determine sensitivity of SS to the critical Ecosimvulnerability parameters by changing each oneslightly then re-running the model to see howmuch SS is changed;

2. search for vulnerability estimates that give better‘fits’ of Ecosim to the time series data;

3. search for time series values of forcing functions,e.g. annual relative primary productivity that mayrepresent historical productivity ‘regime shifts’ im-pacting biomasses throughout the ecosystem.

The searches include a SS minimization procedurebased on a Marquardt nonlinear search algorithm withtrust region modification of the Marquardt steps (see,e.g. More, 1977). For users familiar with the non-linear estimation procedures used in single-speciesstock assessment, e.g. for fitting production modelsto time series CPUE data, the procedure implementedin Ecosim should be quite familiar. In essence, theEcosim search procedure for vulnerabilities is an ‘ob-servation error’ fitting procedure where vulnerabilitychanges usually have effects quite similar to changesin population ‘r’ parameters in single-species mod-els. Allowing the search to also include historical pri-mary productivity ‘anomalies’ corresponds to search-ing also for ‘nuisance parameter’ estimates of whatis usually called the ‘process errors’ in single-speciesassessment (Hilborn and Walters, 1992).

3.9. In search of an optimum fishing policy

Fisheries management aims to regulate fishingmortality rates over time so as to achieve defined


sustainability objectives, and modeling serves a rolefor providing insight about how high these mortal-ity rates should be, and how they should be variedover time. The impacts of alternative exploitation pat-terns can be explored using two different approachesin Ecosim, either by sketching fishing mortalitiesover time and evaluate the results, or by a formaloptimization routine to evaluate the fishing effortover time that would maximize particular perfor-mance measures or ‘objective functions’ for manage-ment.

The objective function is defined (by the user) asa combination of net economic value, employment,mandated rebuilding of target species, and ecologi-cal ‘stability’ criteria, seeWalters et al. (2002)fordetails.

Ecosim uses the Davidson–Fletcher–Powell (DFP;Fletcher, 1987) nonlinear optimization procedure toiteratively improve an objective function by changingrelative fishing rates, where each year/fleet block de-fines one parameter to be varied by the procedure. Theparameter variation scheme used by DFP is known asa ‘conjugate-gradient’ method, which involves testingalternative parameter values so as to locally approxi-mate the objective function as a quadratic function ofthe parameter values, and using this approximation tomake parameter update steps. It is one of the moreefficient algorithms for complex and highly nonlinearoptimization problems.

The search procedure results in what control sys-tems analysts call an ‘open loop policy’, i.e. a pre-scription for what to do at different future timeswithout reference to what the system actually ends updoing along the way to those times. In practice, actualmanagement needs to be implemented using feedbackpolicies where harvest goals are adjusted over time asnew information becomes available and in responseto unpredicted ecological changes due to environmen-tal factors. But this need for feedback in applicationdoes not mean that open loop policy calculations areuseless; rather, we see the open loop calculations asbeing done regularly over time as new informationbecomes available, to keep providing directional guid-ance for where the system can/should be heading. Foran example of this approach to design of policies fordealing with decadal-scale variation in ocean produc-tivity for single-species management, seeWalters andParma (1996).

3.9.1. Maximizing risk-averse log utility foreconomic and existence values

One option in the search procedure for optimumfishing patterns is to search for relative fleet sizes thatwould maximize a utility function of the form

w1 × log(NPV) + w2 × S × log(B) − w3 × V (24)

where thewi’s are utility weights, and the utility com-ponents NPV,S×log(B), andV are defined as follows:

(1) NPV is net present economic value of harvests,calculated as discounted sum of catches over allfleets and time multiplied with prices minus costsof fishing, i.e. the discounted total profit from fish-ing the ecosystem;

(2) S× log(B) is an existence value index for all com-ponents of the ecosystem over time. It is calculatedas the discounted sum over times and biomasspools of user-entered structure weights times logsof biomasses, scaled to per-time and per-groupby dividing the sum by the number of simulationyears and number of living biomass pools;

(3) V is a variance measure for the prediction oflog(NPV)+ S × log(B). It is assumed to be pro-portional to how severely the ecosystem is dis-turbed away from the Ecopath base state, wheredisturbance is measured at each time in the sim-ulation by the multidimensional distance of theecosystem biomass state from the Ecopath basestate. This term is subtracted, implying that in-creased uncertainty about the predictions for moresevere disturbances causes a decrease in the meanof log(NPV). The term represents both aversionto management portfolio choices that have highvariance in predicted returns, and the observationthat the mean of the log of a random variable(NPV × PB) is approximately equal to the log ofthe mean of that variable minus 1/2 the varianceof the variable. Largew3-values can be used torepresent both high uncertainty about predictionsthat involve large deviations of biomass from theEcopath base state, and strong risk aversion topolicy choices that have high uncertainty.

This utility function combines several basic conceptsof utility. First, the log scaling of value componentsrepresents the notion of ‘diminishing returns’, thatadding some amount to any value measure is less im-portant when the value measure is already large than


it is when the value measure is small. Second, the logscaling also represents the notion of ‘balance’, that novalue component should be ignored entirely (unlessit is assigned a zerowi); the overall utility measureapproaches minus infinity if either net economic per-formance (NPV) or if any biomass component of theecosystem (any biomassBi in S× log(B)) approacheszero. Third, it represents the notion that our predictionsabout the future of both economic performance andbiodiversity (biomasses) become progressively moreuncertain for policies that result in more extreme de-partures from the Ecopath base state.

In the terminology of portfolio selection theoryin economics, fishing policies result in a portfolioof value components with ‘expected total returns oninvestment’ equal to NPV+ S × B. But policies thathave higher expected total returns are most oftenalso ones that would push the ecosystem into moreextreme states, and hence represent portfolio choiceswith higher variance in total returns.

3.10. Closed-loop simulations

In order to model not only ecological dynamics overtime, but also the dynamics of the stock assessmentand regulatory process, a ‘closed-loop’ simulation rou-tine has been added to Ecosim (seeWalters et al., 2002,for more details). This routine includes ‘submodels’for the dynamics of assessment (data gathering, ran-dom and systematic errors in biomass and fishing rateestimates), and for the implementation of assessmentresults through limitation of annual fishing efforts. Theclosed-loop policy simulation model, allows specifi-cation of:

(1) how many closed-loop stochastic simulation trialsto do;

(2) type of annual assessment to be used (F = C/BversusF directly from tags);

(3) accuracy of the annual assessment procedures (co-efficient of variation of annual biomass orF esti-mates, by stock); and

(4) value or importance weights for theF’s caused onvarious species by each fishing fleet.

