Beta diversity as the variance of community data: dissimilarity coefficients and partitioning

Beta diversity can be measured in different ways. Among these, the total variance of the community data table Y can be used as an estimate of beta diversity. We show how the total variance of Y can be calculated either directly or through a dissimilarity matrix obtained using any dissimilarity index deemed appropriate for pairwise comparisons of community composition data. We addressed the question of which index to use by coding 16 indices using 14 properties that are necessary for beta assessment, comparability among data sets, sampling issues and ordination. Our comparison analysis classified the coefficients under study into five types, three of which are appropriate for beta diversity assessment. Our approach links the concept of beta diversity with the analysis of community data by commonly used methods like ordination and anova. Total beta can be partitioned into Species Contributions (SCBD: degree of variation of individual species across the study area) and Local Contributions (LCBD: comparative indicators of the ecological uniqueness of the sites) to Beta Diversity. Moreover, total beta can be broken up into within- and among-group components by manova, into orthogonal axes by ordination, into spatial scales by eigenfunction analysis or among explanatory data sets by variation partitioning.