Comparing population recovery after insecticide exposure for four aquatic invertebrate species using...

Ecological Models

COMPARING POPULATION RECOVERY AFTER INSECTICIDE EXPOSURE FOR FOURAQUATIC INVERTEBRATE SPECIES USING MODELS OF DIFFERENT COMPLEXITY

J. M. (HANS) BAVECO,*y STEVE NORMAN,z IVO ROESSINK,y NIKA GALIC,x and PAUL J. VAN DEN BRINKykyAlterra, Wageningen University and Research Centre, Wageningen, The Netherlands

zDow AgroSciences, Abingdon, United KingdomxSchool of Biological Sciences, University of Nebraska-Lincoln, Lincoln, Nebraska, USA

kDepartment of Aquatic Ecology and Water Quality Management, Wageningen University, Wageningen, The Netherlands

(Submitted 30 September 2013; Returned for Revision 16 December 2013; Accepted 3 April 2014)

Abstract: Population models, in particular individual-based models (IBMs), are becoming increasingly important in chemical riskassessment. They can be used to assess recovery of spatially structured populations after chemical exposure that varies in time and space.The authors used an IBM coupled to a toxicokinetic–toxicodynamic model, the threshold damage model (TDM), to assess recovery timesfor 4 aquatic organisms, after insecticide application, in a nonseasonal environment and in 3 spatial settings (pond, stream, and ditch). Thespecies had different life histories (e.g., voltinism, reproductive capacity, mobility). Exposure was derived from a pesticide fate model,following standard European Union scenarios. The results of the IBM–TDM were compared with results from simpler models: one inwhich exposure was linked to effects by means of concentration–effect relationships (IBM-CE) and one in which the IBMwas replaced bya nonspatial, logistic growth model (logistic). For the first, exposure was based on peak concentrations only; for the second, exposure wasspatially averaged as well. By using comparisons between models of different complexity and species with different life histories, theauthors obtained an understanding of the role spatial processes play in recovery and the conditions under which the full time-varyingexposure needs to be considered. The logistic model, which is amenable to an analytic approach, provided additional insights into thesensitivity of recovery times to density dependence and spatial dimensions. Environ Toxicol Chem 2014;33:1517–1528.# 2014 SETAC

Keywords: Chlorpyrifos Lethal effects Multimodel approach FOCUS scenarios Spatial scale

INTRODUCTION

Exposure assessment in Europe is supported by the use ofmodels. For instance, for the higher tier of the aquatic exposureassessment, 10 realistic worst-case scenarios have beendefined [1], collectively representing the variety of aquaticecosystems found in European agricultural land. Based on thesescenarios, models [2] are then used to assess the fate of pesticidesentering the system through spray drift, runoff, and leaching.The predicted environmental concentrations (PECs) obtainedfrom these fate models can be used directly in an effectassessment for a nontarget organism.

Researchers have only recently begun to use detailed exposureassessments, with temporally and spatially varying PECs instead ofpeak values alone, to obtain a more realistic effect assessment.Ecological models are considered to be useful tools to assess theeffects after pesticide exposure to nontarget species at various levelsof biological organization [3–6]. A specific type of ecologicalmodel, the individual-basedmodel (IBM), can easily dealwith suchspatial heterogeneity in exposure and can incorporate essentialdetails regarding life history [7]. Therefore, thismodel appears to bewell suited for population-level risk assessment, with existingexamples of theoretical [8–10] and applied models for bothaquatic [11,12] and terrestrial [13,14] organisms. To extrapolatetime-varying exposure patterns into individual level effects [15],toxicokinetic and toxicodynamic (TKTD)models can be used [16].When TKTDmodels are combined with IBM, complex individualexposure resulting from the interplay between spatially heteroge-

neous, dynamic exposure patterns and themovement of individualscan be accounted for and, through individual mortality risk,extrapolated into population-level consequences [17,18]. Anotherimportant purpose of these models is the estimation of populationrecovery times [19]. Recovery times are difficult to obtainexperimentally but are relevant because population-level effectsmay be considered acceptable if recovery takes place within a shortperiod (e.g., pesticides) [20,21].

Most of the IBMs used or proposed for use in environmentalrisk assessment in the context of pesticide regulation [5] arerelatively complex. For the acceptance of their use, high-qualitymodel documentation is paramount [22], complemented byextensive model testing and sensitivity analyses [5]. It is at leastas important to provide an understanding of model behavior [6].One way to obtain such an understanding is by comparing thebehavior of the complex model with that of simplifiedmodels [7,23]. One main aspect in which the complex modelmay differ from the simpler one is in spatial explicitness.Following an ecoinformatics approach [24], comparison ofspatial IBMs with so-called mean-field models can elucidate therole of space and the spatial pattern formation that may occur inIBMs.

In the present study we applied coupled IBM–TKTD modelsto assess population recovery times for several aquaticorganisms, after application of an insecticide, chlorpyrifos, ina nonseasonal environment. The IBMs represented 4 aquaticspecies with different life histories (e.g., voltinism, reproductivecapacity, mobility): the waterlouse Asellus aquaticus, thenonbiting midge Chironomus riparius, the amphipod Gamma-rus pulex, and a mayfly (mainly based on the life cycle ofCloeondipterum but for the stream scenario based on Baetis sp.). Mostof the complexity in the IBMs was related to spatial processes,that is, different spatial structures of continuous aquatic habitats

All Supplemental Data may be found in the online version of this article.* Address correspondence to [email protected] online 15 April 2014 in Wiley Online Library

(wileyonlinelibrary.com).DOI: 10.1002/etc.2605

Environmental Toxicology and Chemistry, Vol. 33, No. 7, pp. 1517–1528, 2014# 2014 SETAC

Printed in the USA

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(ponds, ditches, and streams), species that were mobile or had atleast a mobile stage, and exposure that was spatially explicit anddynamic in time and space. The full exposure pattern was usedby coupling the IBM to a TKTD model, termed the thresholddamage model (TDM) [25]. The combined model is referred toas the IBM-TDM. We considered only lethal effects ofchlorpyrifos.

