Two pairs of eyes are better than one: Combining individual-based and matrix models for ecological...

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Ecological Modelling xxx (2013) xxx– xxx

Contents lists available at ScienceDirect

Ecological Modelling

jo ur nal ho me page: www.elsev ier .com/ locate /eco lmodel

wo pairs of eyes are better than one: Combining individual-basednd matrix models for ecological risk assessment of chemicals

attia Melia,∗, Annemette Palmqvista, Valery E. Forbesa,b,ürgen Groeneveldc,d, Volker Grimmc,e

Roskilde University, Department of Environmental, Social and Spatial Change, Universitetsvej 1, P.O. Box 260, 4000 Roskilde, DenmarkUniversity of Nebraska-Lincoln, School of Biological Sciences, 348 Manter Hall, Lincoln, NE 68588-0118, USAUFZ, Helmholtz Centre for Environmental Research – UFZ, Department for Ecological Modelling, Permoserstr. 15, 04318 Leipzig, GermanySchool of Environment, University of Auckland, Private Bag 92019, Auckland, New ZealandUniversity of Potsdam, Institute for Biochemistry and Biology, Maulbeerallee 2, 14469 Potsdam, Germany

r t i c l e i n f o

rticle history:vailable online xxx

eywords:cotoxicologyolsomia candidaechanistic effect models

oil invertebrates

a b s t r a c t

Current chemical risk assessment procedures may result in imprecise estimates of risk due to sometimesarbitrary simplifying assumptions. As a way to incorporate ecological complexity and improve risk esti-mates, mechanistic effect models have been recommended. However, effect modeling has not yet beenextensively used for regulatory purposes, one of the main reasons being uncertainty about which modeltype to use to answer specific regulatory questions. We took an individual-based model (IBM), whichwas developed for risk assessment of soil invertebrates and includes avoidance of highly contaminatedareas, and contrasted it with a simpler, more standardized model, based on the generic metapopulationmatrix model RAMAS. In the latter the individuals within a sub-population are not treated as separateentities anymore and the spatial resolution is lower. We explored consequences of model aggregationin terms of assessing population-level effects for different spatial distributions of a toxic chemical. Forhomogeneous contamination of the soil, we found good agreement between the two models, whereas forheterogeneous contamination, at different concentrations and percentages of contaminated area, RAMASresults were alternatively similar to IBM results with and without avoidance, and different food levels.This inconsistency is explained on the basis of behavioral responses that are included in the IBM but notin RAMAS. Overall, RAMAS was less sensitive than the IBM in detecting population-level effects of differ-ent spatial patterns of exposure. We conclude that choosing the right model type for risk assessment ofchemicals depends on whether or not population-level effects of small-scale heterogeneity in exposure
need to be detected. We recommend that if in doubt, both model types should be used and compared.Describing both models following the same standard format, the ODD protocol, makes them equallytransparent and understandable. The simpler model helps to build up trust for the more complex modeland can be used for more homogeneous exposure patterns. The more complex model helps detectingand understanding the limitations of the simpler model and is needed to ensure ecological realism formore complex exposure scenarios.
. Introduction

What is the risk that chemicals released into the environmentave unacceptable effects on populations and ecosystems? In cur-

Please cite this article in press as: Meli, M., et al., Two pairs of eyes are becological risk assessment of chemicals. Ecol. Model. (2013), http://dx.doi.

ent regulatory environmental risk assessment (ERA) of chemicals,cological effects are determined indirectly. Threshold exposureoncentrations for detectable effects on individuals measured in

∗ Corresponding author at: Department of Environmental, Social and Spatialhange, Roskilde University, P.O. Box 260, Universitetsvej 1 – Building 12.1, DK-4000oskilde, Denmark. Tel.: +45 4674 2130; fax: +45 4674 3011.

E-mail address: [email protected] (M. Meli).

304-3800/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.ecolmodel.2013.07.027

© 2013 Elsevier B.V. All rights reserved.

the laboratory are extrapolated to populations in real landscapesby dividing them by so-called assessment, or safety, factors, whichare supposed to take into account ecological characteristics of thespecies, landscape, and ecosystem under consideration. However,whether or not these factors are over- or under-protective remainsan open question (Forbes and Calow, 2002).

As a way to incorporate ecological complexity and bridge thegap between laboratory tests and effects on the ecological entitiesthat current risk assessment schemes aim to protect, ecological

etter than one: Combining individual-based and matrix models fororg/10.1016/j.ecolmodel.2013.07.027

mechanistic effect models (MEMs) have been recommended asthey provide a tool for expressing ecological risks in a way thatinforms the environmental management process (Forbes et al.,2010) and increases the ecological relevance of risk assessments

dx.doi.org/10.1016/j.ecolmodel.2013.07.027


http://www.sciencedirect.com/science/journal/03043800

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ARTICLECOMOD-6967; No. of Pages 13

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Forbes et al., 2008; Thorbek et al., 2009). Population modeling haslso been included by the European Food Safety Authority (EFSA) inhe revised Guidance Document on Risk Assessment for Birds and

ammals (EFSA, 2009) and in a Scientific Opinion on the develop-ent of specific protection goals (EFSA Panel on Plant Protection

roducts and their Residues, 2010) as an appropriate option forigher-tier risk assessment.

Nevertheless, in contrast to exposure modeling (Boesten et al.,995), effect modeling has not yet been extensively used for regula-ory purposes (Schmolke et al., 2010a,b). A main reason for this wasdentified in a survey among stakeholders from academia, industry,nd regulatory authorities involved in ERA (Hunka et al., 2013): theack of official guidance for developing and using mechanistic effect

odels. This includes choosing the model types to be used, whichs influenced by contradicting expectations (Hunka et al., 2013):

odels are supposed to be simple and user-friendly enough to beasily understood, parameterized, and used in a standardized way,ut at the same time complex enough to be realistic and capable ofapturing a wide range of ecological scenarios.

