Environmental Risk Assessment is often directed towards an analysis of the ratio of the Predicted Environmental Concentration (PEC) to the No Effect Concentration (NEC). One may either examine whether the ratio is greater than one, or, equivalently, whether the PEC is greater than the NEC. Due to uncertainties in both quantities, one may encounter several cases depending on how this uncertainty is accounted for. When the PEC is a probability distribution, either from temporal or spatial variation, or from model uncertainty per se, while the NEC is deterministic, e.g. a fixed quality objective, the analysis boils down to the estimation of the probability of exceeding the objective. Current theory of the sensitivity of different biological species for a toxicant, however, deals with unimodal (one-peak) statistical probability density functions describing this sensitivity for a representative sample of (laboratory) species. These are often NOEC distributions. Then the question of PEC being greater than NEC is a matter of comparing two probability distributions, which will often be independent. Whether PEC > NEC can be analyzed from the probabilistic equation PEC - NEC > 0, that can be solved from their joint distribution, that trivially follows due to independence by multiplication of the univariate components. Since the cumulative distribution function of the species sensitivity density denotes the fraction of species affected (FA), it is also possible to attach a quantitative measure to the amount of exceedance by the PEC of the N(O)EC. It is shown how the estimation of the cumulative function from a small set of laboratory species through Bayesian statistics leads to an assessment of the uncertainty of the cumulative function itself.

Go to . . .

1998 SRA-Europe Table of Contents
1998 SRA-Europe Author Index
Main Abstracts Menu Page
RiskWorld Home Page