Of beta diversity, variance, evenness, and dissimilarity

The amount of variation in species composition among sampling units or beta diversity has become a primary tool for connecting the spatial structure of species assemblages to ecological processes. Many different measures of beta diversity have been developed. Among them, the total variance in the community composition matrix has been proposed as a single-number estimate of beta diversity. In this study, I first show that this measure summarizes the compositional variation among sampling units after nonlinear transformation of species abundances. Therefore, it is not always adequate for estimating beta diversity. Next, I propose an alternative approach for calculating beta diversity in which variance is substituted by a weighted measure of concentration (i.e., an inverse measure of evenness). The relationship between this new measure of beta diversity and so-called multiple-site dissimilarity measures is also discussed.