Closed-loop policy simulations could obviously in-clude a wide range of complications related to the de-tails of annual stock assessment procedures, surveydesigns, and methods for directF estimation. We as-

sume that users will use other assessment modelingtools to examine these details, and so need only enteroverall performance information (coefficients of vari-ation in estimates) into the ecosystem-scale analysis.

4. Spatial simulation: Ecospace

Ecospace is a dynamic, spatial version of Ecopath,incorporating all key elements of Ecosim and is de-scribed in detail byWalters et al. (1999). It works bydynamically allocating biomass across a user-definedgrid map while accounting for:

1. symmetrical movements from a cell to its four ad-jacent cells modified by whether a cell is definedas ‘preferred habitat’ or not;

2. user-defined increased predation risk and reducedfeeding rate in non-preferred habitat; and

3. a level of fishing effort that is proportional, in eachcell, to the overall profitability of fishing in thatcell, and whose distribution is sensitive to spatialfishing costs.

4.1. Prediction of mixing rates

The instantaneous emigration rates from a givencell in Ecospace are assumed to vary based on thepool type, the groups preference for the habitat typerepresented by the cell, and a ‘risk ratio’ representinghow the organisms in the cell respond to predationrisk. Base dispersal rates are calculated based on this,but weighted based on a habitat gradient function in-creasing the probability of organisms moving towardsfavorable habitats. The mechanisms involved in thisprocedure are explained in more detail byWalterset al. (1999).

4.2. Predicting spatial fishing patterns

EwE works with multiple fishing fleets, with fishingmortality rates (F) initially distributed between fleetsbased on the distribution of catch rates in the under-lying Ecopath base model. In Ecospace theF’s aredistributed using a simple ‘gravity model’ where theproportion of the total effort allocated to each cell isassumed proportional to the sum over groups of theproduct of the biomass, the catchability, and the prof-itability of fishing the target groups (Caddy, 1975;


Hilborn and Walters, 1987). This profitability of fish-ing includes factors such as the cell-specific cost offishing.

4.3. Numerical solutions

Ecospace is based on the same set of differentialequations as used in Ecosim, and in essence performsa complete set of Ecosim calculations for each cell foreach time step. This represents a formidable amount ofcomputations, but it has been possible to take a numberof shortcuts to speed the processing up to an accept-able rate. Briefly explained the background for thistakes its starting point inEq. (14), which expresses therate of change for each biomass pool over time. If therate constants were constant over time (they are not,but if!) the biomass would change as a linear dynam-ical system, and would move exponentially towardsan equilibrium. Hence, if input and output rates wereconstant, the time solutions would behave as weightedaverages of past values and equilibrium values withweights depending on the mortality and migrationrates. Using such expressions the Ecospace computa-tions can be greatly increased by using a variable timesplitting, where moving equilibria are calculated forgroups with high turnover rates (e.g. phytoplankton),while the integrations for groups with slower turnoverrates (e.g. fish and marine mammals) are based ona Runge–Kutta method. Comparisons indicate thatthis does not change the resulting time patterns forsolutions in any noticeable way—hence, the ‘wrong’assumption of time rate constancy introduced aboveis useful for speeding up the computations withoutnoticeable detraction of the final results. The result-ing computations are carried out orders of magnitudefaster than if the time splitting was not included.

4.4. Advection in Ecospace

Advection processes are critical for productivity inmost ocean areas. Currents deliver planktonic produc-tion to reef areas at much higher rates than would bepredicted from simple turbulent mixing processes. Up-welling associated with movement of water away fromcoastlines delivers nutrients to surface waters, but themovement of nutrient rich water away from upwellinglocations means that production and biomass may behighest well away from the actual upwelling locations.Convergence (down-welling) zones represent places

where planktonic production from surrounding areasis concentrated, creating special opportunities for pro-duction of higher trophic levels.

Ecospace provides a user interface for sketchinggeneral current patterns or wind/geostrophic forcingpatterns for surface currents. Based on these patternsEcospace calculates equilibrium horizontal flow andupwelling/down-welling velocity fields that maintaincontinuity (water mass balance) and effects of Corio-lis force. That is, the advection field is calculated bysolving the linearized pressure field and velocity equa-tions df/dt = 0, dvu/dt = 0, dvv/dt = 0 across thefaces of each Ecospace grid (u, v) cell, wheref is seasurface anomaly, thev’s are horizontal and velocitycomponents (u, v directions) and the rate equations ateach cell face satisfy (omitting grid size scaling fac-tors for clarity):

dh

dt= vuh

u+ vvh

v− Dh (25)

dvudt

= k × Wu − k × vu − f × vv − g × h

u(26)

dvvdt

= k × Wv − k × vv − f × vu − g × h

v(27)

Here, theW’s represent the user sketched forcing orgeneral circulation field,h the sea surface anomaly,kthe bottom friction force,f the Coriolis force,D repre-sents downwelling/upwelling rate, andg accelerationdue to sea surface slope.

Solving these equations for equilibrium is not meantto be a replacement for more elaborate advection mod-els; generally theWu andWv need to be provided eitherby such models or by direct analysis of surface currentdata, so the Ecospace solution scheme is only used toassure mass balance and correct for ‘local’ featurescaused by bottom topography and Coriolis forces. Thatis, absent shoreline, bottom, and sea surface anomaly(h) effects, the equilibrium velocities are justvu = Wu,vv = Wv up to corrections for Coriolis force. Solv-ing the equations using general forcing sketches ofWpatterns allows internal correction for factors such astopographic steering of currents near shorelines, with-out requiring enteredW fields that precisely maintainmass balance (and/or correct upwelling/downwellingvelocities) absent any correction scheme.

Once an advection pattern has been defined, auser can specify which biomass pools are subject


to the advection velocities (vu, vv field) in additionto movement caused by swimming and/or turbulentmixing. This allows examination of whether someapparent ‘migration’ and concentration patterns ofactively swimming organisms (e.g. tuna aggregationsat convergence zones) might in fact be due mainly torandom swimming combined with advective drift.

4.5. Seasonal migration

Larger organisms commonly have seasonal mi-gration patterns that allow them to utilize favorableseasonal resource and environmental conditions overlarge spatial areas. Such movements can be repre-sented in Ecospace through a ‘Eulerian’ approachinvolving explicitly modeling changes in instanta-neous rates of biomass flow among the Ecospacespatial cells, in some way that approximates at leastthe changing center of distribution of the migratoryspecies. The approach is implemented by defining amonthly sequence of ‘preferred’ map cell positions,and how spread out the migrating fish are likely to bearound these preferred cells by specifying north–southand east–west ‘concentration parameters’.