Thus, in addition to developing ecological models for chemicalisk assessment, which just have a certain level of complexity, theosts and benefits of this particular level of complexity for ERA pro-edures need to be demonstrated more often, by contrasting moreimple and more complex models. Fully independent comparisons,hough, would require that the models were developed by differ-nt modelers with no direct or indirect interactions whatsoever,hich would be difficult and so far has never been tried. An alter-ative is starting with a more complex model and then aggregating

t into a simplified one. For mechanistic effect models, this was doney Topping et al. (2005), who compared a very complex spatiallyxplicit IBM to a very simple non-spatial matrix model.

Here we take a recent spatially explicit individual-based pop-lation model, which was developed for risk assessment of soil

nvertebrates (Meli et al., 2013), and contrast it with a simpler,ore standardized model, which is based on the generic metapop-

lation matrix model RAMAS Metapop 5.0 (Akc akaya and Root,005). RAMAS falls into the family of “canned” programs (Reedt al., 2002), which corresponds to the widely held believe amonghe stakeholders involved in ERA of chemicals that using standard-zed software is the best way to establish MEMs for regulatory riskssessment.

In our example models, we focus on soil invertebrates, whichre key drivers of important ecosystem services such as nutrientycling and soil formation (Lavelle et al., 2006). For these species,n important ecological factor that is largely ignored in current reg-latory risk assessments is spatial heterogeneity in exposure. It isell known that in soils both natural properties, such as moisture

nd organic matter concentrations, and chemical contaminationre heterogeneously distributed (Lavelle and Spain, 2001; Beckert al., 2006), which has important consequences for the distribu-ion and functioning of populations of soil organisms (Hoy and Hall,998). Thus, the real risk posed by the use of chemicals in agricul-ural practices or industrial activities is likely not to be adequatelyaptured by current risk assessment procedures.

The two models we are contrasting are mostly based on theame input data and, similarly to Topping et al. (2005), the IBMs used to determine some of the parameters of the metapopu-ation model, as it was not possible to find appropriate values inhe scientific literature. Therefore in this study we are not try-ng to compare independent predictions of two models, but toxplore the consequences of model aggregation. Aggregating aomplex individual-based model into a metapopulation matrix


odel, where all the individuals within a grid cell are not treateds separate entities anymore and the spatial resolution is lower,ill allow us to understand whether it really is necessary to look at

ingle individuals for a species with a relatively simple life-cycle in

PRESSlling xxx (2013) xxx– xxx

order to assess toxic effects at the population level. Furthermore,we will explore which benefits the parallel development of moresimple and more complex models can have within a regulatoryperspective, for instance in terms of trust and model acceptance.

2. Methods

The species used in the simulations is Folsomia candida Willem1902, which belongs to the order Collembola, suborder Ento-mobryomorpha, family Isotomidae. This species is used as astandard test organism for toxicity tests: a 28-day reproduc-tion test (International Organization for Standardization, 1999;Organisation for Economic Co-operation and Development, 2009)is included in the refinement options for ecological risk assessmentof plant protection products to soil organisms in the EU (EC, 2009). Amore detailed description of F. candida is given in Meli et al. (2013).

Copper sulfate (CuSO4) was used as a model contaminant: it isproven to cause toxic effects to F. candida survival and reproduc-tion (LC50 equal to 1810 mg kg−1, EC50 for reproduction equal to751 mg kg−1; Greenslade and Vaughan, 2003) and to elicit behav-ioral responses like avoidance (Boiteau et al., 2011). Moreover it isthe most widely distributed pollutant among all metals, and there-fore it is relevant from the practical point of view of ecological riskassessment.

2.1. Individual-based model

The purpose of the model is to investigate how populations of F.candida are affected by spatial distribution of toxic contaminationin soil, with a special focus on interactions with food availability andlocal population density (Meli et al., 2013). The model comprisesthe entities eggs, juvenile and adult female springtails, and gridcells. Springtails are mobile and are characterized by the state vari-ables age (days), position (continuous coordinates), direction formovement, energetic status (days-to-death), cumulative distance(in cm) walked in each hourly time-step, and time (h) spent on con-taminated grid cells. Grid cells are characterized by their food leveland concentration of toxicant (mg kg−1 soil). The model world is atwo-dimensional grid of 100 × 100 square grid cells, whereas eachgrid cell represents 1 cm2 of soil. The model proceeds on two timescales: hourly time steps are used for the foraging procedure, whilethe following processes are repeated at daily time steps: updatingthe seasonal re-growth of food, aging and growth, reproduction,hatching, density dependence on fecundity and survival, and mor-tality.

Values of almost all parameters are drawn from uniform ornormal probability distributions, in order to reflect heterogeneityamong individuals. Stochasticity is also used for initializing spring-tails’ starting positions, as well as causing individual behaviors(movement, reproduction, hatching, mortality) to occur with spec-ified frequencies. Simulations start with 1000 individuals locatedon the upper left corner of the model arena, in order to simulate arecolonization scenario. The initial population is divided in a stagedistribution that randomly varies around the mean values of all thestable stage distributions used for the metapopulation model. Foodresources are also randomly assigned at the beginning of a modelrun to grid cells which are initialized to be food sources, with dif-ferent maximal food levels. Four different scenarios for the extentand spatial distribution of contaminated areas are used (see Sec-tion 2.3). A key feature of the model is that it represents avoidance


behavior: individuals can, depending on the toxicant’s concentra-tion, sense and avoid contaminated areas. The stage distributionsused to initialize the model and the TRACE documentation of themodel (Schmolke et al., 2010a), which includes a full description


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ollowing the ODD protocol, are provided in the Supplementaryaterial.

.2. Metapopulation model

The model is based on RAMAS Metapop 5.0, a software plat-orm designed to build age- or stage-structured, spatially explicit

etapopulation models, to run simulations, and to predict the riskf extinction, time to extinction, expected metapopulation abun-ance, its variation and spatial distribution (Akc akaya and Root,005). In the following we describe the model according to the ODDrotocol (Grimm et al., 2006, 2010) to facilitate direct comparisono the IBM.

