Confidence intervals and hypothesis testing for beta diversity

Under R. H. Whittaker's "multiplicative" perspective of species diversity, regional (gamma) diversity is viewed as the product of within-assemblage (alpha) diversity and among-assemblage (eta) diversity. An additive perspective, which views alpha and beta as complements, has recently been endorsed for the study of spatial patterns in species diversity. Here we highlight the relation between the two measures of beta diversity, showing the multiplicative beta as a simple summary statistic of the relation between the additive components. We provide analytical solutions for approximate confidence intervals and hypothesis tests for both measures of beta diversity. We also present results of simulation studies that can help delimit the sample sizes needed for future studies, and which suggest the effect-size likely to be detected with samples of a given size.