The mathematical method used in Ecospace to cre-ate migratory behavior is quite simple. Spatial move-ment is represented in general in Ecospace as a setof instantaneous exchange rates across the boundaries

Fig. 4. Representation of the relative movement rate across thesouthern boundary of a cell as a function of gradient steepnessin the seasonal migration module of Ecospace. The function isreversed for movement across the northern cell boundary, anda similar function is used for east–west movements with mapcolumn-preferred column as the independent variable.

of adjacent spatial cells. For migratory species, theseexchange rates are multiplied by relative factors ateach simulation time step, where the factors dependon distance from the preferred cell for that time step asshown inFig. 4. The factor has no effect for cells nearthe preferred cell, and ‘shuts down’ movement awayfrom the preferred cell for cells far from that preferredcell. The base movement rates that are multiplied bythe migration factors may not be the same in all direc-tions to start with; these base rates can include advec-tion effects and/or increased/oriented movement ratestowards preferred habitat types. That is, migration ef-fects can be combined with advection and orientationof movement toward preferred habitats.

5. Capabilities and limitations

EwE has been developed largely through case stud-ies, where users have challenged us to add variouscapabilities and as we have seen inadequacies throughcomparison to data; see as a good example the discus-sions in the proceedings from two recent FAO/UBCworkshops on the application of EwE (Pauly andWeingartner, 1998; Pitcher and Cochrane, 2002). Var-ious capabilities have been added to EwE in responseto these challenges, and there has inevitably beensome uncertainty about what the approach and soft-ware presently can and cannot do, and about how itshould be used in the design of sustainable fisheriespolicies. Such uncertainty may be expressed throughtoo simplistic interpretations of what mass balanceand biomass dynamics models are capable of repre-senting, through to unwarranted optimism about howit should be used to replace or complement existingassessment tools. Here we review the capabilitiesand limitations through a series of ‘frequently askedquestions’, followed by explanations of what we thinkEwE is actually capable of doing.

Note that many of the questions discussed belowhave their root in an assumption that EwE is some-how intended to supplant or replace single-speciesassessment methods. This is clearly not the case;ecosystem-based methods rely on information fromtraditional assessment, and have their force whenit comes to addressing strategic management ques-tions, not tactical management questions to whichsingle-species assessment is much better suited. Our


primary goal when developing EwE has been to de-velop a capability for asking policy questions thatsimply cannot be addressed with single-species as-sessment. Examples are questions about impacts offishing on non-target species, and the efficacy of pol-icy interventions aimed at limiting unintended sideeffects of fishing. Also, as is shown through exam-ples below, EwE can incorporate time series datafrom single-species assessment as input and use thesefor parameter fitting. We indeed advocate an iter-ative process where information is passed betweensingle-species analysis and EwE to check and improveestimates in the process, addressing questions aboutthe degree to which ecosystem events can and cannotbe attributed to impact of fisheries, climate change, etc.

5.1. Does Ecopath assume steady state orequilibrium conditions?

Ecopath provides an ‘instantaneous’ estimate ofbiomasses, trophic flows, and instantaneous mortalityrates, for some reference year or multi-year averagingwindow. Biomasses need not be at equilibrium for thereference year, provided the Ecopath user can providean estimate of the rate of biomass ‘accumulation’ (ordepletion) for each biomass for that reference year. Infact, in a number of cases, e.g. in a model of the NorthSea in 1981 (Christensen, 1995b) it was necessaryto recognize that biomasses were in fact changingover the period for which Ecopath reference data (B,P/B, Q/B, diet composition) were provided. In thesecases, assuming equilibrium for the reference year ledto overly optimistic estimates of sustainable fishingmortality rates.

5.2. Should Ecopath be used even if there isinsufficient local information to construct models, orshould more sampling go first?

It is a fairly common conception that since we donot know enough to make perfect models at the indi-vidual or species level there is no way we can haveenough information at hand to embark on modelingat the ecosystem level. This may hold if we try toconstruct models bottom-up—we cannot account forall the actions and processes involving all the indi-viduals of the world. This is, however, not what Eco-path models do, instead they place piecemeal infor-

mation in a framework that enables evaluation of thecompatibility of the information at hand, gaining in-sights in the process. Adding to this is that there ismuch more information of living marine resourcesavailable than most will anticipate. A good demon-stration of this can be obtained by searching the Fish-Base database on finfish (Froese and Pauly, 2000,http://www.fishbase.org) for Ecopath-relevant infor-mation using the semi-automated search routine avail-able for the specific purpose at the website.

Another aspect is that ecosystem models can helpdirect research by pinpointing critical information andgaps in the present knowledge. As more informationbecomes available it is straightforwardly included inthe model, improving estimates and reducing uncer-tainty (see ‘Addressing uncertainty’ above).

5.3. Does EwE ignore inherent uncertainty inassembling complex and usually fragmentarytrophic data?

Ecopath has a number of routines that encourageusers to explore the effects of uncertainty in input in-formation on the mass balance estimates. In particular,the ‘Ecoranger’ routine allows users to calculate prob-ability distributions for the estimates when they spec-ify probability distributions for the input data compo-nents. Similarly, Ecosim has a graphical interface thatencourages policy ‘gaming’ and sensitivity testing.

Lack of historical data and difficulty in measuringsome ecosystem components and processes will likelyalways plague efforts to understand trophic structureand interactions. This is not a problem with Ecopath,but rather with aquatic ecology in general (Ludwiget al., 1993). We need to respond to it not by complain-ing about the incompleteness of our data, but ratherby using models like EwE to direct research attentiontoward components that are most uncertain and alsomake the most difference to policy predictions. Wealso need to use the models to search for robust policyoptions and management approaches that will allowus to cope with the uncertainty, rather than pretendingthat someday it will just go away.

When EwE is used for policy comparison, it is im-portant to recognize that incorrect comparisons (EwEleading user to favor a wrong policy) are not due touncertainty in general about the model parameters, butrather to errors to which the particular policy compar-

http://www.fishbase.org


ison is sensitive. In other words, EwE can give correctanswers for some policy comparisons but wildly in-correct ones for others, so it is meaningless to claimthat it should not be used because of uncertainty ingeneral. For example, EwE predictions of the impactof increasing fishing rates for a particular species aremost sensitive to assumptions about vulnerability ofprey to that species, since the vulnerability parameterslargely determine the strength of the compensatory re-sponse by the species to increased mortality rate. Buteven if EwE predicts the strength of the compensatoryresponse to fishing correctly, it may still fail to pre-dict response of that same species to a policy aimed atincreasing its productivity by reducing abundance ofone or more of its predators: EwE may have a goodestimate of total mortality rate for the species, but avery poor estimate of how that mortality rate is dis-tributed among (or generated by) predators includedin the model.

