Sublethal effects of binary mixtures of Cu2+ and Cd2+ on Daphnia magna: Standard Dynamic Energy Budget (DEB) model analysis

Abstract

Dynamic Energy Budget theory (DEB) describes mass and energy fluxes that occur in living organisms. DEB models were successfully used to assess the influence of stress, including toxic substances, and changes in pH and temperature, on different organisms. In this study, the Standard DEB model was used to evaluate the toxicity of copper and cadmium ions and their binary mixtures on Daphnia magna. Both metal ions have a significant influence on daphnia growth and reproduction. Different physiological modes of action (pMoA) were applied to primary DEB model parameters. Model predictions for chosen modes of interaction of mixture components were evaluated. The goodness of model fit and the model prediction was assessed to indicate the most likely pMoA and interaction mode. Copper and cadmium influence more than one DEB model primary parameter. Different pMoAs can result in similar model fits, and therefore it is difficult to identify pMoA only by evaluation of the goodness of fit of the model to the growth and reproduction data. Some critical discussion and ideas for model development are therefore provided.

Keywords: Dynamic system; Estimation; Growth model; Numerical methods; Reproduction model.