Modeling the effects of binary mixtures on survival in time

In general, effects of mixtures are difficult to describe, and most of the models in use are descriptive in nature and lack a strong mechanistic basis. The aim of this experiment was to develop a process-based model for the interpretation of mixture toxicity measurements, with effects of binary mixtures on survival as a starting point. The survival of Folsomia candida was monitored daily for 21 d during the exposure to six binary mixtures of cadmium, copper, lead, and zinc in a loamy sand soil. The measurements were used to develop a model to describe survival in time. The model consists of two parts: A one-compartment model that describes uptake and elimination of the compounds, and a hazard model describing survival. The model was very successful in describing the data and at finding possible interactions. The mixture of copper and lead showed a slight antagonistic effect, the other mixtures showed no interaction. The model is straightforward in its biological assumptions and does not require a mode-of-action a priori choice of the mixture that might influence the modeled interaction of the components in the mixture. The model requires measurements at intermediate time points, but runs with relatively few parameters and is robust in finding interactions. When mixture effects are considered at only one time point, care should be taken with the assignment of interactions because these may be different for different points during the time course of the experiments.