5.4. Can Ecopath mass balance assessments provideinformation directly usable for policy analysis?

Instantaneous snapshots of biomass, flows, and ratesof biomass change have sometimes been used to drawinferences about issues such as ecosystem ‘health’as measured by mean trophic level or other indicesof fishing impact (e.g.Christensen, 1995a; Pauly andChristensen, 1995; Pauly et al., 1998). But the snap-shots cannot be used directly to assess effects of pol-icy changes that would result in changes in rates (e.g.reduction in fishing rates) since the cumulative effectsof such changes cannot be anticipated from the systemstate at one point in time. In fact the Ecosim part ofEwE was initially developed specifically to provide amethod for predicting cumulative changes, while rec-ognizing that all rate processes in an ecosystem maychange over time, as biomasses change. For example,one might conclude from the Ecopath mortality rateestimates or mixed trophic impact analysis (see above)that reducing the abundance of some particularly im-portant predator might result in lower mortality ratesof its prey, and hence growth in abundance of theseprey. This prediction may hold for a short time, butmight be reversed entirely over longer time scales dueto increases in abundance of other predators or on anintermediate time scale due to predator prey switchingin response to the initial responses in prey density.

5.5. Can Ecopath provide a reliable way of estimatingpotential production by incorporating knowledge ofecosystem support capabilities and limits?

Ecologists have long sought simple ways of pre-dicting productive potential of aquatic ecosystemsfrom ‘bottom-up’ arguments about efficiency ofconversion of primary production into productionof higher trophic levels (e.g.Polovina and Marten,1982). While Ecopath inputs can be organized so asto provide such predictions, we do not recommendusing EwE for management this way. There are sim-ply too many ways that simple efficiency predictionscan go wrong, particularly in relation to ‘shunting’ ofproduction into food web components that are not ofdirect interest or value in management (e.g. ungraze-able algae, inedible zooplankton, etc.) Ecopath canhelp provide broad bounds for potential abundancesand production in an exploratory research mode, butthese bounds are unlikely to be tight enough to beuseful for management planning related to fisherydevelopment or recovery potential.

5.6. Can Ecopath predict biomasses of groups forwhich no information is available?

We try to avoid using the Ecopath biomass esti-mation capability for more biomass components thanabsolutely necessary. Estimation of biomass withEcopath usually requires making explicit assumptionabout the ecotrophic efficiency, i.e. about the pro-portion of the total mortality rate of a group that weaccount for by the predation, migration, biomass ac-cumulation and fishing rates included explicitly in theEcopath data. There is rarely a sound empirical basisfor using any particular value of EE, except perhapsfor top predators in situations where total mortalityrate (Z = P /B) is well estimated and EE representsa ‘known’ ratio of fishing rate (F) to total Z (and therest ofZ, e.g. the natural mortality (M) is known notto be due to other predators included in the model norto other factors not considered).

Where biomasses really are unavailable or esti-mates are known to be biased, e.g. if the only biomassestimates for pelagics are from swept-area analysisbased on demersal trawling, it may still be better touse assumed EE’s than to stop short of construct-ing an ecosystem model pending, e.g. funding and


development of capabilities to conduct acoustic sur-veys. In such cases one can assume reasonable EEvalues for groups where biomasses are missing—anexample: small pelagics do not die of old age in anexploited ecosystems, most are either eaten or caught,hence EE is likely to be in the range 0.90–0.99.As confidence intervals can be assigned to all inputparameters and can be estimated for the output pa-rameters using the Ecoranger module of EwE (wherea range for acceptable output parameters is also in-corporated as part of the model evaluation process),the mass balance constraints of the model can beused to predict potential ranges for biomasses in thesystem.

5.7. Should Ecopath mass balance modeling be usedonly in situations where data are inadequate to usemore detailed and realistic methods like MSVPA?

Multispecies virtual population analysis (MSVPA)has been used to reconstruct age–size and time-depen-dent estimates of trophic flows and mortality ratecomponents, using the VPA assumption that historicalabundances can be inferred by back-calculating howmany organisms must have been present in order to ac-count for measured and estimated removals from thoseorganisms over time (e.g.Sparre, 1991; Magnusson,1995). In a sense, Ecopath does this as well, butgenerally does not account for age–size dependencyand temporal variation (biomasses are constrainedto be large enough to account for assumed removalsestimated from biomasses, consumption/biomasses,and diet composition of predators, just as inMSVPA).

But the really big difference between Ecopath andMSVPA is not in the detail of calculations; construct-ing an Ecopath model that details age, size and timecomponents is tedious but feasible. The more impor-tant difference is in the use of direct data on totalmortality rate by Ecopath, in the form of theP/B ra-tio that Ecopath users must provide. Ecopath biomassand mortality estimates are ‘constrained’ to fit the to-tal mortality rates entered asP/B data. In contrast,MSVPA (like single-species VPA) can produce cohortabundance patterns (die-off patterns over age–size andtime) that do not agree in any way with apparent co-hort decay patterns evident from direct examination ofthe age–size composition data. In effect, the MSVPA

(and VPA) user must reject or ignore any direct evi-dence about total mortality rateZ that might be presentin age–size composition data, and must treat discrep-ancies between apparentZ from the cohort reconstruc-tions versus apparentZ from composition data as be-ing due to age–size-dependent changes in vulnerabilityto the composition sampling method. As an example,Newfoundland cod VPA’s resulted in much lower es-timates ofZ than would be estimated from catch-curveanalysis of the age composition data, and in this caseit turned out that VPA tuning resulted in underesti-mates of fishing mortality rate, see, e.g.Walters andMaguire (1996).

It is obviously comforting to us as biologists to beable to provide more detailed accounting of preda-tion interactions, which are almost always size andage-dependent. But in assessments of ecosystem-scaleimpacts of changes in trophic conditions, it is not au-tomatically true that the best aggregate estimate is thesum of component estimates, any more than it is auto-matically true in single-species assessment that moredetailed models and data always provide better assess-ments than simpler models. For statistical and logicalreasons, the ‘more is better’ argument is no more validin dynamic modeling than it is in multiple regressionanalysis, where we are familiar with how adding moreindependent variables is often an invitation to betterfits but poorer predictions.

As noted in the following two points, Ecopath andEcosim do not ‘ignore’ the fact that trophic interac-tions are strongly age–size and seasonally structured.Rather, we assume that initial (Ecopath base or ref-erence period) structuring has been adequately cap-tured in preparing average/total rate input data, andthat changes in structural composition over time arenot large enough to drastically and persistently al-ter interaction rates/parameters. This is very similarto the assumption in single-species biomass dynam-ics and delay-difference modeling that stock compo-sition changes produce regular or predictable changesin overall (stock-scale) production parameters, not thatthere is no composition effect in the first place.

