The extrapolation problem and how population modeling can help

Authors

  • Valery E. Forbes,

    Corresponding author
    1. Centre for Integrated Population Ecology, Department of Environmental, Social and Spatial Change, Roskilde University, DK-4000, Roskilde, Denmark
    • Centre for Integrated Population Ecology, Department of Environmental, Social and Spatial Change, Roskilde University, DK-4000, Roskilde, Denmark
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  • Peter Calow,

    1. Centre for Integrated Population Ecology, Department of Environmental, Social and Spatial Change, Roskilde University, DK-4000, Roskilde, Denmark
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  • Richard M. Sibly

    1. Centre for Integrated Population Ecology, Department of Environmental, Social and Spatial Change, Roskilde University, DK-4000, Roskilde, Denmark
    2. School of Biological Sciences, University of Reading, Whiteknights, RG6 6AJ, Reading, United Kingdom
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  • Published on the Web 4/24/2008.

Abstract

We argue that population modeling can add value to ecological risk assessment by reducing uncertainty when extrapolating from ecotoxicological observations to relevant ecological effects. We review other methods of extrapolation, ranging from application factors to species sensitivity distributions to suborganismal (biomarker and “-omics”) responses to quantitative structure–activity relationships and model ecosystems, drawing attention to the limitations of each. We suggest a simple classification of population models and critically examine each model in an extrapolation context. We conclude that population models have the potential for adding value to ecological risk assessment by incorporating better understanding of the links between individual responses and population size and structure and by incorporating greater levels of ecological complexity. A number of issues, however, need to be addressed before such models are likely to become more widely used. In a science context, these involve challenges in parameterization, questions about appropriate levels of complexity, issues concerning how specific or general the models need to be, and the extent to which interactions through competition and trophic relationships can be easily incorporated.

INTRODUCTION

Ecological risk assessment involves quantifying the likelihood that chemicals and other stressors have adverse impacts on ecological systems. Hence, in a chemical context, ecological risk assessment generally involves relating appropriate measures of chemical exposure to relevant measures of ecological impact. Both exposure and effects assessment involve uncertainties, and various methods for dealing with these uncertainties have been incorporated into regulatory paradigms [1]. The term extrapolation generally is used to describe the process by which the information available for a chemical is translated into the kind of information that is needed to assess risk. With few exceptions (e.g., endangered species), ecologically relevant impacts involve populations and the communities and ecosystems of which they are a part. In the present paper, we consider different approaches that have been used for extrapolation, discuss their strengths and weaknesses, and propose a way forward. In our view, one of the most important and challenging aspects is extrapolating between individual-level responses and population-level impacts. Unless these kinds of extrapolations are based on sound science, they can be expected to lead to both false negatives and false positives. Our conclusion is that too much emphasis is placed on individual-level responses and that the critical extrapolation from the individual level to ecologically relevant impacts needs attention. This is because even if effects on individual survival, reproduction, and growth can be measured or predicted, the relationships between these and population dynamics are complex and nonlinear [2]. Hence, we argue that increased efforts to develop population modeling approaches for effectively extrapolating from measurable test endpoints to ecologically relevant impacts can reduce uncertainty and increase confidence in ecological risk assessments [3]. A number of issues need to be resolved, however, before such models achieve standard use in risk assessment. We provide suggestions for resolving these critical issues.

WHY CURRENT APPROACHES TO EXTRAPOLATION ARE NOT SATISFACTORY

Application factors

Application factors (sometimes called uncertainty or safety factors) are the most widely used approach for extrapolating toxicity test data to likely ecological impacts. In this approach, measured effects data (typically 50% lethal concentrations [LC50s] or no-observed-effect concentrations [NOECs]) are divided by some factor to add an additional margin of safety for predicting a likely no-ecological-effect level. Typically, the more test data one has and the closer those data are to field conditions, the lower the factor that is applied. For example, the technical guidance document used for risk assessment of industrial chemicals in the European Union [4] has employed the factors shown in Table 1. A similar philosophy is applied in North America [5].

