On resemblance measures for ecological studies, including taxonomic dissimilarities and a zero-adjusted Bray–Curtis coefficient for denuded assemblages

Bray–Curtis similarity is widely employed in multivariate analysis of assemblage data, for sound biological reasons. This paper discusses two problems, however, with its practical application: its behaviour is erratic (or even undefined) for the vanishingly sparse samples that may be found as an end-point to a severe impact gradient, or a start-point in colonisation studies; and, in common with all similarity measures on species-level data, it is sensitive to inconsistency of taxonomic identification through time. It is shown that the latter problem is ameliorated by application of ‘taxonomic dissimilarity’ coefficients, a natural extension of the concept of taxonomic distinctness indices. Two previous suggestions for use with presence/absence data, denoted here by Γ+ and Θ+, are noted to be simple generalisations of the Bray–Curtis and Kulczynski measures, respectively. Also seen is their ability to permit ordinations of assemblages from wide geographic scales, with no species in common, and for which Bray–Curtis would return zero similarity for all pairs of samples.The primary problem addressed, however, is that of denuded or entirely blank samples. Where it can be convincingly argued that impoverished samples are near-blank from the same cause, rather than by random occurrences from inadequate sample sizes (tow length, core diameter, transect or quadrat size etc.), a simple adjustment to the form of the Bray–Curtis coefficient can generate meaningful MDS displays which would otherwise collapse, and can improve values of the ANOSIM R statistic (increased separation of groups in multivariate space). It is also shown to have no effect at all on the normal functioning of a Bray–Curtis analysis when at least a modest amount of data is present for all samples.Examination of the properties of this ‘zero-adjusted’ Bray–Curtis measure goes hand-in-hand with a wider discussion of the efficacy of competing similarity, distance or dissimilarity coefficients (collectively: resemblance measures) in community ecology. The inherent biological guidelines underlying the ‘Bray–Curtis family’ of measures (including Kulczynski, Sorenson, Ochiai and Canberra dissimilarity) are made explicit. These and other commonly employed measures (e.g. Euclidean, Manhattan, Gower and chi-squared distances) are calculated for several ‘classic’ data sets of impact events or gradients in space and time. Behaviour of particular coefficients is judged against the interpretability of the resulting ordination plots and an objective measure of the ability to discriminate between a priori defined hypotheses, representing impact conditions. A second-stage MDS plot of a set of resemblance coefficients, based on the respective similarities of the multivariate patterns each generates (an MDS of MDS plots, in effect), is seen to be useful in determining which coefficients are extracting essentially different information from the same assemblage matrix. This suggests a mechanism for practical classification of the plethora of resemblance measures defined in the literature. Similarity-based ANOSIM R statistics and Spearman ρ correlations, whose non-parametric structure make them absolutely comparable across different resemblance measures, answer questions about whether the different information extracted by some coefficients is more, or less, helpful to the final biological interpretation.