5.8. Do EwE models ignore seasonality inproduction, mortality, and diet composition?

In most applications, Ecopath calculates compo-nents of biomass change over a 1-year accounting


step. There is no explicit assumption about how mor-tality rates, consumption rates, and diet compositionmay have varied within this step, except that the Eco-path user is assumed to have calculated a correct,weighted average of the rates over whatever seasonal-ity may have been present in the data. Such averagescan be difficult to calculate in practice, and a programinterface component has been developed to help userswith this chore (Martell, 1999).

In Ecosim, model users can define seasonal ‘forc-ing shapes’ or functions that can be applied as sea-sonal multipliers to the modeled production and con-sumption rate functions. Generally, including seasonalvariation in this way results in graphics displays thatare hard to follow visually (strong seasonal oscilla-tions in ecosystem ‘fast’ variables like phytoplanktonconcentration), but very little impact on predicted in-ter annual (cumulative, long term) patterns of systemchange.

5.9. Do biomass dynamics models like Ecosim treatecosystems as consisting of homogeneous biomasspools of identical organisms, hence ignoring, e.g.size-selectivity of predation?

The biomass rate equations in Ecosim (sums of con-sumption rates less predation and fishing rates) can beviewed as ‘sums of sums’, where each trophic flowrate for an overall biomass pool is the sum of ratesthat apply to biomass components within that pool. Inthis view, doing a single overall rate calculation for apool amounts to assuming that the proportional con-tributions of the biomass components within the poolremain stable, i.e. the age–size-species compositionof the pool remains stable over changes in predictedoverall food consumption and predation rates. In fact,the assumption is even weaker: pool composition mayindeed change over time provided that high and lowrate components change so as to balance one anotheror proportional contribution of major components isstable enough so that total rates per overall biomassare not strongly affected.

We know of at least one condition under whichthe compositional stability assumption may beviolated—when ratios of juvenile to adult abundancecan change greatly (e.g. under changes in fishing mor-tality) for a species that has strong trophic ontogeny(very different habitat use and trophic interactions

by juveniles). To deal with such situations, Ecosimallows model users to ‘split’ biomass pools repre-senting single-species with strong trophic ontogeny,into ‘juvenile’ and ‘adult’ pools (or if desired into multiple stanza). If so, the Ecosim biomass dy-namics equations are replaced with an explicit agestructured model for monthly age cohorts in the ju-venile pool, and a delay-difference model for theadult pool. That is, for ‘split pool’ species Ecosimreplaces the biomass dynamics model with a muchmore detailed and realistic population model (seeSection 3.2above). This allows Ecosim users tonot only represent compositional effects, but alsoto examine the emergent stock-recruitment relation-ship caused by density-dependent changes in adultfecundity and juvenile growth and foraging timebehavior.

5.10. Do ecosystem biomass models ignorebehavioral mechanisms by treating speciesinteractions as random encounters?

Historically, trophic interaction rates in biomassdynamics models have been predicted by treatingpredator–prey encounter patterns as analogous to‘mass-action’ encounters between chemical speciesin chemical reaction vat processes, where reaction(encounter, ‘predation’) rates are proportional tothe product of predator and prey densities. Such‘Lotka–Volterra’ models generally predict muchmore violent dynamic changes, and considerablysimpler ecosystem organization, than we see in fielddata.

Ecosim was constructed around the proposition thatthis mass-action principle is deeply incorrect for eco-logical interactions, and instead interactions take placelargely in spatially and temporally restricted ‘forag-ing arenas’ where prey make themselves available topredation through activities such as foraging and dis-persal. To represent this within-pool heterogeneity, wetreat each biomass pool as consisting at any instant oftwo biomass components with respect to any predator,one sub-pool of individuals vulnerable to the preda-tor and another sub-pool ‘safe’ from the predator. Inthis view, predation rate is limited jointly by searchefficiency of the predator for vulnerable prey individ-uals, and exchange rate of prey between the invulner-able and vulnerable states. When Ecosim users set the


vulnerability exchange rates to high values, the modelmoves toward ‘top-down’ or mass-action control ofpredation rates. When users set the vulnerability ratesto low values, the model moves toward ‘bottom-up’control where predation rates are limited by how fastprey move (or grow, or disperse) into the vulnerablestate.

Obviously the two-state (vulnerable/invulnerable)representation of prey biomass composition is a firstapproximation to the much more complex distributionof vulnerabilities among prey individuals that is likelyto be present in most field situations. But it goes aremarkable way toward explaining dynamic patterns(lack of predator–prey cycles, persistence of appar-ent competitors and high biodiversity) that we havebeen unable to explain with simpler Lotka–Volterramass-action models.

5.11. Do Ecosim models account for changes introphic interactions associated with changes inpredator diet compositions and limits to predationsuch as satiation?

In nature, diet compositions and feeding rates canchange due to five broad factors:

(1) changes in ‘habitat factors’ such as water clarity,temperature, and escape cover for prey;

(2) changes in prey abundance and activity, and henceencounter rates with predators;

(3) changes in predator abundance, and hence in-terference/exploitation competition for localizedavailable prey;

(4) changes in predator search tactics (search images,microhabitat used for foraging);

(5) handling time or satiation limitations to predatorfeeding rates.

Ecosim allows (or requires) representation of fourof these factors, namely all but predator search tac-tic changes (4). Type (1) factors can be optionallyintroduced by including ‘time forcing’ functions rep-resenting temporal habitat change, and or ‘trophicmediation’ functions where other biomasses mod-ify predation interaction rates for any predator–preypair(s). Types (2), (3), and (5) are built into the cal-culations by default (though some effects can beswitched off through parameter choices).

In Ecosim, changes in prey abundance (factor (2)above) lead to proportional changes in predator dietcomposition only when prey feeding times are delib-erately held constant by ‘turning off’ Ecosim forag-ing time adjustment parameters. When prey foragingtime is allowed to vary (default assumption), declinesin prey density generally result in apparent sigmoid(type (3)) decreases in predator consumptions of thatprey type: as the prey declines, it generally spends lesstime feeding (reduced intraspecific competition for itsown prey) and hence reduced encounter rates with itspredators. The user can exaggerate this sigmoid effectby turning on parameters that cause the prey to spendless time feeding when predation risk is high (i.e. di-rect response to perceived predation risk).

Predator satiation effects are represented in Ecosimby foraging time adjustments such that predators ‘try’to maintain constant food consumption rates (unlessforaging time adjustments are switched off), by spend-ing more time feeding when feeding rates begin to de-crease due to decreasing densities of one or more preytypes. Likewise, handling time limits to feeding rate(lower attack rate on any one prey type as abundanceof another increases, due to predator spending moretime pursuing/handling individuals of the other type)are represented by a ‘multispecies disc equation’ (gen-eralization of Holling’s Type II functional responsemodel).

