Competing statistical methods for the fitting of normal species sensitivity distributions: recommendations for practitioners

A species sensitivity distribution (SSD) models data on toxicity of a specific toxicant to species in a defined assemblage. SSDs are typically assumed to be parametric, despite noteworthy criticism, with a standard proposal being the log-normal distribution. Recently, and confusingly, there have emerged different statistical methods in the ecotoxicological risk assessment literature, independent of the distributional assumption, for fitting SSDs to toxicity data with the overall aim of estimating the concentration of the toxicant that is hazardous to % of the biological assemblage (usually with small). We analyze two such estimators derived from simple linear regression applied to the ordered log-transformed toxicity data values and probit transformed rank-based plotting positions. These are compared to the more intuitive and statistically defensible confidence limit-based estimator. We conclude based on a large-scale simulation study that the latter estimator should be used in typical assessments where a pointwise value of the hazardous concentration is required.