Modeling the synergistic effects of toxicant mixtures

Background: Toxicants often occur simultaneously. Some combinations show synergistic combined effects that go far beyond what is predicted with current effect models. Up until now, only the combined additive effects of similar acting chemicals have been assessed accurately, whereas the combined effects of dissimilar acting chemicals have been greatly underestimated in many cases. Results: Here, we use the individual tri-phasic concentration-response relationship of two toxicants with different modes of action to model their combined synergistic effect onDaphnia magna. The novel stress addition approach (SA) predicted the combined effects (LC50) of different esfenvalerate and prochloraz combinations with an uncertainty factor of 2.8 at most, while the traditional effect addition (EA) and concentration addition (CA) approaches underestimated the combined effect by a factor of up to 150 and 660, respectively. Data of the single substance concentration-response relationships and on their combined effects enable to determine the degree of synergism. For the evaluation of the combined toxicant effect, we provide the approach as R package and as Indicate model (http:// www.systemecology.eu/indicate/). Conclusion: Adding stressors arithmetically, considering non-monotonic cause-effect relationships, is a decisive component in predicting the combined effects of multiple stressors within test systems. However, the extent of the synergistic effects that multiple stressors exert on populations within the ecosystem context is still highly controversial. Various processes are relevant at the ecosystem level, which are not considered in laboratory studies. However, the present work serves as a building block for understanding the effects of multiple stressors in the field.