Ecosim, for regions of parameter space with fairlyslow dynamics, offers a reasonable approximation ofmost types of studied functional response forms. It ispossible, as in all functional responses that the shapeof the curves as evidenced in Ecosim departs sub-stantially from the actual mechanisms which give riseto those shapes in nature. Further, good fits to onetype of data (e.g. biomass) may hide poor fits to othertypes (e.g. capture inappropriate changes in feedingrate).

Our philosophy in developing Ecosim predation ratepredictions has been to look first at the fine-scale(space, time) behavioral ecology of prey and preda-tors, and in particular at how they vary and ‘manage’their time. Overall predation response patterns, such asType II sigmoid effects of reduced prey density, then‘emerge’ as effects of the time management represen-tation rather than being ‘hardwired’ into the modelby particular overall equations for predation rates anddiet composition.


5.12. Are the population models embedded inEcosim better than single-species models since theyexplain the ecosystem trophic basis for production?

In a number of case studies, Ecosim users havetreated the model as though it were a single-speciesassessment tool, varying its parameters so as to fittime series data for a particular species (e.g.Coxet al., 2002). In such cases, it generally turns out thatthe biomass dynamics or delay-difference ‘submodel’for the target species behaves quite similarly when‘embedded’ in Ecosim (with explicit accountingfor production and mortality rate as function offood resources and predators) to the correspondingsingle-species assessment model where competitioneffects are represented as implicit functions of stocksize (e.g. stock-recruitment model) and predationmortality rates are assumed constant.

So if one has an Ecosim model whose ‘production’parameters have been estimated by fitting themodel to single-species data, and a correspondingsingle-species model also fitted to the data, oneshould not be surprised that the two approaches usu-ally give about the same answers to policy questionsrelated to changing fishing mortality rate for thespecies (e.g. fishing rates for MSY). Ecosim modelsmay diverge from the single-species predictions atvery low stock sizes (Ecosim may predict ‘delayeddepensation’ effects due to changes in predation rateson juveniles), but otherwise do not generally leadus to interpret the single-species data any differ-ently with respect to single-species assessment issues(e.g. MSY) than if we just used the single-speciesmodel.

Thus, it would be wrong when applying Ecosim forsingle-species harvest policy analysis to contend thatEcosim is ‘better’ than a single-species model, whenboth give the same answer. It may comfort us to knowas biologists that the Ecosim representation has some-how explained production in terms of ecosystem re-lationships rather than implicit relationships on stocksize, but making biologists ‘feel better’ should not bea criterion for judging the effectiveness of a policytool. When fitting Ecosim to the data we encounterthe same risks as in single-species assessment of in-correct biomass estimation, misinterpretation of trenddata (e.g. hyperstability of catch per effort data), andfailure to account for persistent effects such as en-

vironmental regime changes or confounding of theseeffects with the effects of fishing.

5.13. Do Ecosim population models provide moreaccurate stock assessments than single-speciesmodels by accounting for changes in recruitment andnatural mortality rates due to changes in predationrates?

As noted above, using Ecosim for single-speciesassessments usually results in similar fits to historicaldata as would be obtained with traditional surplusproduction or delay-difference models. In principleEcosim should be able to improve a bit on modelsthat assume stationary stock-recruitment relation-ships and constant natural mortality rates, at leastfor mid-trophic level species that may be subject tohighly variable predation risk. But in practice we haveso far not obtained substantial improvements in fit todata, which could be due to poor data or to stabilityin mortality rates of the sort predicted when Ecosimvulnerability parameters are set to mimic ‘bottom-up’control of predation rates.

In one case where we have fit Ecosim to multipletime series data on major species (herring, salmon,hake, ling cod, seals) by estimating ‘shared produc-tion anomalies’ attributed in the fitting to changes inprimary productivity, we were able to show that abouthalf the total variance around single-species model fitsto changes in relative abundance over time could beexplained by ecosystem-scale effects (Martell et al.,2002). That is, we were able to ‘improve’ on thesingle-species fitting, but this improvement was due toassuming changes in ecosystem scale ‘forcing’ ratherthan to accounting for temporal variation in preda-tion mortality rates associated with impacts of fishingon predators. In another case (French Frigate Shoals,Hawaii) we were again able to fit time series data(rock lobsters, monk seals) better by including ef-fects of an ecosystem-scale regime shift (decreasedprimary production in the Central North Pacific after1990), and were not able to explain deviations fromsingle-species model fits through changes in trophicinteractions alone (Polovina, 2002).

These cases, along with experience that Ecosimgenerally does not behave much differently fromsingle-species models when only fishing effects areconsidered, lead us to suspect that accounting for


predator–prey effects by itself may not lead to substan-tial improvements in stock size prediction. However,there is a good chance that Ecosim will be very helpfulin interpreting effects of large-scale, persistent regimechanges that are likely to have caused ecosystem-scalechanges in productivity. In such situations, Ecosimmay be particularly helpful in finding some resolutionfor the so-called ‘Thompson–Burkenroad’ debatesabout the relative importance of fishing versus envi-ronmental changes in driving historical changes inabundance (Skud, 1975).

Rather than pretending that Ecosim and single-species methods are competitors, a useful assessmenttactic may be to work back and forth between Ecosimand single-species assessment methods, using each tocheck and improve the other. For example, we haveused ordinary VPA and stock synthesis results forPacific herring as reference ‘data’ (summary of rawage composition, harvest, and spawn survey data)for fitting Ecosim models of the Georgia Strait. TheEcosim herring model predicts somewhat lower abun-dances than VPA during periods of low stock size,and somewhat higher abundances than VPA duringhigh stock periods. Ecosim also estimates lower nat-ural mortality rates (M) for herring during the lowabundance periods. If Ecosim is correct in estimatingthat M has been (weakly) density-dependent, thenVPA has probably overestimated abundance (used toohigh anM in the VPA back calculation) during popu-lation lows, and is probably underestimating juvenileabundance now (due to using anM that is too low forthe current high stock size).

5.14. Can one rely on the Ecosim search proceduretime series fitting to produce better parameterestimates?

Ecosim users are cautioned that the search proce-dure in no way guarantees finding ‘better’ Ecosim pa-rameter estimates. Better fits to data can easily be ob-tained for the wrong reasons, e.g. some time series,particularly catch/effort data, can be misleading in thefirst place, as can historical estimates of changes infishing mortality rates. Many parameter combinationsmay equally well ‘explain’ patterns in the data. Non-linear search procedures can become lost or ‘trapped’at local parameter combinations where there are localminima in the SS function far from the combinations

that would actually fit the data best. The best way toinsure against the technical problems of searching acomplex SS function is to use ‘multiple shooting’: startthe search from a variety of initial parameter combi-nations, and see if it keeps coming back to the samefinal estimates. Look very closely at the time seriesdata for possible violations of the assumption that therelative abundance,y, is a product of a scaling fac-tor and the total biomass, due to progressive changesin the methods ofy or by nonlinearities caused byfactors such as density-dependent catchability. Ify isa biomass reconstruction from methods such as VPAthat assume constant natural mortality rateM, spuri-ous trends iny caused by the sort of changes inM thatEcosim predicts, particularly for younger animals, callfor concern. Alternative combinations of Ecosim pa-rameters may fit the data equally well but would im-ply quite different responses to policy changes suchas increases in fishing rates.