.2.1. PurposeThe purpose of the model is to simulate F. candida population

ynamics and to investigate how they are affected by the spatialistribution of toxic contamination in soil.

.2.2. Entities, state variables and scalesThe basic model for the dynamics of local populations is based on

stage-based Lefkovitch matrix, where the matrix elements incor-orate fecundity, mortality, and growth rates of the three stagesggs, juveniles and adults. F. candida is parthenogenetic, thereforenly females are included in the model. The life-cycle parameterssed to calculate the matrix elements are based on data collectedrom the literature and refer to a temperature range of 19–21 ◦C.he model world is two-dimensional and consists of 5 × 5 squarerid cells, each of which is inhabited by one sub-population and rep-esents an area of 20 cm2 of soil, so that the total modeled area is

m2. One model run lasts for 300 days; one time-step correspondso one day.

.2.3. Process overview and schedulingChanges in population size and structure are determined by

ultiplying, each time step, the vector characterizing the stagetructure of the sub-populations by the Lefkovitch matrix (see Sec-ion 2.2.7). The matrix elements are not constant but can depend onocal population size and structure and include random variation.t each time-step, the following processes are executed; the sub-odels representing the processes are described in detail in Section

.2.7:Population dynamics. At each time-step and for each sub-

opulation, the population vector is multiplied by the correspond-ng stage matrix. Different subpopulations are characterized byifferent stage matrices, according to the level of contaminationhey are initialized with.

Contamination effects. To simulate toxic effects of copper sulfaten vital rates, different stage and standard deviation matrices haveeen implemented for different copper concentrations. Therefore,or sub-populations on contaminated patches, these matrices aresed.

Density-dependence. To model density dependence, each timetep certain elements of the stage matrix are multiplied by a vari-ble representing sub-population density at that time step. Thetages affected by density are juveniles and adults.

Standard deviation matrix and stochasticity. Using the option foremographic stochasticity in RAMAS, each time-step the numberf survivors and dispersers (emigrants) is sampled from binomialistributions, and the number of young is sampled from a Poissonistribution. Furthermore, to represent environmental stochastic-


ty, at each time step the program draws the vital rates from aormal or lognormal distribution; the mean of this distribution isaken from the stage matrix, and its standard deviation is takenrom the standard deviation matrix.

PRESSlling xxx (2013) xxx– xxx 3

Dispersal. Dispersing individuals have a higher chance of endingup in a closer patch than a distant one; dispersal is implemented inRAMAS as a negative exponential function of distance.

2.2.4. Design conceptsTo represent environmental noise, i.e. stochastic variation in

the population’s growth rate, stochasticity has been incorporatedby using the standard deviation matrix option that in RAMAS ismeant for purely environmental sources of variation. Interactionamong individuals is indirectly included in the model as density-dependence of juvenile survival and adult fecundity and survival.To observe model output, size and structure of the population,elasticities of individual life-history parameters, as well as spa-tial distribution of the individuals for different concentrations oftoxicant are compared.

2.2.5. InitializationThe model is initialized with 1000 organisms, divided into the

three stages according to the stable stage distribution defined bythe corresponding stage matrix (see Supplementary Material). Allindividuals are placed in sub-population number one, i.e. in the topleft corner, therefore simulating a recolonization scenario.

2.2.6. Input dataThis model has no time-series inputs or external environmental

drivers.

2.2.7. SubmodelsPopulation dynamics. The stage matrix is

⎛⎜⎝

S1 F2 F3

P1 S2 0

0 P2 S3

⎞⎟⎠ (1)

where S is the probability of remaining in the corresponding stage,F fertility, and P the probability of moving from one stage to thenext stage.

Following Crouse et al. (1987), in RAMAS the probabilities ofremaining in the same stage through the next time step and ofmoving from one stage to the next for eggs and juveniles, havebeen calculated as:

Si = 1 − pdi−1i

1 − pdii

pi (2)

Pi = pdii

(1 − pi)

1 − pdii

(3)

where pi is the probability of surviving to the next time-step and dithe stage duration in days.

We have only direct information on the egg viability, i.e. thepercentage of eggs that have been vital during the hatching periodd1. Therefore, we can calculate daily survival p1 as

p1 = egg viability(hatching time)−1(4)

Similarly, for juveniles survival until maturation is, pd22 , d2 matura-

tion time, and

p2 = juvenile survival(maturation time)−1(5)

Juveniles are not fertile, thus F2 = 0.For adults, fecundity F is expressed as the number of eggs pro-


duced per time step, which can be approximated by dividing thenumber of eggs per brood by the time between broods.

Concerning adult survival, the only information available in theliterature is for typical lifespans (in days). Therefore we inversely


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Fig. 1. (a) Comparison of survival curves for individuals in the adult stage imple-mented in RAMAS (solid line) and in the IBM (dashed line (mean), dotted lines(minimum and maximum)). (b) Survival curves for individuals in the adult stagei

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the mean of this distribution is taken from the stage matrix, and itsstandard deviation is taken from the standard deviation matrix.

mplemented in RAMAS for different copper concentrations.

etermined S3 by making the corresponding survival curve as sim-lar as possible to the corresponding curves of the IBM, which wereased on empirically observed distributions of lifespans (Fig. 1a).he reason for the difference between the survival curves of theBM and RAMAS is that the only option to model survival in RAMASs an exponential function, whereas in the IBM survival emergesrom the implemented lifespan distribution.

Since egg viability and the other measures show large variation,e used the following strategy to take this variation into account.e drew the parameters in Eqs. (2)–(5) from a uniform distribution

imited by the minimum and maximum reported value (Table 1)000 times and calculated the corresponding Si values. We derivedrom this sample the mean Si, which was then used in the stage

atrix, and the standard deviation, which was used in the standardeviation matrix.

