Dose-response functions in aquatic toxicity testing and the Weibull model

Abstract

A linear transformation of the Weibull model for dose-response functions is developed. The transformation is analogous to the probit and logit transformations. Typical dose-response curves in aquatic toxicity testing using macroorganisms and algae are analyzed by the Weibull and probit models, and it is shown that the Weibull model generally provides at least as good a fit to experimental data as the probit model. The expansion of the Weibull model to reflect the survival fraction or yield of organisms under multiple toxicant limiting conditions leads to particularly useful expressions for simple similar joint action (concentration addition with parallel response curves for the individual toxicants) and independent joint action (response multiplication). Explicit water quality criteria are derived based on both formulations. The multiple toxicity models, expanded to include concentration addition with non-parallel response curves for the individual toxicants, are applied to algal assay data for Selenastrum capricornutum exposed to manganese, copper, and lead. The fact that the yield based on response multiplication for the manganese-lead pair is lower than that calculated from concentration addition suggests that water quality criteria based on concentration addition may not always provide safe limits.