We compared the results obtained using the IBM-TDM withthe outcome of 2 simpler models. First, a model was used inwhich the IBM was combined with a classical model for linkingexposure to effects based on concentration–effect relationships(IBM-CE). For this model, a simplified exposure patternsufficed, one defining only peak concentration (although stillexplicit in space and time). Second, a differential-equationmodel, the logistic equation model, was used as a mean-fieldapproximation to the IBM. This nonspatial model (referred to inthe present study as the logistic model) was analytically solvableand allowed for a full understanding of dynamics following astress event. For the logistic model, the same concentration–effect relationship was used as for the IBM-CE. Because themodel was nonspatial, however, the exposure pattern also had tobe averaged in space and time.

Species-specific coefficients for both exposure-effect linkagemodels (CE and TDM) were obtained from laboratory studies.The per capita rate of increase r, which integrated differentrelevant aspects of life history of the species into 1 measure [26],could be obtained by solving the Euler–Lotka equation with thecoefficients defined for the IBM.

The present study had 3 main objectives. First, we wanted toobtain an understanding of the role spatial processes play inrecovery dynamics. We investigated this issue by comparing thebehavior of the IBM-CE with that of the logistic model. Weformulated the insights obtained in terms of general character-istics of spatiotemporal exposure pattern, species traits(movement and dispersal, intrinsic growth rate), and spatialdimensions of the system. Second, we investigated the extent towhich estimates of recovery time differ, taking into account a fulltime-varying exposure pattern versus a simplified exposurepattern based on peak concentrations. We explored this issue bycomparing the results for IBM-CE and IBM-TDM. The outcomemay provide an indication of the conditions under which themore complex IBM-TDM approach is better suited. Third, wewanted to understand the behavior of and the results produced bythe most complex model, the IBM-TDM, as it was used in a riskassessment based on a multitude of exposure scenarios. We didthis by a comparison with models that simplified differentaspects of the IBM–TDM complexity (the exposure part, theecology, or both). This is the overarching objective of the presentstudy. The comparisons between models may indicate underwhich conditions the most complex model is mandatory to use inrisk assessment and when it can safely be replaced by simplerpopulation models. An additional advantage of comparison withsimpler models is that these simpler models—especially whenamenable to analytic approaches—can provide general insights.In our case, the relevant insights we obtained from the logisticmodel relate to the role of density dependence [27] and theinfluence of spatial settings (dimensions of pond, stream, andditch) on population recovery.

MATERIALS AND METHODS

We simulated the population dynamics of 4 aquaticinvertebrate species exposed to chlorpyrifos in 3 spatial setups(pond, ditch, and stream). Spatially explicit exposure data were

used, obtained from a fate model (Toxic Substances in SurfaceWaters [TOXSWA]), for different Forum for the Coordinationof Pesticide Fate Models and their Use (FOCUS) scenarios. Inaddition to the main model (IBMwith a TDM), 2 simpler modelswere used, an IBM with a CE link between exposure and effect,and a differential equation model for logistic growth. Thesimpler models did not use the full spatiotemporal exposurepattern, but required aggregated data derived from it.

We characterized the different species by their per-capitagrowth rate r, which was also needed as a coefficient in thelogistic model, and by their movement and dispersal attributes.In stagnant to slow-flowing water bodies (pond and ditch), 2species moved on a daily basis (Asellus and Gammarus), withGammarus being themoremobile, and 2 species had a very shortmobile stage (Chironomus and the mayfly), with the mayflybeing the more mobile. In streams, 2 species (Asellus and themayfly) could in addition be transported downstream by drift ona daily basis, and mayfly had an upstream movement bias.

We characterized exposure patterns by their temporal andspatial dynamics. All patterns had a peak concentration,followed by decay. Local decay rate and the speed with whichpeak concentrations traveled through the system differed perscenario and spatial setup.

Total population size was followed in all simulations, andrecovery times were calculated from this size for all scenarios.

Landscape

Modeled landscapes consisted of 1-m2 cells. The ditch andstream had 600 cells in a row, of which 100 were directlyexposed to chlorpyrifos via spray drift and the other 500indirectly through processes occurring in the water column. Forthe animals, the first and the last cells were linked (periodicboundary conditions). Compared with the standard FOCUSscenarios from 2001 [1], the length of the systems was increasedfrom 100m to 600m to take into account the impact of thelandscape context (500m of potentially less-exposed habitat).The pond measured 30 cells� 30 cells, had an inflow andoutflow, and was uniformly exposed through spray drift.

Species models

The 4 species models were parameterizations of a single IBMwith a generic, simple individual life cycle. Modeled events inthe life cycle included birth, death, reproduction, and dailymovement or aerial dispersal of ovipositing females. Only thefemale part of the population was represented in the models.After birth, each female individual lived and developed tomaturation in a time interval of length t, and produced after thistime interval a clutch of size b. For species with multiple broods(only Gammarus), after an interbrood period of length t, asecond clutch was produced of size b, and so on for the totalnumber n of broods. All individuals experienced during their lifethe same constant background mortality risk mb. Thus, averagelifetime under low-density conditions was set to 1/mb. Inaddition, individuals were assumed to experience a density-dependent mortality that scaled directly with local density withproportionality coefficient mDD (m2 ind�1 d�1). Local density(N) was defined as the number of individuals in the same spatialunit (1m2). Total daily mortality risk thus amounted to

m ¼ mb þ mDD � N ð1Þ

To reflect natural variability in development, the timing-related coefficients t and g were stochastic and drawn from(Gaussian) probability density functions. The values of the vital

1518 Environ Toxicol Chem 33, 2014 J.M. Baveco et al.

rates are given in Table 1. For all species, the density-dependentmortality coefficient was set to 0.001 (ind�1 d�1). Mortality riskswere defined as daily probabilities, effectuated on an individualbase. For further justification, see Supplemental Data A.