Although application factors are easy to apply, they suffer a number of important disadvantages [5]. The most serious criticism is that they are rather arbitrary, are not based on any firm scientific understanding, and therefore, can only provide rough, order-of-magnitude guesstimates. Second, they generally are applied to the lowest of the available measured effect endpoints. This means that as more data are gathered for a chemical, giving in principle a better estimate of likely effects, these data will only influence the risk assessment if they are lower than the values already in the data set. An exception is when the data set is increased from one to three chronic NOECs and these three are from three different trophic groups; in this case, the application factor is reduced by an order of magnitude (Table 1). If one started with the standard base set of acute toxicity data (e.g., alga, Daphnia, and fish), however, and found that Daphnia was the most sensitive of the species for which test data were available, the application factor would be applied to the LC50 for Daphnia. If one then collected additional LC50 data for 100 species, all of which were less sensitive than Daphnia, these data would have no bearing on the effects assessment. If just one of them were found to be more sensitive than Daphnia, however, the effects assessment would be based on this single most sensitive species.

Table Table 1.. Application factors used in the technical guidance documents for existing and new substances legislation within the European Uniona
 Application factor
  1. a This table is a simplified version of that presented in the technical guidance documents [4], after Forbes and Calow [6]. L(E)C50 = concentration resulting in lethality or some other effect in 50% of the test population; NOEC = no-observed effect concentration.

At least one acute L(E)C50 from each of three trophic levels1,000
One chronic NOEC100
At least three chronic NOECs from each of three trophic levels10
Field data or model ecosystemsReviewed on a case-by-case basis

Finally, the kinds of uncertainty accounted for by the application factors used in ecological risk assessment have not been made explicit in the regulatory guidance, which makes their accuracy difficult to assess. Forbes and Calow [6] determined that the application factor intended to extrapolate from acute to chronic toxicity (ACR) in the European Union technical guidance document (and also commonly used in the United States by the Office of Pollution Prevention and Toxics [7]) is 10. In their reanalysis of data from Roex et al. [8] on 107 chemical and species combinations, Forbes and Calow [6] found that on average, the ACR was 9.1, which is very close to the value used in the technical guidance document. Unfortunately, the range in the ACR values was very large—between 0.79 and 5,495. In addition, 36% of the ACR values were greater than 10, 9% were greater than 100, and 5% were greater than 1,000. Clearly, it is not satisfactory to get the extrapolation right on average—that is, by underestimating it for some chemicals and overestimating it for others. The analyses of Roex et al. [8] and of Forbes and Calow [6] also showed that interspecies variability in both acute and chronic toxicity varies widely among chemicals and that the species that is most/least sensitive to acute exposure is not necessarily the species that is most/least sensitive to chronic exposure. These results are not at all surprising and can be explained by differences in toxicant mode of action and in species' biology, but they clearly demonstrate that using standard factors that are multiples of 10 to extrapolate available toxicity data to likely ecological impacts is difficult to justify on scientific grounds.

Statistical extrapolation among species

Partly in recognition of the weaknesses of the application factor approach, the species sensitivity distribution (SSD) approach was developed to extrapolate single-species toxicity data to the community/ecosystem level. Although they have the important advantage over the application factor approach of using all available toxicity data, SSDs suffer from several disadvantages in terms of the assumptions involved in generating them and in how they are interpreted. These issues have been dealt with in detail by Forbes and Calow [9] and are only briefly mentioned here. First, in our view, the most serious problem with SSDs is that they rarely, if ever, are composed of species from an actual community or ecosystem but often are interpreted as if they are (i.e., that the hazard concentration [HC] corresponding to the xth percentile of the SSD is protective for 1 — x% of the species in a given ecosystem [10]). Forbes and Calow [9] demonstrated that generating SSDs with more realistic trophic group distributions than those normally used to construct them could either increase or decrease the resulting HCx. Second, the relationship between the endpoints used as input data to the SSDs and ecologically relevant impacts has both uncertainty and variability. In other words, SSDs implicitly assume that toxicity measured by standard individual-level endpoints is equivalent to population-level impacts (but see below). Often, SSDs are constructed from a mixture of different individual-level end-points for the different species going into them. Thus, we are forced to ask, “What is the risk for a particular ecosystem if the NOECs (for reproduction, survival, and/or growth) for 5% of the species available in existing toxicity databases are exceeded?” This raises questions about the ecological relevance of NOECs [11] as well as the biases in available toxicity databases. Some authors have tried to address these issues by comparing calculated SSD percentiles for particular chemicals with the responses measured in mesocosm systems, and in general, the available results indicate that HC5s estimated from SSDs are lower than concentrations at which impacts are detectable in intact model ecosystems [12].

