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(M/MF141) Multiple-toxicant Hazardous Concentration and Fraction Affected from correlated single-toxicant Species Sensitivity Distributions. Aldenberg, Tom1, Jaworska, Joanna 2, 1 2 ABSTRACT- Species Sensitivity Distributions (SSD) are mostly univariate unimodal statistical PDFs (Probability Density Functions) describing the variation of NOECs or other endpoints of different biological species. When a fixed set of species is tested for different toxicants, each applied separately, the bi- or multivariate scatter of species sensitivities can be described by bi- or multivariate PDFs, that may or may not show correlation. While the FA (Fraction Affected) at a given log-concentration for a single-toxicant SSD is given by the value of the CDF (Cumulative Distribution Function) at that concentration, the classical CDF (Cumulative Distribution Function) of multivariate PDFs describes the fraction of species that have all individual toxicant NOECs exceeded by a given mixture of concentrations. The multiple-toxicant FA is defined to be the fraction of species exceeded by one, more, or all toxicants simultaneously. For two toxicants, FA is the integral of the bivariate PDF over an L-shaped region being the union of the sets of species that are exceeded by either one of the toxicants or both. FA is a surface for which contour lines can be plotted overlayed with contour lines of the bivariate PDF. The mathematics is similar to that of Plackett and Hewlett in 1948 for correlations of tolerance distributions of individual insects. The two-toxicant HC5 (Hazardous Concentration for 5% of the species) is the 5th FA contour line of the FA surface. For the bivariate normal with elliptic PDF contour lines, the FA at the midpoint, i.e. a mixture of two log HC50's is equal to: 1-ArcTan[Sqrt[(1+rho)/(1-rho)]]/Pi, with rho the correlation coefficient of the SSDs. A data set of Slooff and Canton (1983) for the susceptibility of 11 freshwater species to 8 toxicants is used to illustrate multivariate correlated SSDs. Correlation plays an important role in estimation of FA because the higher the correlation the smaller the FA for the mixture. Lack of correlation leads to the most severe results i.e. the highest FA affected. Key words: mixtures, effects assessment, uncertainty |
