Effects of dinoseb on the life cycle of Daphnia magna: Modeling survival time and a proposal for an alternative to the no-observed-effect concentration

Risk assessment is in urgent need of more accurate toxic effect endpoints than those currently in use, especially for low concentrations. Often such endpoints are estimated by analysis of variance, linear interpolation, or smoothing. As these statistical methods are not always satisfactory, some authors have proposed to describe the entire dose-response curves by fully formalized parametric regression models whose parameters have toxicological meaning. These models allow a better evaluation of pollutant effects, including inter- and extrapolation to any other than the measured effect values. Following this line, a four-parameter logistic regression model (standard model) was fitted to survival data of `Daphnia magna' under pesticide (dinoseb) stress. The heterogeneity of the variance was taken into account with a both-sides logarithmic transformation. Besides the standard model, a hormesis and a threshold model were tested too. These two others models have been described in the literature and might better represent the dose-response function we are looking for. All three models showed a good fit to our data, and the statistics gave no hints as to which model is the most appropriate. As no evidence was seen for hormesis or for the existence of a threshold concentration, we used the simplest, namely, the standard model, for most of our calculations. Model calculations allow the quantification of the effects on individuals' longevity as well as on mean survival time of the population. We used them to define a no-effect value, the statistical-no-effect concentration (SNEC). The SNEC is based on the confidence bands of the modeled regression and represents the highest value for which an effect is statistically not different from the control. The SNEC is an alternative to classical endpoints, like the no-observed-effect concentration (NOEC) or the low-effect concentrations (e.g., EC10, EC5, EC1).