Contamination effects. To simulate toxic effects of copper sul-ate on vital rates, different stage and standard deviation matricesave been implemented for different copper concentrations. Thelements of these matrices have been calculated following the sameationale as described above for the control matrices, using theame dose–response relationships for each affected life-cycle traits in the IBM. The life-cycle traits affected by copper are:

Egg viability. For each copper concentration used in the simula-ions, egg viability values derived from the concentration-response


urve (Table 2) have been used to calculate new values of the matrixlements S1 and P1 through Eqs. (2) and (3).

PRESSlling xxx (2013) xxx– xxx

Fecundity. The number of eggs per brood is reduced by cop-per contamination, therefore the matrix element F3 is also reducedaccordingly.

Juvenile survival. In the stage matrix, the sum of the S2 and P2elements gives the total survival for the juvenile stage of the popu-lation. Because no other information is available, we assumed thatthe proportion of individuals remaining in the same stage and theproportion of individuals moving to the next stage at each time-step remains the same under copper contamination, i.e. that copperdoes not affect maturation time, as no evidence for this was found inthe literature. Therefore, for each copper concentration used in thesimulations, the new total survival (S2 + P2) has been determinedfrom the dose–response regression for survival (Table 2), and S2and P2 have then been calculated using the same proportion as inthe control: S2 is 95.1% of total survival and P2 4.9% of total survival.

Adult survival. Values for the S3 matrix element for the differentconcentrations were selected on the basis of the observation thatthe survival rate implemented for the control (Fig. 1a) resulted in aresidual survival of about 10% after a time equal to the averageof the empirically observed lifespan range (Table 1). To repre-sent effects of copper sulfate, we used the same approach, usinglifespans deduced from the dose–response regression (Table 2).For instance, for individuals exposed to a copper concentration of500 mg kg−1, the average lifespan is 62 days. Therefore, after tryingdifferent values for the survival rate, we chose the one that resultedin a residual survival after 62 days of 10%, as in the control. The sur-vival curves for control and the simulated copper concentrationsare reported in Fig. 1b.

Density dependence. To model density dependence in RAMAS,each time step the elements of the stage matrix are modifiedaccording to the density of the sub-population at that time step.We assumed that density dependence is based on the abundanceof juveniles and adults, and that density dependence influencesfecundity and survival. We assumed scramble competition for mostsimulations with the exception of the F. candida 2500 mg Cu kg−1

matrix, since the corresponding � value (i.e. population growthrate expressed as population multiplication rate) was less thanone, which is not compatible with the scramble model. Thus, forthis high contamination level, we assumed ceiling-type densitydependence.

Scramble-type density dependence is defined by maximumpopulation growth rate (Rmax) and carrying capacity (K). It was notpossible to find a precise value for carrying capacity in the litera-ture, but some observations (Hopkin, 1997; Fountain and Hopkin,2005) show that the highest recorded F. candida population den-sities are in the range of 105 individuals m−2. Therefore this value,equally divided among sub-populations, was used in the model asK. Rmax was set to the same value as the eigenvalue of the corre-sponding stage matrix. For the ceiling-type density dependence,the same carrying capacity used as in the scramble model was usedas the ceiling density.

Standard deviation matrix and stochasticity. Stochasticity can beincorporated in RAMAS as demographic or environmental stochas-ticity. For the former, the program does not have any customizationoptions, but only allows the number of survivors and dispersers(emigrants) to be sampled from binomial distributions, and thenumber of young to be sampled from a Poisson distribution.

To account for environmental stochasticity, RAMAS has theoption to fill in a standard deviation matrix, which has the samestructure as the stage matrix and should contain standard devia-tions of the vital rates. Then, each time step the program draws thecorresponding vital rates from a normal or lognormal distribution;


To avoid bias in the estimation of vital rates due to truncationabove 1.0, a lognormal distribution has been specified, rather than


Please cite this article in press as: Meli, M., et al., Two pairs of eyes are better than one: Combining individual-based and matrix models forecological risk assessment of chemicals. Ecol. Model. (2013), http://dx.doi.org/10.1016/j.ecolmodel.2013.07.027

ARTICLE IN PRESSG Model


M. Meli et al. / Ecological Modelling xxx (2013) xxx– xxx 5

Table 1Parameters used in the individual-based and in the RAMAS model.

Parameter Units Temperature = 19–21 ◦C Use of the parameter inIBM

Use of the parameter in RAMAS

Empiricallyrecordedrange

Empiricallyrecordedmean value

Maturation time: time toreach adulthood

Days 13–29 Empirically observed rangeof values directlyimplemented

Used to calculate, throughresampling, stage and standarddeviation matrices elements S2

and F2

Hatching time: timeneeded for the eggs todevelop and hatch tojuveniles

Days 7–15 Empirically observed rangeof values directlyimplemented


and F1

Number of eggs per brood,general value for theseason

Number 30–50 Empirically observed rangeof values directlyimplemented

Used to calculate, throughresampling, stage and standarddeviation matrices element F3

Nr of broods per female:max number ofreproductive events

Number 3–20 Empirically observed rangeof values directlyimplemented

Not used

Time between broods Days 6–16 Empirically observed rangeof values directlyimplemented


Egg viability: percentage ofeggs that successfullyhatch

Number 0.75– 0.97 Empirically observed rangeof values directlyimplemented


and F1

Juvenile survival.,expressed as probabilityto survive until age atmaturity

Number 0.95 Empirically observed rangeof values directlyimplemented


and F2

Adult survival., expressedas the age of death of theindividual

Days 6–198 140 Empirically observed rangeof values directlyimplemented

Used to calculate, throughresampling, stage and standarddeviation matrices element S3

Probability to reproduce atevery reproductive instar

Number 0.98 Empirically observed rangeof values directlyimplemented


Distance within which foodand conspecifics aresensed

Cm 2.5 Empirically observed rangeof values directlyimplemented

Food is not included in theRAMAS model

Energy level Days-to-death Max: 30Min: 0a

Parameter value directlyused in the IBM

No energy budgetimplemented; energy level isassumed to be optimal andconstant

Energy reduction pertime-step

Days-to-death 0.042a Parameter value directlyused in the IBM


Energy gained by foodintake


No energy budget or foragingbehavior implemented

Energy reduction per stepmoved


No energy budgetimplemented; energetic cost ofmovement implicit in thedispersal function

Probability to move at eachtime-step

Number 0.1a Parameter value directlyused in the IBM

Implicit in the dispersalfunction

Maximum energy spent forforaging at eachtime-step



Tradeoff between energyand reproduction

Days-to-death 20a Parameter value directlyused in the IBM

No energy budgetimplemented

Maximum energy spent foravoiding high density ateach time-step


No energy budgetimplemented; energetic cost ofmovement implicit in thedispersal function

a Values determined via sensitivity analysis and parameterization (see Meli et al., 2013).