Extrapolation from suborganismal to higher-level responses

A variety of physiological, biochemical, histological, and molecular responses (so-called biomarkers) has been investigated during the last 20 to 25 years for use as indicators of either exposure to or effects of toxic chemicals [13]. Earlier literature is dominated by publications dealing with single biomarkers, whereas more recent papers often include suites of biomarkers. The main advantage of such measures is that they often can be performed on a small sample of body fluid or tissue and, thus, are nondestructive. This can be critical for sampling long-lived, rare, or endangered species. Another advantage is that such suborganismal responses can potentially provide insights regarding specific mechanisms of action by toxic chemicals. Advances in molecular biology and gene chip technology are making it possible to extend the biomarker approach to the examination of the up-regulation and down-regulation of many different genes (genomics) at the same time. Similar methods are used to quantify the expression of specific proteins (proteomics) or other metabolic products (me-tabolomics). In carefully designed experimental settings, such approaches may provide a mechanistic understanding of how chemicals affect organisms. Typically, these “-omics” approaches are designed to investigate particular metabolic pathways of interest. Although this is a sensible approach, it does not necessarily ensure that observed up- or down-regulation correlates with observed responses at the whole-organism level.

In the context of extrapolation, it is essential that suborganismal responses be consistently linked to specific exposure levels, be predictive of ecologically relevant effects, or both. A fundamental weakness in the biomarker approach to extrapolation has been that the links between the suborganismal level and exposure to or effects of chemicals have been largely empirical, and mechanistic models to link suborganismal to whole-organism or higher-level responses generally have been lacking [14]. Correlations between biomarker response and either toxicant body burden or whole-organism responses sometimes are statistically significant but often rather weak and/or vary among exposure scenarios and species. This should not be surprising given that such empirical models ignore the vast majority of processes taking place in organisms that contribute to determining what happens at the whole-organism level.

Table Table 2.. Overview of the most common methods for extrapolation used in ecological risk assessmenta
Type of extrapolationFromToForm of relationship
  1. a QSARs = quantitative structure-activity relationships; SSD = species sensitivity distributions.

Application factorsIndividual-level effects in test speciesIndividual-level effects in other speciesDivide by fixed factor
 Individual-level acute effectsIndividual-level chronic effects 
 Laboratory effectsField effects 
QSARsChemical structureIndividual-level effectsEmpirical
Biomarkers and -omicsSuborganismal effectsLargely individual-level effectsEmpirical
SSDsIndividual-level effectsMultispecies effectsEmpirical
Model ecosystemsPopulation-level effects, ecosystem structure, ecosystem processesNatural ecosystemsDivide by (small) fixed factor, or treat as equivalent
Population modelsIndividual-level effectsPopulation-level effectsMechanistic

Although the eventual aim of -omics approaches is mechanistic understanding, the relationship between the up- and down-regulation of specific suites of genes and higher-level responses generally is correlative at present. Unless robust causative links can be established between the gene regulatory level and whole-organism performance, it would be inappropriate to use such measures for risk assessment. Even if the responses of individual genes could be extrapolated confidently to the responses of whole organisms, the problem of extrapolating to ecologically relevant impacts (i.e., on populations and the ecosystems of which they are a part) remains.

The problems in extrapolating from “-omics” responses are no different than those involved in extrapolating from other biomarkers: At the very least, a mechanistic understanding of the links with individual-level endpoints (survival, reproduction, and development) is needed. In most microarrays, only a subset of the organism's genes is observed, and other genes of importance in causing higher-level effects may be omitted. Even if all the genes in an organism could be observed, the only way to convincingly demonstrate which genes are caus-atively linked to higher-level changes (e.g., in survival or reproduction) would be by genetic manipulation [15]. The likely experimental effort involved in demonstrating causal links between gene responses and whole-organism responses will be substantial, though worthwhile. This, however, still does not address the extrapolation from whole-organism performance to the population level, which is essential for assessing ecological risks.

Extrapolation from chemical structure to biological responses

Quantitative structure–activity relationships (QSARs) that make connections between chemical structure and hazard criteria (bioaccumulation potential, persistence, and toxicity) have a long history in ecotoxicology [16]. With increasing pressure to speed up assessments and to reduce animal testing [17], more emphasis likely will be placed on QSARs in the future. Indeed, QSARs already are an important feature of screening techniques, and increasing efforts to build chemical groupings for read-across from one chemical to another in terms of their likely hazard properties will put even more emphasis on these approaches. Although QSAR models often are based on hypotheses about the relationship between chemical structure and their fate or effects in the environment, the relationships are statistical rather than mechanistic and, thus, are based on correlation analysis. Moreover, the models relate structure to individual-level responses (most frequently, survival) and, again, do not address the crucial extrapolation from whole-organism performance to the population level.