Movement and dispersal attributes differed per species and,to some extent, per habitat (Table 2). Two of the species, Asellusand Gammarus, were considered to be relatively mobile duringtheir juvenile and adult stage and moved on a daily basis. Theother 2 were assumed to have relatively immobile instar stages.Their mobile stage was the short-lived adult stage for which weassumed a duration of a single day, when females swarmed andoviposited (together referred to as dispersal in the following). Allmovement was assumed to be a random walk.

For the pond, a kernel representation was not as straightfor-ward; thus we simply simulated the randomwalk, with a species-specific number of steps (displacements to a randomly chosenneighbor cell of 1 m2). For Asellus and Gammarus this explicitrandom walk was limited to cells with aquatic habitat. ForChironomus it could include terrestrial habitat as well, becauseChironomus females were assumed to head for the nearestaquatic habitat after dispersal. For the mayfly, realistic dispersaldistances were much larger than the dimensions of the pond;therefore, for this species all locations within the pond wereassumed to be reachable with equal probability (randomdisplacement within the whole aquatic habitat).

Setup

The basic time step was 1 d in the IBM. The within-individual continuous-time dynamics of the TDM were solvedwith a simple Euler–Forward integration with a time step of5min. All scenarios were run with initial populations indynamic equilibrium (equilibrium state was obtained byrunning the simulations for at least 2000 d) and lasted for2 yr (730 simulated d). All models were implemented in theNetLogo platform version 5.0.3 [29].

Concentration–effect model

Concentration–effect relationships for each of the 4 specieswere obtained from laboratory experiments, applying theregression model in Genstat [30]

c ERCð Þ ¼ cð0Þ1þ e�bðlnðERCÞ�aÞ ð2Þ

where ERC is the ecotoxicologically relevant concentra-tion [31], c(ERC) is the expected numbers at a certain ERCconcentration, c(0) is the expected number in control, a is thenatural log of the expected (ERC)50, and b is the slopeparameter. Note that we used 4-d median effective concen-tration (EC50) values, which should be worst case whenactual exposure is shorter than 4 d [18]. For A. aquaticus, G.

pulex, and C. dipterum the values for a and b were obtainedfrom Rubach et al. [32] (Table 3). The a parameter for C.riparius was obtained by calculating the geometric mean forboth 4-d median lethal concentration (LC50) values reportedby Hooftman et al. [33]. Unfortunately, this publication [33]does not provide information on the slope, the b parameter.The b parameter was set in such a way that the 4-d 10% lethalconcentration (LC10) of the resulting concentration–effectrelationship corresponded with the acute 4-d no-observed-effect concentration reported in the same publication [33].The values in Table 3 correspond very well with calculatedfield EC50 values based on semifield data [34]. Note that,based on EC50 values for chlorpyrifos, Chironomuswould becharacterized as the most sensitive species, followed byGammarus and the mayfly, while Aselluswould be consideredrelatively insensitive.

Threshold damage model

We used the TDM [25,35], to predict effects of time-varyingexposure. The TDM model consists of a toxicokinetics part(Equation 3), accounting for chemical uptake, biotransforma-tion, and elimination processes, and a toxicodynamics part(Equations 4–6), representing the damage accrual and recovery.

dCintðtÞdt

¼ kinCwðtÞ � koutCintðtÞ ð3Þ

dDðtÞdt

¼ kkCintðtÞ � krDðtÞ ð4Þ

dHðtÞdt

¼ u �max DðtÞ � threshold; 0½ � ð5Þ

SðtÞ ¼ e�HðtÞ � SbðtÞ ð6Þ

In Equation 3, Cint is the internal concentration (amountmass�1), Cw is the concentration in the water (amountvolume�1), kin is the uptake rate constant (volume mass�1

time�1), and kout is the elimination rate constant (time�1). Thefirst part of Equation 4 simulates the accrual of damage in time asa function of the internal concentrations and the second part therecovery/repair of damage, where kk is a killing rate constant(mass amount�1 time�1), kr is the damage recovery/repair rateconstant (time�1), and D(t) is the damage (–). In Equation 5, dH(t) is the hazard rate, which describes the probability of aindividual to die at a given time t, and u (time�1) is a probabilityconstant without biological meaning. When the threshold fordamage is exceeded, the rate gets a value above 0. Hazard andsurvival are linked in Equation 6, where S(t) is the survivalprobability (–) for a given time, which is corrected for thebackground survival (Sb).

Table 1. Life-history coefficients of the 4 species used to calculate population growth ratea

Species mb (d�1) tb (d) b (females) g (d) No. r (d�1) l (¼er) (d�1)

Asellus 0.001 70 (10) 20 — 1 0.0418 1.0427Gammarus 0.01 130 (20) 16 20 5 0.0173 1.0175Chironomus 0.0007 22 (2) 87 — 1 0.2022 1.2165Mayfly 0.006 101 (15) 38 — 1 0.0300 1.0305Mayfly (stream) 0.006 120 (18) 80 — 1 0.0305 1.0310

aSee references in Supplemental Data A.bStandard deviation in parentheses.mb¼ background mortality; t¼ age at reproduction; b¼ clutch size (female offspring); g¼ time between broods; no.¼ number of broods; r and l¼ calculatedpopulation growth rates. See references in Supplemental Data A.