Table 2Dose–response regressions used in the metapopulation model.

Independent variable Dependent variable Regression R2 Reference

ln concentration Reduction of survival y = 0.0824x − 0.1366 0.847 Sandifer and Hopkin (1996)ln concentration Reduction of fecundity y = 0.2189x − 0.8743 0.919 Sandifer and Hopkin (1996)ln concentration Nr of hatched eggs (normalized to the control) y = −0.2243x + 1.8893 0.932 Xu et al. (2009)




6 M. Meli et al. / Ecological Modelling xxx (2013) xxx– xxx

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ig. 2. Heterogeneous contamination scenario in the metapopulation (a) and individrea. Arrows in (a) indicate sub-populations within dispersal distance from the upp

normal one. This means that survival rates are sampled from aognormal distribution if the mean is less than 0.5, and from a “mir-ored” lognormal if the mean is above 0.5. Fecundities are alwaysampled from a regular lognormal distribution, since they are notruncated above 1.0.

Dispersal. Dispersal is distance-dependent, i.e. dispersing indi-iduals have a higher chance of ending up in a closer patch than aistant one. The generic dispersal-distance function implemented

n RAMAS has the form:

ispersal rate = a × exp(

−distanceb

)if distance ≤ Dmax

ispersal rate = 0 if distance > Dmax

The dispersal-distance function assumes the negative-xponential form, which has been shown to be a generallyppropriate model of dispersal (Wolfenbarger, 1946; Kitching,971).

Dmax is assumed to be equal to 40 cm: from 20 IBM simulationst has been measured that the maximum net distance moved byn individual during a simulation time equal to one day (dispersalistance is measured as number of visited grid cells; each grid cell

s 1 cm wide) is 22 cm. Therefore, since the spatial scale introducedy dividing the whole population into discrete sub-populations was0 cm, the dispersal function implemented in RAMAS should allowispersal from a population to the eight neighboring patches, butot further (Fig. 2a).

The value for the parameter b, set to 17.24, has been chosen sohat the corresponding negative exponential function would give aispersal rate of about 0.2 to the population situated on the diagonal

n respect to the original population, as in the IBM only a smallraction of the observed individuals covered an equivalent linearistance.

The parameter a is a coefficient that multiplies the exponen-ial function. When there are several populations within dispersalistance of each other, dispersal rates to single populations areummed up, and the total rate of dispersal must be less than orqual to one, otherwise the number of dispersers would be higherhan the actual number of individuals. Therefore, the value for a has


een set to 0.2 to meet this condition.A model summary generated by RAMAS for the control, which

ncludes all our parameter settings, is included in the Supplemen-ary Material.

sed (b) model. Contaminated areas (dark gray) are equal to 80% of the total modeledt corner sub-population during one time-step.

2.3. Simulation experiments

For the simulations with homogeneous contamination, the con-centrations tested were 0, 125, 500 and 2500 mg Cu kg−1. In thefirst set of experiments with heterogeneous contamination, thecontaminated area in the scenario was 80%, corresponding to 20sub-populations in the metapopulation model (Fig. 2); the con-centrations used were 160, 625 and 3125 mg Cu kg−1, so that theaverage contamination was the same as in the homogeneous sce-nario.

In the second set of experiments with heterogeneous contami-nation, the effects of progressively increasing contaminated habitatand the smallest area needed to sustain a viable population wereinvestigated, starting with 20 sub-populations with toxicant (equalto 80% of the total metapopulation), and progressively increasingthis number to 21 (84%), 22 (88%), 23 (92%) and 24 (96%). The con-centrations tested in this set of experiments were the same as inthe first one, i.e. 160, 625 and 3125 mg Cu kg−1. To better under-stand how avoidance, which is implemented in the IBM but not inthe metapopulation model, influences the differences between thetwo models, in a third experiment simulations of the IBM were runboth with and without avoidance.

Furthermore, for all three experiments, different levels of foodabundance were tested in the IBM; results were compared to themetapopulation model, where food resources are not explicitlymodeled, and are assumed to be optimal and homogeneously dis-tributed. For each level of food abundance simulated, the samepercentage of grid cells was initialized to be food sources, so thatthe total amount of food was kept constant among simulations, butthe distribution of food resources on the grid cells was randomizedat the beginning of every model run.

3. Results

3.1. Homogeneous contamination

Fig. 3 shows the results, expressed as population abundanceover time (sum of juvenile and adult stages), of the first simula-tion experiments, conducted with homogeneous concentrations of0, 125, 500 and 2500 mg Cu kg−1. Three different food levels were


simulated with the IBM by increasing the percentage of grid cellsinitialized as food sources from 10 to 25 and 50%, and in the fol-lowing will be referred to as low, medium and high food level.With the metapopulation model it was not possible to explicitly





Fig. 3. Results of simulations with homogeneous contamination. Black lines represent RAMAS outputs, red lines outputs of IBM simulation with 10%, green lines with 25%and blue lines with 50% food cells. Dotted lines indicate one standard deviation around the mean (100 replicates with RAMAS, 10 replicates with the IBM). Scales on y-axesd th difffi

rd

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iffer due to unlike orders of magnitude of population abundance in simulations wigure legend, the reader is referred to the web version of this article.)

epresent foraging behavior, therefore optimal and homogeneouslyistributed food resources were assumed.