Extrapolation using controlled ecological systems

Mesocosms and field studies are used most frequently in connection with pesticide risk assessment, in which, for example, mesocosms can be included at the highest tier of the risk assessment for nontarget aquatic species [18]. Mesocosms have the advantage that a high level of ecological complexity and realism can be incorporated directly into the test system. In addition, interactions among species—and, therefore, indirect effects of toxic chemicals—can be measured. Not all systems are amenable to such test designs, and issues of scale, cost, and reproducibility often are raised as disadvantages [19]. Although mesocosms and field tests often can provide very useful tools for studying recovery from toxic chemicals, design constraints often prevent recovery from occurring during the course of the study. These constraints include too short a study duration and study designs that do not permit contact with natural sources of immigrants (e.g., from upstream). There also may be artifacts from scale effects [20], difficulties in sustaining the systems for long periods, and sensitivity of responses to starting conditions [21]. Whereas mesocosms and field studies can provide valuable tools that empirically explore the fate and ecological impacts of chemicals in complex systems, their main limitation is that in practice, it is not feasible to test the breadth of ecological conditions and species for which we wish our risk assessments to apply.

Limitations of current methods

Table 2 summarizes the kinds of extrapolation methods most commonly used in ecological risk assessment. As the above overview indicates, a range of methods has been used in ecological risk assessment to extrapolate from what we measure to what we want to know. Application factors can be interpreted as extrapolating from the individual level to the field level, but in a somewhat arbitrary, nontransparent way. Biomarkers (including -omics responses) and QSARs extrapolate, for the most part, to the individual level only. Species sensitivity distributions extrapolate to multispecies individuallevel effects, but on the presumption that species sensitivity to contaminants directly corresponds to individual-level effects. Model ecosystems, on the other hand, directly measure effects on populations, biodiversity, and ecosystem processes. Their main limitations are in terms of cost, reproducibility, that not all systems are amenable to mesocosm designs, and that even for those systems that are, it can be extremely difficult to experimentally test all potentially relevant risk scenarios.

Table Table 3.. Classification of population models with key references
Model classExampleReference
Demographic modelsTwo-stage modelSibly and Calow [33]
 Matrix modelCaswell [29]
 Metapopulation modelAkçakaya et al. [24]
Energy budget modelsSimpleCalow and Sibly [48]
 DynamicKooijman [47]
Individual-based modelsIndividual-basedGrimm and Railsback
 models[27]

Even the newest international chemicals legislation, REACH (Registration, Evaluation, Authorization, and Restriction of Chemicals) [17], has done nothing to improve extrapolation. On the contrary, REACH prioritizes reduced animal testing, which will place more emphasis on in vitro methods and ecotoxicogenomics techniques and an increased focus on chemical structure models (e.g., QSARs) for assessing chemical hazards. Thus, although REACH is expected to result in the generation of much more information for industrial chemicals, it is not at all clear whether the information generated will be used in a way that leads to better risk assessments.

ECOLOGICAL MODELS AND WHAT THEY CAN OFFER

For the present discussion, we define population models to be those mechanistic models that relate individual-level responses to changes in population size and structure. Such models are used primarily for effects assessment, but some (i.e., individual-based models [IBMs]) may incorporate exposure assessment as well. Many types of population models have been developed. and it is beyond the scope of the present paper to review the range of population models available for use in ecological risk assessment. For recent reviews and classifications of these models, see Pastorok et al. [22], Barnthouse et al. [23], and Akçakaya et al. [24]. Our aim is to draw attention to the key features of broad classes of population models and to discuss their advantages and limitations for ecological risk assessment.

We recognize three broad classes of population models (Table 3). The first class, demographic models, describes individuals in terms of their contribution to recruitment and their survivorship. These models may be unstructured (i.e., all individuals within the population are treated as identical) or structured (i.e., individuals are separated into defined size or age classes, and all individuals within each class are treated as identical). Spatial structure also may be added, as in metapopulation models [25]. Likewise, demographic and environmental stochasticity can be added if necessary [26]. The second class of models, energy budget models, is similar to the first in treating all individuals as the same but characterizes the responses of individuals in terms of energy intakes and outputs that relate, ultimately, to growth rates and reproductive performance. On the other hand, the third class of models, IBMs, represents each individual within a population as being distinct and describes individual responses with more or less detail. The dynamics of the population emerge as a result of the combined effect of the responses by the individuals of which it is composed [27].