Recovery of four aquatic invertebrate species Environ Toxicol Chem 33, 2014 1519

Fully parameterized models were available for A. aquaticus,G. pulex, and C. dipterum, whereas data from Chaoborusobscuripeswere used forC. riparius ([32,35]; N. Diepens, 2010,Master’s thesis, Wageningen University, The Netherlands)(Table 3).

Logistic model

We assumed that populations were regulated by density-dependent mortality, according to Equation 1. We also assumeda nonseasonal environment, with populations having a stable agestructure. Under this condition, and also when spatial processescan be ignored (fast mixing and/or no heterogeneity), populationdynamics in the IBMs can be captured by the nonspatial logisticgrowth equation

dN

dtðb� mb � mDDNÞN ¼ r 1� mDD

rN

� �N ð7Þ

where b represents the birth rate and r, the intrinsic rate ofincrease, equals birth minus death rate (b –mb). The dynamics ofthe logistic equation are well understood. It has an explicitsolution given by

Nt ¼ N0

1� N0mDDr

� �e�rt þ N0mDD

r

ð8Þ

implying that the population will always grow asymptotically toits equilibrium density �N ¼ r

mDD.

The value of r can be derived from the geometric growth ratel. We calculated l using the discrete version of the Euler–Lotkaequation [36] with age-class size of 1 d

1 ¼Xw

x¼1ðmxlxl

�xÞ ð9Þ

wheremx is the number of female offspring produced by a femaleof age class x, lx is the probability of surviving from birth to ageclass x, and w is the lifespan of the females (d). With pulsedreproduction and a single brood with (female) clutch-size b, mx

will only be non-0 at age of first reproduction (t). Withm being aconstant background mortality, Equation 9 simplifies to

1 ¼ bð1� mÞtl�t and thusl ¼ b1=tð1� mÞ ð10Þ

For Gammarus, with up to 5 broods (n¼ 5) and a time betweenbroods of g, we summed the terms for all broods to solve theequation

1 ¼Xn

i¼1bð1� mÞtþði�1Þgl�ðtþði�1ÞgÞ ð11Þ

For all 4 species, we thus obtained estimates of growth rate r (¼ln(l)) using the coefficients t, mb, b, and n, defined for the IBM(Table 1).

Recovery in the logistic model

With Equation 8, exact recovery times can be calculated for apopulation at equilibrium (N¼ �N), exposed to a stress factorreducing population size. After reduction to a surviving fraction d,the time required to grow back to a fractiona (e.g., 0.95) of originalpopulation size just before the stress event is found by solvingEquation 12 for t with N0 ¼ d�N and with Nt ¼ a�N, resulting in

T ¼ 1rlnað1� dÞdð1� aÞ ð12Þ

The intensity of density dependence, defined by themagnitude of mDD, affects the effective growth rate of thepopulation (Equation 7) and the equilibrium population size �N(Equation 8), but it does not influence the time to recovery(Equation 12). Because this seemed counterintuitive, we testedfor the conditions under which this statement also holds for theIBM with similar density-dependent mortality (see Supplemen-tal Data C). If it does, an implication is that we can use mDD as ascaling factor in IBMs to lower population size to a convenientlevel without affecting the calculated time to recovery.

Table 2. Movement and dispersal processes relevant for each species in ditch(D), stream (S), and pond (P), and their coefficientsa

Asellusaquaticus

Chironomusriparius

Gammaruspulex Mayfly

DitchDaily movement X XAdult dispersal X X

StreamDaily movement X XDownstream drift X XAdult dispersal XUpstream adult

dispersalX

PondDaily movement X XAdult dispersal X X

CoefficientsDrift probability

(S) (�)0.25 1

Drift-distance (S) (m) 10 17.5Kernel, mean (DS) (m) 0 0 0 200 (S),

0 (D)Kernel, sd (DS) (m) 4.4 2.2 23.4 20RW-steps (P) (�) 28 10 100

aSee references in Supplemental Data A.

Table 3. Concentration-effect (4-d EC50 and Slope) and toxicokinetic and toxicodynamic parameters of the freshwater arthropod species for the insecticidechlorpyrifosa

Species EC50 (mg/L) Slope kin (mL/mg� d) kout (1/d) kk (mg/nmol� d) kr (1/d) Threshold

Asellus aquaticus 3.421 3.0 0.596 0.185 7072 494 0.0481Gammarus pulex 0.225 22.3 0.747 0.450 47 0.169 0.022Chironomus riparius 0.176 1.94Cloeon dipterum 0.313 3.56 0.349 0.196 228 1.331 1.4 E–9Chaoborus obscuripes 0.318 0.131 88 0.518 3.3 E–8

aFrom Rubach et al. [32], Hooftman et al. [33], Van Wijngaarden et al. [34], and Ashauer et al. [35].EC50¼median effective concentration; kin¼ uptake rate constant; kout¼ elimination rate constant; kk¼ killing rate constant; kr¼ damage recovery/repair rateconstant.