Search procedures are most useful in diagnosingproblems with both the model and data. That is, thegreatest value of doing some formal estimation iswhile it seems not to be working, when it cannot findgood fits to data. Poor fits can be informative aboutboth the model and the data.

5.15. Does Ecosim ignore multispecies technicalinteractions (selectivity or lack of it by gear types)and dynamics created by bycatch discarding?

By separating groups into juveniles and adults, eachwith different biomasses and catches (and hence fish-ing mortalities), fundamental differences in selectioncan be accounted for. Moreover, Ecosim users canspecify fishing mortality patterns over time either atthe group level (fishing rate for each group over time)or the fleet level. Fleet level changes are specified aschanges in relative fishing effort (relative to the Eco-path baseline model), and these changes impact fish-ing rates for the species caught by each gear in propor-tion to Ecopath base estimates for the species compo-sition of the gear. That is, technical interactions (fish-ing rate effects on a variety of species caused by eachgear type) are a basic part of the Ecopath data inputand Ecosim simulations. However, Ecosim does notprovide simple scenario development options for sim-ulating tactics that dynamically might make each gearmore or less selective.


Discarded bycatch can be treated as a biomass poolin Ecopath, i.e. as a diet component (and hence com-ponent of production) by species that consume dis-cards (e.g. sharks, birds, shrimp). Ecopath input dataon bycatch and discard rates are passed to Ecosim, andEcosim does time accounting for changes in discardrates and biomass in relation to simulated changes infishing fleet sizes. In scenarios where some speciesare heavily dependent on bycatch, Ecosim will thentrack impacts of bycatch management on food avail-ability and feeding rates of such species. For instance,Ecosim has produced some very interesting scenariosfor shrimp fishery development and how shrimp of-ten appear to become more productive under fishing,by including effects of both reducing abundance ofpredatory fishes (when they are killed as bycatch) andproviding biomass from those fishes as food for theshrimp.

5.16. Does Ecosim ignore depensatory changes infishing mortality rates due to range collapse at lowstock sizes?

Ecosim users have two options for specifying fish-ing mortality rate patterns: (1) direct entry of fish-ing rate (F) values over time; or (2) entry of rela-tive fishing effort values over time, with fishing ratecalculated asq(B) × (relative effort), whereq(B) is abiomass-dependent catchability coefficient. Under thesecond option,q is modeled as a hyperbolic functionof B (q = qmax/(1 + kB)), so thatq can be increaseddramatically with decreases in stock size. The conceptin this formulation is to recognize that catchabilityqcan be expressed as a ratioq = a/A, wherea is thearea swept by one unit of effort andA is the area overwhich fish are distributed. Increases inq with decreas-ing stock biomass are usually assumed to be causedby decreases in stock areaA occupied with decreasesin B.

5.17. Does Ecosim ignore the risk of depensatoryrecruitment changes at low stock sizes?

Depensatory recruitment changes are apparently notcommon (Myers et al., 1995; Liermann and Hilborn,1997), but should not be ignored in risk assessmentsfor situations where a depensatory recruitment declinewould have large economic or social consequences.

Depensatory effects are usually assumed to be dueto Type II predator feeding effects, where predatorswould exert an increasing mortality rate on juvenilefishes if they tend eat a constant number of juvenilesdespite decreasing juvenile density. There are rela-tively few field situations where we would expect suchType II predator feeding effects (like migrating pinksalmon fry being eaten by resident trout in a smallstream).

Ecosim has helped identify another possible depen-sation mechanism that may be more common, whichwe call the ‘delayed depensation’ or ‘cultivation-depensation’ effect (Walters and Kitchell, 2001).When a large, dominant species is fished down,Ecosim often predicts a substantial increase insmaller-sized predators that have been kept down inabundance by a combination of direct predation andcompetition effects with the large dominant species.These predators then cause an increase in predationmortality rate on (or compete for food with) juvenilesof the large, previously dominant group. This causesa depensatory decrease in the recruitment rate perspawner for the large dominant, slowing or prevent-ing population recovery even if the fishing effectsare removed. Thus, far from ignoring depensatory re-cruitment effects, Ecosim warns us to be more carefulabout the risk of these effects. It warns us to be espe-cially wary in the management of the most common,large, and dominant fish species that are the mostvaluable components of most fisheries.

6. Major pitfalls in the application of EwE

EwE can produce misleading predictions about eventhe direction of impacts of policy proposals. Erroneouspredictions usually result from bad estimates or er-rors of omission for a few key parameters, rather than‘diffuse’ effects of uncertainties in all the input infor-mation. We warn EwE users to be particularly care-ful about the following problems that we have seen invarious case studies.

6.1. Incorrect assessments of predation impacts forprey that are rare in predator diets

It is easy to overlook a minor diet item in specifyingdiet composition for some predator. Unfortunately,


while that prey type may not be important for thepredator, it may represent a very large component oftotal mortality for the prey type. This is a particu-larly important problem in representation of mortalityfactors for juvenile fishes, which usually suffer highpredation mortality rates but are often not majorcomponents of any particular predator’s diet and arenotoriously difficult to measure in diet studies (fastdigestion rates, highly erratic and usually seasonaloccurrence in predator diets).

Another way that ‘minor’ diet items can cometo assume considerable importance is through‘cultivation-depensation’ effects (Walters and Kitchell,2001) as discussed above. Suppose for example thatsome small predatory fish is kept at low densities byanother, larger predator, but the number of predationevents needed to exert this control is small comparedto the total prey consumption by the larger preda-tor. It would be easy to miss this linkage entirely informulating the initial Ecopath model. But then sup-pose the larger predator is fished down, ‘releasing’the smaller predator to increase greatly in abundance.The smaller predator may then cause substantial de-crease in juvenile survival rates of the larger predator,creating a ‘delayed depensation’ effect on the largerpredator’s recruitment. Possibly the larger predatorwas abundant in the first place at least partly becauseit was able to exert such control effects on preda-tors/competitors of its own juveniles. Even if such‘perverse’ trophic interactions are rare, they are cer-tainly worth worrying about because they imply arisk that overfishing will result in delayed recoveryor a persistent low equilibrium abundance for largerpredators.