Figure Fig. 1..

Location of the different classes of population model based on level of generality and complexity. IBM = individual-based models.

An important feature of all the above population models is that they have a solid grounding in ecological theory and are based on a thorough mechanistic understanding of the key processes contributing to the ecological phenomena of interest. On this basis, they can be used to extrapolate from observations made on individuals in test systems (in terms of survival, growth, and reproduction) to population-level impacts (e.g., abundance, population growth rate, carrying capacity, age/size structure, and spatial distribution). Moreover, the models can be used to explore possible outcomes of a range of risk scenarios. That said, each of these broad classes has advantages and disadvantages to their use in extrapolation in terms of their generality, realism, and accuracy [28].

Figure 1 locates the different classes of models in a matrix based on level of generality and complexity. The effort needed to construct and validate the models increases with their complexity and specificity. Thus, the demographic models have high generality and a long history of use in ecology, but they may trade that off against low levels of ecological realism and accuracy in predictions. Indeed, such models are not used to predict population size or state at some future time or place; rather, they are used to project what would happen to the population should the organisms' life-history traits remain as they are [29]. It is possible to incorporate density-dependent effects into demographic models, but doing so may greatly complicate the mathematics [29]. There also may be difficulties in parameterizing matrix models, particularly for large animals and if density-dependent effects are included. In addition, in contrast to IBMs, demographic models do not include exposure directly (see below). The energy budget models also have high generality, are based on observations that purportedly can be made more easily and quickly than those for demographic responses, but have low realism in that they do not include survivorship responses (unless they are coupled to demographic models [30,31]) and, hence, have low levels of accuracy in terms of predicting the actual dynamics of field populations. Individual-based models can be very simple but, as a result, may suffer from the disadvantage of low realism. On the other hand, IBMs add value when they incorporate high levels of detail about individual exposures and responses. In such cases, however, they tend to have low generality, can require a lot of effort to build and run, and validation is a major issue. Thus, demographic and energy budget models are useful for assessing how defined effects of a chemical on life-history traits are likely to impact population dynamics under the assumption that fertilities and survival probabilities remain constant over time [2]. In contrast, IBMs allow individuals in the population to vary their life-history traits in space and time in response to changing environmental conditions. Therefore, IBMs potentially provide more accurate predictions of population dynamics in complex and varying landscapes but require considerable effort to build and validate. Certainly, as many of the references cited in the present review indicate, the ability of demographic models to project population structure and dynamics is well proven, and their usefulness has been shown in many management applications. Energy budget models have been less widely applied, but some have demonstrated their ability to assess risk for field populations [31]. So far, the use of IBMs in ecological risk assessment has been rather limited, though reasons exist to expect that their use may increase in future [32].

Examples illustrating advantages of population modeling in extrapolation

Population modeling can add value to ecological risk assessment in a number of distinct, but not mutually exclusive, ways. Population models integrate all the individual-level processes that contribute to population growth rate. This is important, because the relationships between individual responses in survival, fecundity, and development are complex and nonlinear. For example, the Euler-Lotka model describes population growth rate as a function of age-specific birth rate and death rate [33]:

equation image

where n is the number of offspring produced per individual of age t, St is the probability of surviving to age t, and r is population growth rate.

The value of r can be used to forecast future population size provided that the life histories and the relative numbers of individuals in each age class do not change (i.e., that the population has a stable age distribution). The equation can be modified to include immigration and emigration if these are relevant for the system under study. The models may be deterministic (i.e., the same inputs produce the same output no matter how many times the models are run), or they may be made stochastic by the addition of random components. The latter may be particularly useful if population sizes are small and random fluctuations become more important for the population's dynamics [26]. So, in the context of extrapolation, such models are mechanistically complete. This is in direct contrast to extrapolation using biomarkers, in which one (or more) suborganismal process is correlated with whole-organism performance, ignoring all others. Just as it would be naive to expect survival or fecundity alone to correlate tightly and consistently with the population growth rate, it likewise is unrealistic to expect single suborganismal process to do so.