Equations 8 and 12 thus describe the response of a well-mixed system to a single stress event. The actual stress (pesticidemortality) does not need to be spatially uniform; as long as itoccurs in a more or less synchronized fashion for all locations, aspatially averaged value can be derived.Whether the assumptionof perfect mixing holds depends on the combination of speciesmovement/dispersal attributes and the system’s spatial dimen-sions. For realistic systems, the actual situation of the populationwill be in between the extremes of complete mixing and nomixing at all. Also, the latter extreme can be explored with thesimple model of Equations 8 and 12. As an example, assume thatsA represents the fraction of the total system area where thepopulation density is reduced to fraction DA of equilibriumdensity, whereas density is reduced to dB in the rest of the system(area B with fraction 1–sA of total area). The time to recovery tofraction a for the total system is then found by (numerically)solving for t

a ¼ SAdA

ð1� dAÞe�rt þ dA

� �

þ ð1� SAÞ dB

ð1� dBÞe�rt þ dB

� � ð13Þ

When area B is not exposed at all, dB¼ 1, and recovery time forthe whole system becomes

T ¼ 1rlnða� ð1� sAÞÞð1� dAÞ

dAð1� aÞ ð14Þ

Calculated recovery time thus depends in the first place on theimpact in exposed area A; however, as a comparison withEquation 12 shows, it will be shorter than predicted for area Aalone, simply because a larger system is considered, including anarea with lower or no exposure. Recovering to a lower effectivefraction of control population size a-(1-sA) is sufficient.

Exposure scenarios

As ERCs [37], we used PECs of chlorpyrifos, originatingfrom TOXSWA [2] simulations based on FOCUS [1] scenarios.For pond, ditch, and stream systems, and for 4 crop scenarios,these data provided concentration dynamics of chlorpyrifos,all in mg/L, for all (1-m2) cells of the habitat (details inSupplemental Data A). The scenarios considered representedworst-case situations under southern European conditions (butsee Knabel et al. [38] for a critique). The crops were stone fruit,wine grapes, brassicas, and citrus fruit; their main use in thepresent study is to illustrate potential variability in results.

Full exposure patterns were quite similar for all FOCUSscenarios, showing inmost cases a single peak concentration thatlocally decreased slowly to fast (depending on water move-ment), and travelled downstream fast (stream), slowly (ditch), ornot at all (pond). Maximum chlorpyrifos peak concentrationswere approximately 1.5mg L�1 to 1.7mg L�1 in stream andditch. In the pond, maximum peak concentrations weresubstantially lower, approximately 0.3mg L�1. Fast transportof peak concentrations in the stream resulted in short localduration of peaks and little decrease of chlorpyrifos concentra-tion in space. For the ditch, with slower transport, there was aslower local concentration decrease in time together with aconsiderable decay going downstream (Figure 1). Exposure inthe pondwas by definition spatially uniform. Because of absenceof transport, pond scenarios had the slowest concentrationdecrease in time. A characterization of the spatial scenarios by

the spatiotemporal exposure pattern they resulted in is given inTable 4.

The IBM-TDMused the full exposure pattern.With the IBM-CE some of the spatiotemporal differentiation was conserved,because it used peak height and timing for each locationseparately. The duration of peaks did not play a role with IBM-CE, because only the maximum (peak) value was used. Thus, forIBM-CE, the exposure patterns in stream and pond wereeffectively spatially uniform. For the logistic model, a system-averaged mortality was calculated. We applied the concentra-tion–effect relationship for each species on the local peak valueand used the local mortality rates obtained (Figure 1) to calculatea system-wide average mortality. For the stream system, withpeaks occurring everywhere on the same day, this estimatewould be precise; for the ditch system, with peak valuespotentially on different days, its value would be anapproximation.

Time to recovery

The outputs from the treatment scenarios were comparedwith the control, using the approach described in Galic et al. [9].For the analysis of recovery times, we used 20 replicatesimulations for each of the treatments and the control. Wecompared daily abundances in controls and exposed populationsand considered an exposed population recovered if itsabundance reached 95% of the abundance of the controlpopulation, so Ratio(t)¼Exp(t)/Con(t)� 0.95. To remove the

µµ µµ

Figure 1. Spatial heterogeneity in the highest peak concentration (inmg/L) ofchlorpyrifos for the ditch (predicted environmental concentration [PEC]) andthe translation of peak concentration into a mortality gradient, using theconcentration–effect relationships for each species. ASE¼Asellus aquaticus;GAM¼Gammarus pulex; CHI¼Chironomus riparius; MAY¼mayfly.[Color figure can be viewed in the online issue which is available atwileyonlinelibrary.com]

Table 4. Spatiotemporal characterization of exposure scenariosa

Temporal pattern

Spatial pattern

Uniform Heterogeneous

Fast local decay StreamIntermediate DitchSlow local decay Pond

aAlmost all exposure patterns had a single peak concentration. Only ditchscenarios led to spatially heterogeneous exposure. Pond scenarios had bydefinition uniform exposure.


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impact of day-to-day stochastic fluctuations, we definedrecovery as achieved when the moving average (with a windowof 11 d) of Ratio(t) exceeded 0.95. Daily population abundancesof each of the 20 treated replicates were compared with each ofthe 20 control replicates, yielding 400 estimations of recoverytimes. Recovery times are relative to the day of the peakconcentration for both CE and TDM models. To filter outscenarios for which the maximum impact did not reduce theexposed population to below 0.95 of control populationabundance, we considered only the scenarios in which theminimum of the mean ratio for all compared runs, defined asRatio ðtÞ ¼ 1

400

P20i

P20j ExpiðtÞ=ConjðtÞ; was lower than 1

minus the mean (over time) of the standard deviation amongthe control runs, mean(sd[Coni(t)/Conj(t)]). Recovery could, bydefinition, occur only after the day with the maximum impact(lowest Ratio ðtÞ).Simulations and model analysis

We investigated the following aspects: First, we calculatedfor all species the population growth rate r, from the vital ratesdefined for the IBM, using the Euler–Lotka equations (Equations9–11). Second, for a hypothetical spatially uniform stress eventwe tested whether population recovery dynamics were similarfor the logistic model and the IBM-CE. The stress event wasdefined as a reduction in population size to approximately 90%of equilibrium density and applied in a pond system where thenecessary spatial condition (fast mixing) is likely to be met.Third, for all scenarios and spatial setups we compared recoverytimes predicted by the logistic model with the results obtainedby the IBM-CE. The differences would be the result of spatialprocesses and would depend on the chosen spatial scale inrelation to the movement and dispersal attributes of the species.For the pond, with its small dimensions and uniform exposurepattern, only minimal differences were expected. Fourth, for allscenarios we compared recovery times for the IBM-CE based onpeak exposure with recovery times for the IBM-TDM based onthe full exposure pattern. The differences were expected tooriginate from the TDM’s ability to deal with time-varyingexposure. For the scenarios in which peak and full exposurepatterns were similar (stream), few differences in predictedrecovery times were expected. For ditch and pond, concentrationdecay was slow, and therefore a larger impact and longerrecovery times were expected from TDM.

