Mixture toxicity with the dynamic energy budget (DEB) theory and individual-based models (IBM): effects of Cu and Zn on Daphnia magna populations

The current regulatory framework of risk assessment considers the effects of single substances that are assessed through standardized laboratory tests, e.g. the 21-day Daphnia magna reproduction test. However, in the environment, individual organisms are being exposed to mixtures of chemicals. Protection goals in EU legislation (e.g. Water Framework Directive) state that protection of populations is needed to maintain ecosystem functioning. In our research, we developed an Individual-Based Model of the Dynamic Energy Budget theory (DEB-IBM) to predict effects of metal mixtures on Daphnia magna populations. The DEBtox model was calibrated using apical effects (i.e. growth, reproduction and survival) of Cu and Zn assessed in standardised tests. To validate our model and determine the most appropriate mixture toxicity mode at the population level, a population experiment (75 days) with D. magna exposed to Cu and Zn (both single and mixtures) was performed. We tested three implementations of mixture toxicity in DEB-IBM: independent action (where effects of the compounds are considered independent), concentration addition (where the compounds have the same toxic mode and act as dilutions of each other) and effect addition (where compounds have the same toxic mode but effect levels are summed). Each implementation was evaluated for predictability against the data of the population experiment using the normalised mean square error (NMSE). All three implementations perform well compared to the data, indicating that none of the mixture models is preferred at the population level. We extrapolated the experiment with DEB-IBM to untested concentrations and determined effect levels for Cu and Zn based on equilibrium population density. The effect levels of the three mixture toxicity implementations were compared to assess the applicability of our model for mixture toxicity risk assessment at the population level. The current implementation of mixture toxicity in DEB-IBM could accurately predict mixture toxicity effects observed in a population experiment. The concentration addition model seemed to be the more conservative mixture toxicity mode. More fine-tuning and comparison with experiments is needed to further validate our approach and increase confidence in the predictions.