Empirical Comparison of Seven two-parameter Sigmoid Equations for the Evaluation of the Concentration-response Curves from Standard Acute Ecotoxicity Assays

The acute ecotoxicity of a set of mixture samples (washing powders, wastes, fuel extracts etc.) was assessed using four acute ecotoxicity assays with aquatic organisms (Daphnia magna, Poecilia reticulata, Artemia salina and Desmodesmus subspicatus). The experimental concentration-response curves were fitted by seven two-parameter sigmoid equations using non-linear regression. The regression performance of the equations was compared in three categories (overall fit, mid-range fit, and low-effect fit) using non-parametric statistics. The best overall fit was achieved by Weibüll, Bolztman (i.e. logistic), modified Gompertz and log- Weibüll equations. The best low-effect fit was achieved by a modified Gompertz curve. Those equations transforming concentrations to log c fitted significantly worse than those not transforming them. The obtained EC50 values calculated by all of the equations were comparable to those calculated by the probit model. The results show that regardless of the knowledge of the susceptibility distribution or the mechanisms of toxic action simple two-parameter equations fit the data from acute ecotoxicity assays well and might be used for their evaluation.