6.2. Trophic mediation effects (indirect trophiceffects)

We use the term ‘mediation effect’ for situationswhere the predation interaction between two biomasspools is impacted positively or negatively by abun-dance of a third biomass type. For example, predationrates on juvenile fishes by large piscivores may bemuch lower in situations where benthic algae, corals,or macroinvertebrates provide cover for the juveniles.Pelagic birds like albatrosses that feed on small fishesmay depend on large piscivores to drive these smallfishes to the surface where they are accessible to the

birds. Some large piscivores may create enough pre-dation risk for others to prevent those others from for-aging on some prey types in some habitats.

When a mediation effect is in fact present but isnot recognized in the Ecosim model development, itis not unlikely for the model to predict responses thatare qualitatively incorrect. For example, fishing downtunas in a model of a pelagic ecosystem is likely toresult in predicted increases in abundance of foragefishes, and hence to predicted increases in abundanceof pelagic birds. But in fact, reducing tuna abundancemay have exactly the opposite effect, resulting in birddeclines due to the baitfish spending less time at thesurface when tuna are less abundant.

6.3. Underestimates of predation vulnerabilities

Predation impacts can be limited in Ecosim byassuming low values of the exchange parameters(v’s) between behaviorally invulnerable and vulnera-ble prey ‘states’. We call these exchange parameters‘vulnerabilities’, and they are estimated by assumingratios of maximum to Ecopath base estimates of preymortality rates for each predator–prey linkage. Thatis, if M(o)ij = Q(o)ij/B(o)i is the base instantaneousnatural mortality rate for prey typei caused by preda-tor j base (Ecopath estimate) consumption rateQ(o)ijon prey base biomassB(o)i, we assume that the maxi-mum possible rate for very high predatorj abundancewould bevij × Bi, wherevij = K × M(o)ij , K > 1,represents the rate at which prey become vulnerableto predatorj. By using aK near 1, i.e.vij only alittle larger thanM(o)ij , Ecosim users can simulatethe ‘bottom-up’ control possibility that changes inpredator abundances do not cause much change inprey mortality rates because these rates are limited byphysiological or behavioral factors of the prey. Theassumption that there are such limitations is supportedby scattered observations where total mortality rates(Z) were poorly correlated with changes in predatorabundances.

Another way expressing that vulnerabilities of preyto predators are very limited is to say that predatorsare already eating almost every prey that does be-come vulnerable. If this is indeed true, then there islikely intense exploitation competition among preda-tors for the prey that do become vulnerable, i.e. thenumber of vulnerable prey seen by each predator is


severely limited by the number of other predators com-peting for those prey. This has potentially large impli-cations for the dynamics of the predator: reductions inpredator abundance may be accompanied by large in-creases in the densities of vulnerable prey available toeach remaining predator. In such cases, Ecosim willpredict a strong compensatory effect on the predatorof reduced predator abundance (strong increases infood consumption rate and growth, or large decreasesin predator foraging time with attendant decreases inmortality risk faced by the predator).

So the net effect of assuming low prey vulnerabil-ities is also to assume that predators should exhibitstrong compensatory responses to reduced abundanceof conspecifics, which in simulations of increased fish-ing pressure means strong compensatory responsesand hence lower risk of overfishing. An enthusiasticproponent of ‘bottom-up’ control of trophic processesmust therefore also be a strong proponent of the ideathat it is hard to overfish. This is a very risky assump-tion.

6.4. Non-additivity in predation rates due to sharedforaging arenas

The default assumption in Ecosim is to treat eachpredation rate linkage as occurring in a unique ‘for-aging arena’ defined by the behaviors of the specificprey and predator. In this formulation, elimination ofone predator will result in a decrease in total preymortality rate equal (at least initially) to the Ecopathbase estimate of that predator’s component of the preytotal mortality rate. This may be partly compensatedby increases in mortality rate due to other predatorsif the prey increases in abundance and spends moretime foraging in response to increased intraspecificcompetition, but in general this compensatory effectwill not completely replace the initial mortality ratereduction.

But suppose this formulation is wrong, and in factthe mortality rate of the prey represents movement ofthe prey into behavioral or physiological states (e.g.parasite loads) for which it is vulnerable to predatorsin general. In this case, removal of any one predatormay simply result in the vulnerable prey individualsbeing taken just as fast, but by other predators. In thiscase, the total mortality rate of the prey will changemuch less than predicted by Ecosim.

6.5. Temporal variation in species-specific habitatfactors

Attempting to fit Ecosim models to time series datahas revealed some cases where an important speciesor biomass pool shows dramatic change that cannot beattributed to any known change in trophic relationshipsor harvesting. Then this dramatic but ‘unpredictable’change appears to result in major trophic impact on therest of the ecosystem. An example would be a plank-tivorous fish species, which shows high recruitmentvariation and occasional very strong year classes. Ifthis species is important to piscivores in the system,the piscivores may respond strongly to changes in theplanktivores abundance. It is quite possible for such re-cruitment ‘events’ to be linked to very localized habi-tat factors that affect juvenile survival of the plank-tivore, so that each event results in a persistent cas-cade of abundance changes throughout the food web.Another example would be loss of specific spawningsites or habitat for one species that causes it to declinedespite favorable trophic conditions in terms of foodsupply and predation risk.

Ecosim can help us detect possible habitat prob-lems, by revealing prediction ‘anomalies’ frombiomass patterns expected under trophic and fishingeffects alone. But there is also a risk of producing‘spurious’ good fits to Ecosim, when Ecosim parame-ters are varied so as to explain as much of the biomasschange as possible; that is, Ecosim may explain pat-terns as trophic/fishing effects that in fact have beendue to habitat changes. This is a particular risk insituations where habitat change involves some fairlyregular ‘regime shifts’ or cycles in habitat variables.Ecosim may well attribute cyclic biomass changes insuch situations to predator–prey instabilities ratherthan environmental forcing.

Acknowledgements

We thank the Pew Charitable Trust for funding the‘Sea Around Us’ project at the Fisheries Centre, Uni-versity of British Columbia, making the further de-velopment of the Ecopath with Ecosim approach andsoftware possible. Villy Christensen also acknowl-edges support from the European Union INCO-DCConcerted Action ERBIC18CT97175, while Carl


Walters acknowledges support from Canada’s Na-tional Scientific and Engineering Research Council.The paper has benefited from discussions with andcomments by Daniel Pauly, who participates activelyin the development of EwE, and who has encouragedus to use material from the unpublished EwE User’sGuide in this contribution. We also benefited fromsubstantive reviews from three anonymous reviewers,to whom we are grateful.

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