RESULTS

Life history, population growth rate, and time to recovery

Growth rates r, calculated with the Euler–Lotka equations(Equations 9–11), decreased from Chironomus, Asellus, andmayfly to Gammarus (Table 1). Recovery times (after identicalstress) are thus predicted (Equation 12) to increase in the sameorder. Equation 12 summarizes the relationship betweenpopulation growth rate r, intensity of the stress, and recoverytimes. Recovery time will increase steeply with lowered r andwill decrease steeply with lower induced mortality.

Exposure and recovery times: Logistic versus IBM-CE

Pond simulations of dynamics after a generic stress, whichresulted in a reduction to approximately 10% of equilibriumpopulation size, showed that the behavior of the IBM-CE isdescribed very well by Equation 8 (Figure 2). Small differencesare visible, however, including dampened fast (Chironomus)or slow (mayfly) oscillations. For the mayfly, the fit is not asgood.

None of the simulations with spatiotemporal exposure fromthe FOCUS scenarios resulted in significant impacts on Aselluspopulations. This was expected, as Asellus had a high EC50(3.43mg/L; Table 3), more than twice as high as the highest peakvalue. For the other species, the EC50 values were much lower(lowest forChironomus, followed byGammarus) and within therange of experienced concentrations.

For the pond and stream systems, the recovery timesobserved in IBM-CE simulations were comparable to the timespredicted by Equation 12 (Figure 3). For both systems, spatialprocesses thus did not play a role, most likely because there wasno spatial pattern in exposure (uniform exposure in the pond,

Figure 2. Time series of the ratio of control population/exposed populationsize for Asellus aquaticus, Gammarus pulex, Chironomus riparius, andmayfly from the individual-based model (IBM) and the logistic model after a90% reduction in population size. IBM results were averaged over 3 runs.[Color figure can be viewed in the online issue which is available atwileyonlinelibrary.com]



almost uniform in the stream) in either system. In the pondscenarios, peak concentrations were relatively low with impactsonly on Gammarus and mayfly (Figure 3). In the streamscenarios peak concentrations were relatively high, leading toextinction of Chironomus, Gammarus, and mayfly for mostscenarios. With additional drift mitigation leading to a reductionof 80% in PEC, extinction of Chironomus and mayfly no longeroccurred (Figure 3).

For the ditch scenarios observed recovery times were muchlonger than predicted by the logistic model for the mayfly and inparticular for Chironomus (Figure 3). For Gammarus, however,they were as predicted. Space–time plots (Figure 4) showed thatlocal extinctions (empty cells) occurred for all 3 species.

Exposure and recovery times: IBM-CE versus IBM-TDM

For the ditch scenarios, the IBM-TDM predicted largerimpact and longer recovery times for Gammarus and, to a lesserextent, for the mayfly (Figure 5). For Chironomus, however, theopposite occurred, and the IMB-TDM showed much shorterrecovery times.

For the pond scenario, with a slower decay of concentrationswith time (Table 4), much longer recovery times were foundwith IBM-TDM for Gammarus and mayfly (Figure 5). Peakconcentrations were almost 1 order of magnitude lower than forditch and stream; therefore, no (local) extinctions occurred. For

scenarios with lower peak values, the IBM-CE predicted noimpact, while the IBM-TDM predicted long recovery times.

For the stream scenario all IBM-CE populations went extinct,whereas the IBM-TDM populations showed recovery, quicklyfor Chironomus and slowly forGammarus and the mayfly. Withadditional mitigation (exposure reduced by 80%; Figure 5)Gammarus still went extinct with IBM-CE, while Chironomusand the mayfly recovered more quickly with IBM-TDM.

DISCUSSION AND CONCLUSIONS

Our overarching goal in the present study was to betterunderstand the behavior of a complexmodel by comparing it withsimpler models. In particular, we wanted to understand how 2main sources of complexity, the spatial processes occurring in thepopulations and time-variable spatially heterogeneous exposuredetermining the mortality risk of mobile individuals, interacted indetermining recovery at the population level. In addition, wewanted to evaluate choices made in the IBMs, related to intensityof density dependence and the spatial dimensions of the systems.

Logistic versus IBM-CE

For the hypothetical stress event (90% reduction) acting onthe pond population, the behavior of the IBM is approximatedvery well by the logistic model (Figure 2). Small deviations are

Figure 3. Recovery times (median) calculated from the individual-based model, concentration–effect relationship (IBM-CE) simulations versus the recoverytimes obtained from the logistic model for ditch, pond, and stream. Data points are for the 4 crops (3 in pond). ASE¼Asellus aquaticus; GAM¼Gammarus pulex;CHI¼Chironomus riparius; MAY¼mayfly. [Color figure can be viewed in the online issue which is available at wileyonlinelibrary.com]



the result of the inherent stochasticity of the IBM and, likely, lifehistory details leading to dampened fast (Chironomus) or slow(mayfly) oscillations. The fit is not as good only for the mayfly,because density dependence is based on local densities in theIBM, and densities become more spatially heterogeneous atlower densities as a result of clumped reproduction (seeSupplemental Data C). With density dependence defined asacting on the global (system-averaged) density, the recoverydynamics are predicted very well for all species by the logisticmodel.

