Revisiting assessment factors for species sensitivity distributions as a function of sample size and variation in...

To use species sensitivity distributions (SSDs) for ecological risk assessment, there are various uncertainties, which require applying assessment factors (AFs) accordingly. This study aims to quantify the uncertainty of estimating statistical distributions. Given a management goal of protecting 95% of species, the concentration that affects 5% of the species (HC5) is estimated. Since the true concentration affecting 5% of the species (population HC5) is unknown, the estimated HC5 is divided by an AF to derive the predicted no-effect concentration (PNEC), which is set as the protection goal, to compensate for the deviation in the estimated HC5 from the population HC5. Although the deviation between these two HC5 values depends on the sample size and the variation in sensitivity (standard deviation of the distribution) among species, there has been little discussion of how to quantify the degree of uncertainty. By assuming that toxicity values are a random sample from a lognormal distribution, we mathematically analyzed the SSD to derive the magnitude of AF needed to achieve a given protection goal (as an example, the protection of 95% of species with a probability of 95%). We successfully derived an equation that explicitly relates the magnitude of AF to the sample size and the variation in species sensitivity, providing a new basis to statistically determine the magnitude of AF for ecological risk assessments.