Simplified Dynamic Energy Budget model for analysing ecotoxicity data

Models based on Dynamic Energy Budget (DEB) theory offer important advantages in the interpretation of toxicant effects on life-history traits. In contrast to descriptive approaches, they make use of all of the data (all time points, and all endpoints) in one framework, and yield time-independent parameters. In 1996, a suite of simplified DEB models for the analysis of standard toxicity tests was presented under the name ‘DEBtox’. Unfortunately, the original equations contained a few errors and inconsistencies. In this paper, we revisit DEBtox, presenting a new and consistent set of simplified DEB equations. The full derivation is presented in the supplementary material to facilitate critical examination of our work. The simplification is appropriate for situations where body size at the start of investment in reproduction remains constant, as well as the egg costs (and thus hatchling size). These conditions are probably met in many ecotoxicological tests, allowing this framework to be used, at least as a first approach. Additionally, we present a statistical framework for fitting the model to experimental data sets, and to calculate intervals on parameter estimates, model curves and model predictions. As an illustration, we provide a case study for the effects of fluoranthene on Daphnia magna, although the framework is by no means limited to this species or toxicant.