All Individuals Are Not Created Equal; Accounting for Interindividual Variation in Fitting Life-History Responses to Toxicants

The individuals of a species are not equal. These differences frustrate experimental biologists and ecotoxicologists who wish to study the response of a species (in general) to a treatment. In the analysis of data, differences between model predictions and observations on individual animals are usually treated as random measurement error around the true response. These deviations, however, are mainly caused by real differences between the individuals (e.g., differences in physiology and in initial conditions). Understanding these intraspecies differences, and accounting for them in the data analysis, will improve our understanding of the response to the treatment we are investigating and allow for a more powerful, less biased, statistical analysis. Here, I explore a basic scheme for statistical inference to estimate parameters governing stress that allows individuals to differ in their basic physiology. This scheme is illustrated using a simple toxicokinetic-toxicodynamic model and a data set for growth of the springtail Folsomia candida exposed to cadmium in food. This article should be seen as proof of concept; a first step in bringing more realism into the statistical inference for process-based models in ecotoxicology.