Fluctuations in population abundance were more marked inhe control IBM simulations (0 mg Cu kg−1), due to the fast initialrowth of the population that leads to food and space limitation,ut abundance tended to stabilize after a few, dampened oscilla-ions, especially for the high food level. Population abundance inhe RAMAS simulations with 0 and 125 mg Cu kg−1 reached themposed carrying capacity (105 individuals m−2) and therefore wastable for the length of the simulations. With 500 mg kg−1 of toxi-ant, population growth was much slower than in the control, bothn RAMAS and IBM simulations, although in the latter the growthate was lower, even at high food levels. At the highest simulatedoncentration, in both models the population goes extinct afterbout 100 days.


.2. Heterogeneous contamination

Fig. 4 shows the results, expressed as population abundancever time (sum of juvenile and adult stages), of the second

erent toxicant concentrations. (For interpretation of the references to colour in this

simulation experiment, conducted with heterogeneous local con-centrations of 160, 625 and 3125 mg Cu kg−1. The contaminatedarea was equal to 80% of the simulation arena, therefore the aver-age amount of toxicant the organisms were exposed to was thesame as in the homogeneous scenario; despite this, both in themetapopulation and in the individual-based model, the populationabundance is generally higher for medium and high local con-tamination (Fig. 4c and d). Comparing the decrease in populationabundance with increasing concentrations, it is apparent that thisdecline is more pronounced in RAMAS than in the IBM (Fig. 4).

In Fig. 5, bar plots show the final population abundances (sumof juvenile and adult stages) for the third simulation experiment,where the contaminated area was 84, 88, 92 and 96%, whilemaintaining the same concentrations as in the previous set of sim-ulations. Simulations with the IBM were run both with and withoutavoidance. In order to account for fluctuations in population size,


the average abundance over the last 50 days of simulation hasbeen considered as the final value. Fig. 5 shows that population-level effects of reducing the proportion of uncontaminated habitatincrease with the concentration of toxicant present in the system:





Fig. 4. Results of simulations with 80% of modeled area contaminated. Black lines represent RAMAS outputs, red lines outputs of IBM simulation with 10%, green lines with2 und thd th difffi

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5% and blue lines with 50% food. Dashed lines indicate one standard deviation aroiffer due to unlike orders of magnitude of population abundance in simulations wigure legend, the reader is referred to the web version of this article.)

n both models, whilst at a concentration of 160 mg Cu kg−1 theame final population abundance is reached in all the different per-entages of contaminated area, at 3125 mg Cu kg−1 the populationeclines with the increase of contaminated area. In the IBM theame trend is visible for the effects of including avoidance behavior:t 160 mg Cu kg−1, simulations with and without avoidance reachhe same final population abundance, while at 3125 mg Cu kg−1 theopulation goes extinct in several food level/percent of contami-ated area combinations if avoidance is not implemented.

.3. Sensitivity of model outputs to different exposure patterns

Combining results from all three simulation experiments, weere compare scenarios without toxicant, with homogeneous2500 mg Cu kg−1) and with heterogeneous contamination (80, 84,


8, 92 and 96% of contaminated area; 3125 mg Cu kg−1; Fig. 6).BM results illustrated in this comparison refer to simulations withvoidance behavior and medium food level. The overall rangesf population abundance, between the most favorable set-up (no

e mean (100 replicates with RAMAS, 10 replicates with the IBM). Scales on y-axeserent toxicant concentrations. (For interpretation of the references to colour in this

contamination) and the worst case scenario (homogeneous con-tamination), predicted by the two models, are for the most partoverlapping. However, the sensitivity of the two models towardchanges in spatial distribution of the toxicant is different: compar-ing simulations where the toxicant is distributed on 80% of the gridcells with simulations where the toxicant is present on 92% of thegrid cells, the reduction in population density predicted by RAMASis around 10,000 individuals m−2, while the reduction predicted bythe IBM is of 40,000 individuals m−2. A further increase in the per-centage of contaminated area, from 92 to 96%, led in RAMAS to asudden decline of population abundance, to the point of extinction,whereas the reduction of population size predicted by the IBM isless dramatic.

4. Discussion


In the present study we aggregated a spatially explicitindividual-based population model into a stage-structured demo-graphic metapopulation model, and compared population-level


Please cite this article in press as: Meli, M., et al., Two pairs of eyes are better than one: Combining individual-based and matrix models forecological risk assessment of chemicals. Ecol. Model. (2013), http://dx.doi.org/10.1016/j.ecolmodel.2013.07.027




Fig. 5. Final population size (averages over the last 50 simulation time-steps), for different percentages of contaminated areas: 84% (white), 88% (light gray), 92% (dark gray)and 96% (black). Error bars represent standard deviations (100 replicates with RAMAS, 10 replicates with the IBM).





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ig. 6. Mean population size (in base-10 log scale) predicted by RAMAS (a) and the

reas (3125 mg Cu kg−1).

ffects of different spatial distribution of a model contaminant (cop-er sulfate) predicted by the two models.

Individual-based population models are often seen as too com-lex and somewhat obscure, and questions are often raised aboutow much and which complexities need to be incorporated to get aobust estimate of population risk (Forbes et al., 2008). In contrast,atrix population models may offer a simpler approach, have a

ong history of use in applied ecology, and are easier to analyzePagel et al., 2008).

All simulations performed for this study lasted 300 days, whichs assumed to be appropriate for a regulatory context, as in the EUhe time scale usually considered to assess recovery of a populationn the field is one growing season, which is generally shorter thanne year. The modeled spatial scale was equal to 1 m2, but could beepresentative for a larger area of similar conditions (e.g. cultivatedeld). In both models, in fact, the modeled area is larger than theispersal distance of an individual during one time-step, and evenn a longer time scale, the dispersal ability of this species is ratherimited. Furthermore, one of the refinement options for soil orga-isms currently used in higher tier ERA of pesticides are Terrestrialodel Ecosystems (TMEs): these experiments are usually carried

ut in tubes smaller than 1 m2 (e.g. 17.5 cm diameter: Knacker et al.,004), which is considered an ecologically meaningful scale. In allimulation experiments, 100 replicates were run with RAMAS and0 with the IBM. Using different numbers of replicate runs for thewo models did not affect the results, as results for 100 and 10eplicates for RAMAS were virtually identical (data not shown).

