Abstract-A promising tool for the risk assessment of chemical mixtures is the prediction of their toxicities from the effects of the individual components. For that purpose, concentration addition is uniformly regarded as valid for mixtures of similarly acting chemicals. Whether this concept or the competing notion of independent action is more appropriate for mixtures of dissimilarly acting chemicals is still in dispute. Therefore, the presented study analyzed and compared the predictive capabilities of both concepts for a multiple mixture designed of strictly dissimilarly acting compounds. Experimental investigations were conducted using a longterm bioluminescence inhibition assay with Vibrio fischeri. Results show an excellent predictive power of independent action, while concentration addition overestimates the mixture toxicity. Thus, the precise prediction of mixture toxicities depends on a valid assessment of the similarity/dissimilarity of the mixture components. However, concentration addition underestimates the EC50 of the mixture only by a factor of less than three. As the similarity of components is often unknown for mixtures found in the environment, it is concluded that concentration addition may give a realistic worst case estimation of mixture toxicities for risk assessment procedures.

Current approaches to the assessment of chemical hazards focus on toxicity studies with single, pure chemicals. In the environment, however, organisms are exposed to numerous pollutants simultaneously. We studied the toxicities of multiple mixtures of pesticides and antibiotics in algal and bacterial bioassays. The test mixtures were composed of 14 to 18 components with either identical or completely different specific mechanisms of action. The results reveal that reliable predictions of mixture toxicities can be derived from concentration response data of single toxicants by applying two different concepts: concentration addition in cases of similarly acting mixture components and independent action for substances with dissimilar mechanisms of action.

Risk assessments of toxic chemicals currently rely heavily on the use of no-observed-effect concentrations (NOECs). Due to several crucial flaws in this concept, however, discussion of replacing NOECs with statistically estimated low-effect concentrations continues. This paper describes a general best-fit method for the estimation of effects and effect concentrations by the use of a pool of 10 different sigmoidal regression functions for continuous toxicity data. Due to heterogeneous variabilities in replicated data (i.e., heteroscedasticity), the concept of generalized least squares is used for the estimation of the model parameters, whereas a nonparametric variance model based on smoothing spline functions is used to describe the heteroscedasticity. To protect the estimates against outliers, the generalized least-squares method is improved by winsorization. On the basis of statistical selection criteria, the best-fit model is chosen individually for each set of data. Furthermore, the bootstrap methodology is applied for constructing confidence intervals for the estimated effect concentrations. The best-fit method for the estimation of low-effect concentrations is validated by a simulation study, and its applicability is demonstrated with toxicity data for 64 chemicals tested in an algal and a bacterial bioassay. In comparison with common methods of concentration-response analysis, a clear improvement is achieved.

The prediction of combined effects based on the effects of the individual components of mixtures by using the pharmacological concepts of concentration addition and independent action might be a promising tool for the risk assessment of pollutant mixtures. To analyze and compare the predictive capabilities of the reference concepts for similarly acting chemicals, the overall toxicity of a multiple mixture was determined in a bioluminescence inhibition assay with Vibrio fischeri. The mixture was composed of 16 similarly and specifically acting chemicals, anticipated to have a common mode of action via weak acid respiratory uncoupling of oxidative phosphorylation. Results show that the observed mixture toxicity is rather well predicted by both concepts. Concentration addition shows an excellent predictive power; the median effective concentration (EC50) of the mixture is predicted with an error of about 10%. Independent action, in contrast, underestimates the EC50 of the mixture by a factor of a little more than three. With respect to risk assessment procedures, it may be concluded that concentration addition gives a valid estimation of the overall toxicity for multiple mixtures with similar and specific mechanisms of action of the mixture components in this type of biotest.

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