For the spatiotemporal exposure scenarios, the comparison oflogistic model and IBM-CE results shows that there areconditions under which the spatial processes in the IBM donot affect the recovery dynamics. When exposure is spatiallyuniform, as in the pond and, approximately, in the streamscenarios, the population is affected everywhere to the sameextent, and recovery will not be influenced by movement anddispersal [9]. And when exposure is far from uniform, butindividuals are sufficiently mobile to quickly blur any densitygradients resulting from the heterogeneous exposure, as observedfor Gammarus in the ditch (Figure 3) [9]. The latter condition

implies that when species do not move on a daily basis, recoverywill take longer than predicted by the logistic model, as we see forthemayfly and in particular forChironomus (Figure 3) [28].Withall 3 species, the higher exposure in the first stretch of the ditchresults in 100%mortality and thus local extinction (Figure 1) overa stretch that is the longest for Gammarus. For Chironomus andto a lesser extent the mayfly, this local extinction results in acolonization bottleneck (Figure 4) and therefore slow recovery.Under these conditions, recovery time becomes dominatedentirely by the species’ movement attributes instead of by thespecies’ growth rate r (Chironomus has by far the highest r;Table 1). The gradual recolonization of an empty stretch alsoexplains the approximately linear return to control densityobserved for Chironomus (see Supplemental Data B, exposed/control plots).

CE versus TDM

For the stream, the full and the peak exposure patterns werevery similar. Thus, the IBM-TDM and IBM-CE were expectedto lead to identical results. We found that populations go extinctwith the IBM-CE; and when we compared the results for the

Figure 4. Time–space plots of the population density (indm�2) in ditch simulation with the individual-based model, concentration–effect relationship (IBM-CE)with x-axis¼ space (m) and y-axis¼ time (each row of pixels represents 1 d; tick-marks are 100 d apart; time increases from top to bottom). Figure panels showGammarus pulex (top left), Chironomus riparius (top right), and mayfly (bottom left). [Color figure can be viewed in the online issue which is available atwileyonlinelibrary.com]



scenario with additional mitigation (Figure 5), recovery timeswere shorter for the IBM-TDM. The explanation is most likelyrelated to the EC50 and other coefficients of the CE relationshipbeing based on 4 d of exposure. In the CEmodel, a concentrationpeak of 1-d duration will result in the mortality that wasmeasured experimentally after 4 d of exposure. For the defaultscenario, this means that peak concentrations are above EC50and lead to 100% mortality in the whole stream. While theexposure patterns are similar, the slightly more worst-caseapproach takenwith the IBM-CE can thus lead to a very differentoutcome (the opposite was found by Galic et al. [18]).

In the pond, the expected longer recovery times for the IBM-TDM are indeed observed. Although the impact of the peakvalues might have been overestimated for the IBM-CE (seeabove), recovery times are much longer for the IBM-TDMbecause it takes into account all days with exposure, before andafter the peak (Figure 5) [25]. In our pond scenarios, none of theexposure patterns led to extinction. For other combinations ofexposure patterns and species coefficients, it is quite possiblethat extinction would be predicted with the IBM-TDM, whereaswith the IBM-CE acting only on peak values, the populationwould be predicted to persist.

In the ditch, exposure is muchmore heterogeneous (Figure 1),with a steep spatial gradient but a faster decay in time comparedwith the pond. The impact of peak values is again larger with the

IBM-CE and results in local extinction for the 3 species(Figure 4). For Chironomus the colonization bottleneck leads toslow recovery (Figure 5). ForGammarus, there is no colonizationbottleneck, because it mixes much faster, but the lower impact ofpeak concentrations with the TDM is compensated for by itstaking into account the decaying concentrations [15], resulting inslightly longer recovery times. For the mayfly, we observe bothtypes of outcomes: for some crop scenarios, a considerablylonger recovery time for the IBM-CE (local extinction withrelatively fast recolonization), and for other crop scenarios,longer recovery times for the IBM-TDM (less or no localextinctions but impact of exposure continuing after the peakday).

If the CE relationship were to be based on 1-d instead of 4-dexposure experiments, the single difference expected in outcomebetween the 2 approaches would occur because of the TDMtaking into account all time-varying exposure. The TDMapproach would thus predict larger impact, but the extent towhich this affects recovery is difficult to determine when aspatial gradient is combined with mobile individuals. Littlemobility may lead to local extinctions and a colonizationbottleneck (the Chironomus-ditch case in the present study);high mobility may lead to a spatially averaged-out exposure, fewextinctions, and no colonization bottleneck at all (the Gamma-rus-ditch case in the present study).

Figure 5. Median recovery time (d) for the individual-based model, threshold damage (IBM-TDM; y-axis) against median recovery time for the IBM,concentration–effect relationship (IBM-CE; x-axis) for ditch, pond, and stream. Data points are for the different crop scenarios (Supplemental Data B).ASE¼Asellus aquaticus; GAM¼Gammarus pulex; CHI¼Chironomus riparius; MAY¼mayfly. [Color figure can be viewed in the online issue which isavailable at wileyonlinelibrary.com]



Density dependence

The logistic model suggested that there would be no influenceof the intensity of density dependence on recovery times. Weobserved the same in the IBM, when density dependence wasdefined to act on global (system-averaged) density (seeSupplemental Data C). When density dependence acted onlocal density, as is typical for the IBM formalism, the recoverydynamics in the IBM could be identical to the dynamicspredicted by the logistic model if no mechanisms had beenincorporated that created persisting spatial heterogeneity inabundance or if model coefficients stayed outside the range ofvalues for which these mechanisms could create these patterns.In the IBM, clumped reproduction (all offspring located in thesame cell) combined with immobility of instars constituted sucha mechanism. In general, it may not be clear whether a modelincorporates such a mechanism and whether coefficients are inthe sensitive range. Therefore, the safest approach seems to be toalways test for impact of density dependence on recoverydynamics when density dependence acts through local density. Itmay still be possible to use the intensity of density dependence toscale densities in the IBM to (computationally) feasible levels;however, the validity of the underlying assumption that thisleaves recovery times unaffected should always be ascertained.