Results of the first set of simulations (Fig. 3; homogeneous con-amination) show that the two models’ predictions are in goodgreement for the control, the lowest, and the highest concen-rations, at least when comparing IBM simulations with medium25%) and high food level (50%), while the abundances reachedith low food were much lower than the ones predicted by RAMAS.

his was to be expected, as the carrying capacity implemented inhe metapopulation model reflects an amount of food resourceshich is not limiting for the growth of the population. Over-

ll, it should be kept in mind that the design of the two models


as not independent: the RAMAS model was in fact designed, oralibrated, to mimic the behavior of the IBM for homogeneous sce-arios. Fig. 3 shows that the aggregation toward the simpler model,hich required quite a few assumptions, was appropriate, so that

ith 25% food and avoidance behavior (b) for different percentages of contaminated

differences between the two models for other scenarios can beascribed to factors which cannot be represented in the simplermodel.

At the highest toxicant concentration simulated in both models,the populations go extinct after nearly the same interval of time;the peak at the beginning of IBM simulations can be explained bythe fact that individuals are not instantaneously affected by thecontaminant (i.e. toxic effect builds up over time), therefore at thebeginning of a simulation their survival and fecundity allow for apositive growth rate, which is then disrupted by constant exposureto the toxicant.

The biggest difference between predictions produced by thetwo models appears to be at 500 mg kg−1, where RAMAS predicteda much faster population growth than the IBM. In all the graphsshown in Fig. 3 the same pattern is repeated: at the beginning ofthe simulations the IBM curves are above the RAMAS one, then theyswitch, and in RAMAS simulations stable size is always reachedbefore the IBM. For the control and low concentration this happensrather quickly, while in the 500 mg kg−1 simulations it takes longerbecause of the higher toxicant concentration. Despite this differ-ence in growth rate, longer simulations (not shown) demonstratedthat eventually a similar stable population size is reached in thetwo models.

As all toxic effects implemented in the two models are basedon the same empirical data, and population abundances reachedin the homogeneous scenario with 500 mg Cu kg−1 are too low fordensity-dependence to have a significant role that can justify thedifference, we hypothesize that the disparity in population growthrate is due to the different level at which toxic effects act in the twomodels. In the metapopulation model toxicity is implemented as areduction of vital rates, i.e. constant values that multiply the num-ber of individuals present in the model at each time-step, whereasin the IBM, the toxicant influences single individuals, reducing theirhatching success, fecundity and lifespan. As individuals are dif-ferent from each other in terms of life-cycle parameters, at thebeginning of simulations, when population density is low, appli-cation of toxic effects to single individuals enhances demographic


stochasticity, causing the population to grow more slowly.The main point that emerges from the results of simulations

with heterogeneous contamination (Figs. 4 and 5) is that RAMASand IBM predictions are not always consistent. This is apparent, for


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nstance, from the results of the third set of simulations, shown inig. 5, where at different concentrations and percentages of con-aminated area, RAMAS results are alternatively similar to IBMesults with and without avoidance, and different food levels. Inhese simulations we did not factor down exposure concentra-ions while factoring up the percentage of contaminated area.owever, the increased toxic effects in simulations with 84–96%ontaminated area, compared to simulations with 80%, cannot bettributed to the increase in total exposure. In fact Fig. 3d showshat under homogeneous conditions (concentration 2500 mg kg−1)opulation abundance drops below 100 within the first 50 days.herefore every bar in Fig. 5 that represents populations with aigher abundance than 100 is due to the spatial heterogeneities ofhe contamination. The slightly higher average concentration doesnly suppress slightly the beneficial effect of spatial heterogeneityn the final abundance.

The RAMAS model does not include avoidance behavior, becausenly one dispersal function can be defined for the entire metapop-lation. Therefore, the difference between RAMAS simulations and

BM simulations without avoidance can be explained mainly on theasis of how foraging behavior and density-dependence are imple-ented: dispersal in RAMAS has been modeled as an average of

he movement procedure implemented in the IBM, but the finercale of the latter, which varies from individual to individual andas a step-length of 1 cm, leads to high variability in the individ-als’ exposure. Furthermore, density-dependence is implemented

n the metapopulation following a top-down approach, while inhe IBM is an emergent property of the modeled system. In the lat-er, density-dependence acts independently on each grid cell: this

eans that even though the global population abundance is lownd would not give rise to density-dependent effects, locally situa-ions of high density may occur (for instance, around food sources)hat reduce the growth of the population.

In summary, the flexibility of the individual-based model makest more suitable to investigate the effects of multiple stressors, fornstance chemical contamination and food scarcity, on populations.n fact, to implement different food levels in a matrix model, it

ould be necessary to recalculate all the mean values and prob-bility distribution of the matrix elements for each food level andoncentration of toxicant. On the contrary, both these factors aremplemented in the IBM as functions that dynamically modify theife-cycle parameters of the organisms; therefore it is not necessaryo modify the model to test other combinations of the two stressors.

The importance of taking into account food availability on therowth of collembolan populations is apparent from several pub-ished studies. Usher et al. (1971), for instance, investigated theffects of food availability on the growth and production of F. can-ida, and found that food appeared to play a major role in regulatinghe rate of population growth and in determining the maximumopulation density. van der Kraan and Vreugdenhil (1973) demon-trated under field conditions that populations of Hypogastruraiatica are sometimes limited by food supply. Joosse and Testerink1977) showed that natural factors, such as food and soil moisture,ave a great influence on field populations of Orchesella cincta. Fur-hermore, results published by Bengtsson et al. (1985) indicate thaturvival and growth of the collembolan Onychiurus armatus in aetal-polluted soil are dependent on the availability of food.Another important take-home message, related to the above-

entioned flexibility of individual-based modeling approaches, ishat the IBM allows exploring different scenarios, and detectingner-scale effects (for instance reductions in population abundance

or small decreases in % of contaminated area, as shown in Fig. 6). As


consequence, we found that RAMAS is less sensitive than the IBMn detecting population-level effects of different spatial patternsf exposure (Fig. 6). The overall ranges of population abundance,etween the most favorable set-up (no contamination) and the


worst case scenario (homogeneous contamination), predicted bythe two models, are for the most part overlapping. Simulating inter-mediate percentages of contaminated area with the two models,instead, did not give the same results, as RAMAS predicted a muchlower decrease of population size with increasing percentages ofcontamination. This is a critical point when a model is supposedto be used to answer questions related to spatial heterogeneity ofexposure.