Population modeling allows an analysis of the relative importance of toxicant impacts on different individual-level responses for the population dynamics. In addition, the models provide valuable insights regarding the mechanisms behind observed or predicted ecological impacts. For example, population dynamics models often are used in combination with elasticity and decomposition analyses [29,34]. These analyses are used to quantify the relative importance of changes in lifehistory variables to population dynamics as well as to provide insight regarding the life-history causes of observed dynamics. For example, Widarto et al. [35] performed a life-table response experiment with the collembolan Folsomia candida. An elasticity analysis showed that the population growth rate (λ) was most sensitive to changes in juvenile survival and least sensitive to changes in adult survival. Decomposition analysis indicated that fecundity was the main contributor to the positive (but nonsignificant) changes observed in λ; however, because the elasticity of fecundity was very low, the large stimulation in fecundity resulted in a minimal effect on λ. These kinds of analyses also can be helpful in performing interspecies extrapolations. For example, one can explore how the same effect on fecundity would impact population dynamics in other (untested) species [36,37]. Other approaches (e.g., SSDs) implicitly assume that the endpoints measured in tests provide the appropriate measure of species sensitivity; however, because of differences in elasticity patterns, this may not be the case.

Population modeling facilitates the assessment of risks under different exposure and effect scenarios. For example, using measured data from laboratory life-table response experiments, Hansen et al. [38] explored how changing the starting values of life-history traits to simulate more realistic field conditions would potentially influence the response of Capitella sp. I populations to nonylphenol exposure and how elasticity and decomposition patterns were modified under the more realistic scenarios.

Population modeling allows exploration of how the addition of different types of ecological complexity influences risk. Such models have been used to perform virtual experiments in systems that are too large on a spatial scale or too long on a time scale for ordinary field experiments to be feasible. Recent work by Sibly et al. (University of Reading, Reading, UK, unpublished data) has demonstrated how such sophisticated IBMs not only can simulate highly realistic ecological phenomena but also can be used to explore questions of fundamental ecological interest, such as how carrying capacity varies over space and time.

Population models are a powerful tool for exploring comparative risks across species, chemicals, and exposure scenarios. Population models can help to focus toxicity testing efforts, both by identifying the types of species that are most or least likely to be at risk from chemicals [36,37] and by identifying exposure scenarios that are more or less risky. Thus, the model outputs can aid in designing empirical tests in a cost-effective manner.

Some population models (i.e., IBMs) can incorporate exposure and effects together in a realistic and mechanistic way to provide an integrated assessment of ecological risk. The concentrations of chemicals to which individual animals are exposed in the field depend on many factors. For pesticides, for example, such factors as the method of application of the chemical, the time at which it is applied, and weather conditions are important [39]. If the pesticide is applied as a spray, for example, then its distribution on the ground and on foliage will depend on wind speed and direction, and the amount that individuals ingest will depend on whether they eat the foliage, eat animals that ate the foliage, and so on. The timing of application will have different implications depending on where individuals are in the breeding cycle [40,41]. Furthermore, individuals are likely to acquire the chemical not just once but on different occasions, so some kind of integrated effect over time must be calculated. Individual-based models can capture all this detail in mechanistic simulations and provide any desired ecological outputs, such as the effects of the chemical on population growth rate or carrying capacity [32,42].

Population modeling is the only practical way that we can effectively capture all the combinations of variables we may wish to explore in a risk assessment context. Neither mesocosms nor field trials can do this as comprehensively. Models also avoid the problems of uncontrolled variables that may confound interpretation of mesocosm or field test results. Nevertheless, the parameterization of models is, to say the least, challenging, and it likely will involve some or all of the experimental methods described above.

CONCLUSION

Currently, in ecological risk assessment, we seek to extrapolate from observations on the effects of chemicals on individual-level (or subindividual) traits to ecological-level responses. The methods for doing this using application factors, SSDs, biomarkers, QSARs, and mesocosms have a number of limitations. These methods can be arbitrary, nontransparent, and empirical rather than mechanistic, and they also can neglect potentially important variables in the key step between individual-level responses and population-level impacts (see Table 2).

Population models have the potential for adding more value to ecological risk assessment by incorporation of better understanding of the links between individual-level responses and population size and structure and by incorporating greater levels of ecological complexity. Hence, we believe that these models should be used to help provide more accurate risk assessments.

