PERMANOVA, ANOSIM, and the Mantel test in the face of heterogeneous dispersions: What null hypothesis are you testing?

ANOSIM, PERMANOVA, and the Mantel test are all resemblance‐based permutation methods widely used in ecology. Here, we report the results of the first simulation study, to our knowledge, specifically designed to examine the effects of heterogeneity of multivariate dispersions on the rejection rates of these tests and on a classical MANOVA test (Pillai's trace). Increasing differences in dispersion among groups were simulated under scenarios of changing sample sizes, correlation structures, error distributions, numbers of variables, and numbers of groups for balanced and unbalanced one‐way designs. The power of these tests to detect environmental impacts or natural large‐scale biogeographic gradients was also…