Other studies [39–42] investigating the role of densitydependence in population-level risk assessment focused mainlyon potential differences in impact on vital rates of a chemical atdifferent population densities. In our models, there was no suchinteraction defined between impact (mortality) and density.Density dependence in the IBM and logistic models acted as astabilizing mechanism, leading to exact compensation (return toequilibrium density) after a stress event. Different mechanismsof density dependence (e.g., competition vs predation orimmediate vs delayed effects) may lead to different dynamicsafter a population reduction, and thus to different recoverytimes [41]. For risk assessment, therefore, it will be important toobtain information on the nature of the density dependencemechanism in the population modeled. In many cases, however,this information may be absent.

Spatial dimensions

Several of the aspects discussed above point to theimportance of the choice of spatial dimensions of the systemunder consideration. As we showed (Equation 14), recoverytimewill decrease simply by choosing a larger area over which tocalculate it, when larger dimensions imply the incorporation of agreater area of less-exposed or unexposed habitat, even if thereare no functional links (dispersal, movement) between the highlyexposed and less-exposed parts. This phenomenon will alwaysplay a role when less-exposed habitat surrounds highly exposedhabitat and should be taken into account when setting systemboundaries [43]. When a highly exposed area and itssurrounding landscape are strongly connected by dispersal,the system considered should include some of the surroundinglandscape; otherwise, a potential impact on the population in thesurrounding landscape, depletion [44], will go unnoticed.

With the insights obtained, we may predict the impact ofchoosing different spatial dimensions under the FOCUSscenarios investigated and to a limited extent extrapolate tolandscape scale risk assessment [45] for species living in acontinuous habitat arrangement (unlike the classical metapop-ulation). For the pond, with uniform exposure, larger dimensionswill not affect the outcome. The assumption of uniform exposuremay no longer be appropriate though. For the stream, increasing

the length considered will not change the results either, becauseconcentration barely decays along the stream. On the landscapescale, however, a stream is likely to have tributaries that have notbeen exposed and thus may contribute to recovery by acting assources of colonizers (in case of extinction in the main stream) orby just boosting population size through movement anddispersal [46,47]. The quantitative impact will very muchdepend on the species movement and dispersal attributes. Ourresults indicate that, in general, the more that such tributaries areincluded in the system considered, the more the recovery timewill decrease.

For the ditch, increasing the length implies inclusion of moreless-exposed habitat, as all concentrations decrease considerablyfollowing the ditch downstream. Thus, considering a longerditch will lead to shorter recovery times. On a landscape scale,the presence of unexposed tributaries will have an impact onlywhen they are connected to highly exposed parts, (i.e., next to thefield on which the pesticide is applied) [45].

Levels of complexity

The present study shows that the understanding of thebehavior of a complex model can be greatly enhanced bycontrasting it to the behavior of simpler models. If thesemodels simplify in a single main aspect, the comparisonmakes immediately clear to what extent this aspect deter-mined the results. For example, our comparison of thespatially explicit IBM and the mean field logistic modelindicated when spatial processes were relevant to recoveryand when they were not. Our approach was a multimodel onein another sense as well, considering 4 species with differentlife histories. Explaining the differences between modelresults required consideration of the traits of the triangle:species (movement/dispersal attributes, sensitivity to thepesticide, per capita growth rate r), exposure (spatiotemporalpattern), and spatial structure (dimensions, shape). Taking amultimodel approach helped in defining essential traits and inclarifying the subtle differences in their definitions when usedin different models (e.g., the spatiotemporal exposure patternas it was used in the IBM-TDM, IBM-CE, and logisticmodels). Delving into the actual mechanisms behind thedifferences in outcome between models of different com-plexity and between the 4 species spawned further insights,indicating interaction between, for example, spatial explicit-ness and density dependence.

Our most complex model, the IBM-TDM, excludedsources of complexity commonly encountered in IBMs [5]:seasonality, detailed individual growth and development, andcomplex density-dependent feedback mechanisms. Whenprecision and realism are valued most in risk assessment,even the IBM-TDM could be considered too simple. Ouranalyses, however, show that the outcome in terms of recoverycould have been predicted by or could have been derived fromeven simpler models for many of the exposure scenarios. Whenexposure is effectively spatially uniform or when theorganisms are relatively mobile on the scale of system andon a daily base, spatially explicit approaches may not berequired. The more spiked the exposure in time becomes, themore the outcome of TDM and CE models coincide. Thus,defining the minimum level of model complexity that is neededrequires careful consideration of the combination of speciestraits, exposure patterns, and spatial settings. Our analysisshows that an approach replacing or combining complex withsimple models can lead to clear benefits in terms of providinggeneral insights and understanding.


SUPPLEMENTAL DATA

Supplemental Data A. (6.7 MB DOC).Supplemental Data B. (5.2 MB DOC).Supplemental Data C. (453 KB DOC).

Acknowledgment—The present study was financially supported by the DutchMinistry of Economic Affairs (project BO-20-002-001) and by DowAgroSciences. The quality of the manuscript benefited greatly from thecomments of an anonymous reviewer.

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