The main motivation of this study was that MEMs are not yetwidely used in regulatory risk assessment because most stakehol-ders involved do not know how and when to trust such models.Hunka et al. (2013) report that this lack of trust is largely due to thelack of transparency in the way models are presented and, mostimportantly, the lack of guidance on what type of models to use forwhat kind of questions. A major bottleneck in establishing trust inmodels is thus to provide tools for standardized testing and docu-mentation of ecological models, following good modeling practice.Examples are the ODD (Overview, Design concepts, Details) proto-col (Grimm et al., 2006, 2010) and the framework for transparentand comprehensive ecological modeling (TRACE) documentation(Schmolke et al., 2010a).

Our study shows a possible way to increase trust in mechanisticeffect models with regard to model choice and transparency. Ourpoint of departure was the ongoing debate on whether simple orcomplex models should be favored for supporting environmentalrisk assessment of chemicals. Similar debates exist in ConservationBiology (Beissinger and Westphal, 1998) and other fields of ecolog-ical application (Pagel et al., 2008). Our main conclusion is that theeither/or question is not meaningful. Every model type has its ownpros and cons (Schmolke et al., 2010a); it is impossible to combineall pros in one single model. We therefore recommend, wheneverpossible, to develop and use both types of models for the samequestion and data set (Grimm et al., 2009). This requires additionalresources for model development, testing, and analysis, but has anumber of important benefits.

First, “canned” models like RAMAS are black boxes to userswhich have no training or experience in modeling. There is a highrisk that model assumptions are not fully understood, or defaultsettings uncritically used (Grimm et al., 2004). Trying to make theoutput of an IBM and a simpler, canned model match for appro-priate simple scenarios means that the canned model has to beunderstood and parameterized in all detail. This detailed under-standing can then be communicated using the ODD protocol, astandard format for describing individual-based models (Grimmet al., 2006, 2010). Here, for the first time a spatially explicit matrixmodel was described using this protocol. This allows to better com-pare the simple and complex models, and it makes all assumptionsof the “canned” more simple model transparent. On the other hand,detailed IBMs, which are developed from scratch, have their ownlimitations. They are more complex and their output can thus behard to test and understand. How can we be sure that model resultsindeed emerge from reasonable model assumptions and not fromundetected bugs in the code and wrong assumptions? One wayto build up trust in IBMs is to develop, like we did here, a sim-pler matrix model and demonstrate that results are the same forscenarios which can be represented with both models.

Ideally, one would develop both a simple and complex modelfor all models which are supposed to support environmental deci-sion making. In practice, however, resources are limited and onestill has to decide with which model type to start with. Here, theobvious advice is that the choice of model type should depend onthe questions one wants to address. For instance, if any behavior,


other than dispersal, matters, an IBM approach should be chosen.In Table 3 we listed a series of questions a hypothetical model usershould try to answer about which model approach should be cho-sen first. In fact, as Stephens et al. (2002) pointed out, how much





Table 3Recommendations for choosing a model type: specific purposes for which one model type is more suitable than the other, allowing for an easier or better solution to theproblem.

Individual-based model RAMAS model

Are subpopulations properties time-dependent? XDoes any behavior other than dispersal matter? XAre you interested in the effects of more than one stressor? XDoes fine-scale spatial resolution matter? XIs the modeled system best described as a discontinuous

set of subpopulations within a matrix of unsuitablehabitat?

X

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Do you want to perform rigorous statistical analysis on themodel and its outcomes and/or may it be necessary tosolve the model numerically?

cology is included in an ecological model matters for some ques-ions we want a model to answer, but not for others. In theirtudy they compared the ability of different models to reproducebserved, for the Alpine marmot, population abundance, its varia-ions, and behavioral responses. They concluded that any attempto prove that model predictions are true or false is misguided. Inde-endent data sets are needed, and even when they are available,he levels of variance inherent in each model make it difficult tostablish accurate patterns: only qualitative judgments are possibleStephens et al., 2002).

Therefore, because “validation” of population models is oftenery difficult, we suggest as a way to increase trust in models toe used for decision-making purposes to use “two pairs of eyes”ather than one, i.e. combine the use of two different model types.he main conclusion from the present study, in fact, is that when

well-tested IBM exists, it can be worthwhile to develop a simpli-ed matrix model or, if spatially explicit, metapopulation model.his can be done using “canned” models like RAMAS, or simpleodels developed from scratch. The effort for this is far below that

equired for the original IBM. On the other hand, if a matrix modelas developed first, describing it using the ODD protocol helps tonderstand that matrix models are, if they are used for projection,

ust simulation models with a certain structure which can easily beummarized by using matrices. Starting from the ODD description,eveloping a corresponding IBM and then exploring the effects ofxplicitly representing individual life cycles and behavior requiresome effort but is straightforward.

Facing the benefits of using “two pairs of eyes” rather than onlyne, it is not unlikely that combining simple and complex modelill be recommended in guidance documents for regulatory risk

ssessment.

cknowledgments

We acknowledge support by the European Union under the 7thramework Programme (project acronym CREAM, contract numberITN-GA-464 2009-238148).

ppendix A. Supplementary data

Supplementary data associated with this article can be found,n the online version, at http://dx.doi.org/10.1016/j.ecolmodel.013.07.027.

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