Despite the promise that population models hold for risk assessment, a number of issues need to be addressed before these models become more widely used. These issues involve development of the science, development of appropriate guidance for risk assessors and risk managers, as well as a broader stakeholder consensus on how the models should be used. Here, we focus on the science issues, recognizing that regulator guidance and stakeholder involvement also are necessary requirements in facilitating the most effective use of the models in a regulatory context.

A number of key scientific questions and developments need to be addressed. First, models can be used only if they can be parameterized, and some difficult challenges exist in parameterizing population models for risk assessment. These relate to limitations in the available laboratory data and numerous difficulties in extrapolating between species and from laboratory to field. Most standard laboratory tests focus on effects at what are considered to be the most sensitive stages of the life cycle in a limited number of species. Effects on the most sensitive life stages, however, do not necessarily drive pop ulation-level effects, and indeed, effects on less sensitive life-history traits may actually drive the impacts at the population level [43,44]. Also, problems exist in extrapolating the laboratory data to other, more relevant species. Issues such as differences in metabolic rates and detoxification likely are important in this regard. Attempts already have been made to consider the way that the same impacts on survival, reproduction, and development affect populations of species having different life-cycle types [36,37,45]. We need much additional information, however, about the relative importance of toxicity versus life cycle in determining population sensitivity to chemicals as well as distributions of different life-cycle types in different kinds of communities [9]. Difficulties arise in knowing the concentrations of chemicals to which species might be exposed in the field. Most current methods for exposure assessment assume that all individuals are exposed continuously to the expected environmental concentration unless, as in pesticides, specific knowledge exists regarding application scenarios [46] (http://visco.jrc.it/focus/). To get more realistic estimates of exposure, we need to know more about the spatial variability of chemicals in the environment relative to the spatial distribution of exposed populations and the way that the behavior of the organisms affects their likelihood of becoming exposed to the chemical. This is the kind of complexity that can be addressed in IBMs [32,42], provided that the models can be adequately parameterized using experimental methods such as those described above.

How much complexity is needed for different risk assessment questions? Under what situations is it sufficient to use simple matrix models, and when are sophisticated IBMs required? The answer is likely to depend, at least in part, on whether the models need to be protective or more precisely predictive. For example, when they are used in screening-level or comparative assessments, protection is the aim, and this places fewer requirements on the models. On the other hand, for higher-tier risk assessments or for particular management scenarios relating to specific sites and populations, the emphasis is on prediction, and this requires more complex modeling approaches, such as IBMs.

Related issues of specificity versus generality also are a concern. Models that are developed for particular species occupying defined landscapes can be made very specific (e.g., IBMs). It can be difficult, however, to generalize model outputs to other species or to other landscapes. Generality is important in risk assessment scenarios where regional exposures are being considered that are likely to impact a broad range of ecosystems and species (as has been the case in regional risk assessments of existing substances in the European Union [4]). Also, generality may be of importance in exploring the likely impacts of a particular toxicological effect in a range of life-cycle types. The ideal would be to achieve generality by experimentation with models of proven local accuracy over a representative range of scenarios and species. If this is too costly, it may be appropriate to use demographic or energy budget models [36,45,47].

Interactions through competition and trophic relationships rarely are incorporated into the models and yet are likely to have an effect on the outputs and the assessments of risk. In principle, however, no reason exists why these kinds of complexities cannot be incorporated into existing models as a step toward understanding communities and ecosystems, but some difficulties occur in doing so [42]. Two approaches may be employed. First, the models can be used in a theoretical analysis to consider the extent to which the increased complexities associated with competition and trophic relationships are likely to lead to reduced or enhanced risks and, hence, the added value from incorporating the complexity for the risk assessment. Second, the models can be used to guide experimental programs that are involved in incorporating particular complexities to the extent deemed to be necessary in refining risk assessments.

Currently, extrapolation is problematic and might generate false positives as well as false negatives. We are of the view that population modeling can reduce this uncertainty and add value to the ecological risk assessment process when used with appropriate experimental methods for model parameterization. We do not advocate any particular model, because in our view, different models will be appropriate in different circumstances. An important challenge is to develop general guidance for when and how different modeling approaches should be applied. The present review suggests an agenda both for the incorporation of population models into the regulatory framework and for a research program to support this. We believe that ecologists and regulators need to work closely together to effectively develop transparent tools that are understood by all stakeholders.

Acknowledgements

The Centre for Integrated Population Ecology (CIPE) is an international center of excellence supported by the Danish Natural Sciences Research Council. All authors are members of CIPE. This review benefited from discussions with additional members of the CIPE team.

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