Dispersion-based weighting of species counts in assemblage analyses

Multivariate analysis of species assemblage data often begins with transformation of abundances, to downweight contributions from dominant taxa to Bray-Curtis dissimilarities computed among samples. Although usually effective, global transformation is a blunt tool: it ignores differences in the variance structure of counts of individual species. Species which are highly spatially clustered should logically be given less weight than those with similar mean abundance but whose replicate counts have the lower variance associated with Poisson distributions (for which individual organisms arrive randomly and independently into the sample). Where replicates are available within sample groups specified a priori, this differential downweighting is achieved by dividing the counts for each species by their index of dispersion D, the variance to mean ratio, a clustering ('clumping') measure calculated from replicates within a group, and then averaged across groups. The procedure is justified by assuming a generalised Poisson model for counts, allowing different species to have arbitrarily differing degrees of clustering. Downweighting is applied only where a species shows significant evidence of clumping, this being tested by a powerful, exact permutation test that replaces the standard (large-sample) 2 test for D = 1, which is often invalid because of low 'expected' frequencies. The resulting dispersion-weighted data matrix has a common (Poisson-like) variance structure across species, but unchanged relative responses of a species in different groups. Transformation may still be needed but now only to downweight consistently abundant species relative to equally consistent but less numerous species, rather than also dealing with erratic counts. Dispersion weighting is shown to be effective in 3 studies that examine: soft-sediment copepods in the metal-polluted Fal estuary, UK; benthic macrofauna of mangrove forests in Bicentennial Park, New South Wales, Australia; and sediment nematodes within and outside seagrass beds in the Yealm estuary, UK. A fourth data set, on macrobenthos from Loch Creran, UK, is added to a comparison of the differing cross-species distributions of the dispersion index.