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Flammarion, P. and A. Péry (2004). Contributions from modeling toxic effects at the individual and population levels in aquatic ecotoxicology.. Rev. Sci. Eau 17 (4) : 489-502. [article in French]

Original title: Apports de la modélisation des effets des toxiques sur l’individu et la population en écotoxicologie aquatique.

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Traditional analysis of toxicity tests provides toxicity parameters that are estimated with purely statistical methods. Consequently, these parameters do not have any intrinsic biological meaning and these methods provide no information about the mode of action of the tested chemicals. It is also difficult for these methods to change scale from the individual level to the population level, or to account for temporal and spatial heterogeneity. Modelling is an important tool in ecotoxicology and recently it appears to have gained more interest. Developments in modelling are currently expanding in two directions, modelling effects at the individual level and applying toxicity data obtained at the individual level to responses at the population level. The objective of the current study was to present these two complementary modelling approaches together with the opportunities they offer.

Modelling at the individual level provides parameters that are biologically relevant. Modelling also facilitates the formulation and the testing of hypotheses concerning toxicity processes (physiological mode of action and kinetics). Confounding factors such as time, varying exposure concentrations, or feeding can also be incorporated into models. In this paper, two kinds of models were examined: biochemistry-based models (Hill models) and energy-based models (Dynamic Energy Budget models). In the Hill approach, effects are modelled as the interaction between chemicals and receptors in the organisms, which leads to a relationship between concentration and effects close to the logistic equation often used in toxicity test analysis. In the energy-based approach, models are built on the dynamic energy budget theory, in which energy derived from food is used for maintenance, growth and reproduction. The effect of compounds is then described as a change in one of the parameters describing these physiological functions. Kinetics are taken into account by a one-compartment model. The uptake rate is proportional to the exposure concentration, whereas the elimination rate is proportional to the concentration in the tissue. This model is simple but is relevant for many organisms and compounds (KOOIJMAN and BEDAUX, 1996). As time is taken into account through kinetic modelling, the estimation of the other parameters, such as the No Effect Concentration, does not depend on the exposure duration. An energy relevant model has many advantages. First, observed effect profiles are more in agreement with expectations (KOOIJMAN and BEDAUX, 1996). Second, it becomes possible to account for the fact that an effect on survival increases the amount of food consumed per surviving organisms, which in turn partly compensates for the negative effects of pollutants. Third, it allows for the examination of effects at the population level on density and biomass, complementary to the usual study of population growth rate.

Most of the recent modelling research is related to deriving effects at the population level from effects at the individual level, because ecosystems are the target of ecotoxicology. Until recently, classical approaches, like the Euler equation or Leslie matrices, were used with population growth rates as endpoints. They provide interesting tools to determine the impact of life cycle parameters at the population level and to assess which level of effects has to be assessed. Even a simple approach such as that proposed by CALOW et al. (1997), separating the population into two different classes, juveniles and adults, can produce very interesting results. For instance, the authors showed that in populations for which females die just after reproduction, juvenile survival had much more importance than for populations where females can reproduce several times during their lifetime. The opposite is true concerning adult survival. However, these approaches do have some limits that make complementary approaches necessary to fully understand the effects of pollutants at the population level. First, they do not account for effects on the carrying capacity. SIBLY (1999) pointed out that there is a need for ecological studies on the effects of pollutants that measure their effects on density dependence and carrying capacity. Indeed an effect on population growth rate only accounts for a risk of disappearance for the population, but cannot help in the understanding of effects on biomass or density. Effects on the carrying capacity can have substantial effects at the ecosystem level, especially when studying species that constitute a food resource for other species. Second, more complex tools have to be developed to take into account spatial heterogeneity of pollution and habitats in order to be relevant from an ecosystem point of view. Indeed, it has been shown that uncontaminated sites can be significantly disturbed if they are connected, through the migration of organisms, with contaminated sites (SPROMBERG et al., 1998).


Models, aquatic ecosystems, biomathematics, ecotoxicology, energy, mode of action.

Corresponding author

Alexandre Péry, Laboratoire d’écotoxicologie, CEMAGREF, 3b quai Chauveau, 69009 Lyon, FRANCE

Email : alexandre.pery@cemagref.fr
Telephone : (33) 4 72 20 87 88 / Fax : (33) 4 78 47 78 75

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Update: 2006-12-19
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