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(60-06) The Fraction Affected Distribution (FAD) in relation to Exposure Concentration and Species Sensitivity Distributions. Aldenberg, Tom*,1, Jaworska, J.S.2, Traas, T.P.1, 1 RIVM, Bilthoven, /, Netherlands2 Procter & Gamble, Strombeek-Bever, /, Belgium ABSTRACT- The estimation of the risk of toxicants to biological species, when both concentrations and species sensitivities are uncertain is a central issue in Probabilistic Ecological Risk Assessment (PERA). When the Exposure Concentration Distribution (ECD) overlaps with the Species Sensitivity Distribution (SSD), there is a risk of Exposure Concentration (EC) to exceed Species Sensitivity (SS). The method of Joint Probability Curves (JPCs) is a way to graphically summarize this risk. Exceedence Profile Plots are JPCs of EC exceedence probabilities against Fraction of species Affected (FA) over varying EC. Cumulative Profile Plots are JPCs of FA against ECD CDF values over varying EC. The latter are easier to construct and interpret than the former. The area under the curve (AUC) of either JPC is a measure of the risk of the substance to the species represented by the SSD. The problem of a random EC to exceed a random SS is called the Probability of Failure (POF) in Reliability Engineering. Mathematically, it can be shown that the AUC is identical to the POF for any combination of ECD and SSD statistical functions. With Normal CDFs, this risk is easily calculated and tabulated. Another interpretation of the risk of EC to species is Expected Total Risk (ETR), as advocated in the WERF method. The term "Expected" follows, because the risk of species affected at varying EC is multiplied by the probability of occurrence of ECs, and summed. The major result of the paper is the derivation of the distribution of FA that indeed has ETR as a mean. General expressions for PDFs and CDFs of this so-called Fraction Affected Distribution (FAD) are derived for arbitrary PDFs of EC and SSD. FADs can have Beta PDF-like shapes, as well as asymptotes at 0%, and/or 100% FA. The latter occurs when the EC is more variable than the SSD. From the FAD, percentiles of the Ecological Risk to species can be calculated and reported in addition to the ETR. Key words: Probabilistic Risk Assessment , SSD |
