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Robert H. Whittaker defined beta diversity as the variation in species composition among sites in a geographic area. Beta diversity is a key concept for understanding the functioning of ecosystems, for the conservation of biodiversity, and for ecosystem management. This paper explains how hypotheses about the origin of beta diversity can be tested by partitioning the spatial variation of community composition data (presence– absence or abundance data) with respect to environmental variables and spatial base functions. We compare two statistical methods to accomplish that. The sum‐of‐squares of a community composition data table, which is one possible measure of beta diversity, is correctly partitioned by canonical ordination; hence, canonical partitioning produces correct estimates of the different portions of community composition variation. In recent years, several authors interested in the variation in community composition among sites (beta diversity) have used another method, variation partitioning on distance matrices (Mantel approach). Their results led us to compare the two partitioning approaches, using simulated data generated under hypotheses about the variation of community composition among sites. The theoretical developments and simulation results led to the following observations: (1) the variance of a community composition table is a measure of beta diversity. (2) The variance of a dissimilarity matrix among sites is not the variance of the community composition table nor a measure of beta diversity; hence, partitioning on distance matrices should not be used to study the variation in community composition among sites. (3) In all of our simulations, partitioning on distance matrices underestimated the amount of variation in community composition explained by the raw‐data approach, and (4) the tests of significance had less power than the tests of canonical ordination. Hence, the proper statistical procedure for partitioning the spatial variation of community composition data among environmental and spatial components, and for testing hypotheses about the origin and maintenance of variation in community composition among sites, is canonical partitioning. The Mantel approach is appropriate for testing other hypotheses, such as the variation in beta diversity among groups of sites. Regression on distance matrices is also appropriate for fitting models to similarity decay plots.
Legendre et al. (Tue,) studied this question.