Multi-substance species sensitivity distributions and non-interactive action: a bivariate example

Hickey, Graeme ORCID: 0000-0002-4989-0054 and Aldenberg, Tom (2009) Multi-substance species sensitivity distributions and non-interactive action: a bivariate example. [Poster]

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Abstract

The concept of Species Sensitivity Distributions (SSDs), a proxy distribution used to model inter-species variation within a biological assemblage, has been well researched in the literature. However, research has been limited to a univariate (1D) setting; i.e. species tolerance to an individually acting toxicant. We extend the SSD model to a bivariate setting (2D), i.e. modelling species sensitivity to two substances. Although the univariate SSD is usually assumed to be (log-) Normal, assumptions regarding the 2D-SSD are not as straightforward; hampered by requirements to account for association between species sensitivity to the two substances. We utilise an area of statistical modelling known as copulas to explore possible dependence structures for the 2D-SSD, and show how to estimate the SSD parameters. The key strength of copulas is that the marginal distributions can be chosen in advance; which is appealing to risk managers for consistency. When one has estimated a 2D-SSD, it practical to extend the univariate concept of the Potentially Affected Fraction (PAF), which is defined to be the proportion of species in a biological assemblage who have their toxicological endpoints violated at prescribed environmental concentration. To enable us to extend this concept, which has been called the multi-substance PAF (msPAF), we restrict ourselves to non-interactive action (a.k.a. independent action – a misnomer). We utilise the modelling of Plackett and Hewlett to show how the msPAF reduces to a class of integrals over the 2D-SSD. We critique the differences between this method and an alternative by Traas et al. (2002; In: Posthuma L, II Suter GW, Traas TP. 2002. Species Sensitivity Distributions in Ecotoxicology. Lewis Publishers, Boca Raton, USA. 315-344.).

Item Type:	Poster
Depositing User:	Symplectic Admin
Date Deposited:	27 May 2015 08:33
Last Modified:	17 Dec 2022 01:30
URI:	https://livrepository.liverpool.ac.uk/id/eprint/2012068