Extended dissimilarity: a method of robust estimation of ecological distances from high beta diversity data

It is widely accepted that reliable ordination of ecological data requires a strong linear or ordinal relationship between the dissimilarity of sites, based on species composition, and the ecological distance between them. Certain dissimilarity measures, having the property that they take a fixed maximum value when sites have no species in common, have been shown to be strongly correlated with ecological distance. For ecological gradients of moderate length (moderate beta diversity), such measures, in conjunction with non-metric multidimensional scaling, will reliably yield successful ordinations. However, as beta diversity increases, more sites have no species in common, and such measures invariably under-estimate ecological distance for such sites. Thus ordinations of data with high species turnover (high beta diversity) may fail. Extended dissimilarities are defined using an iterative adaptation of flexible shortest path adjustment applied to the matrix of dissimilarities with fixed maximum values. By means of theoretical argument and simulations, this is shown to lead to far stronger correlations between the adjusted site dissimilarity and ecological distance for ecological gradients of greater length than previously considered. Hence ordinations of extended dissimilarities, by means of either metric or non-metric scaling techniques, are shown to outperform corresponding ordinations of unadjusted dissimilarities, with the difference increasing with increasing beta diversity.