Statistical performance of a multicomparison method for generalized species diversity indices under realistic empirical scenarios

The Pallmann-Scherer test is a promising multicomparison procedure to test statistical hypotheses regarding generalized diversity/entropy indices, such as Tsallis family and Hill numbers (Sq and Hq, respectively), which represent alternative ways of profiling species diversity along a gradient of emphasis on species richness versus evenness in abundance distributions. Given the pressing importance of reliably comparing diversity across ecological communities, and since only a few of such procedures are currently available, knowing its statistical performance under realistic ecological scenarios is of strategic importance. In this paper, we evaluated the performance of the Pallmann-Scherer test using computer simulations of communities following different species-abundance distributions, spatially aggregated as widely observed empirically, and sampled by a commonly used quadrat procedure. We found that the test is very conservative for both Sq and Hq, leading to biased significance levels, with low probabilities of type-I error but high probabilities of type-II error (i.e., low statistical power). Although it should be acknowledged that the current method represents an important starting point, further improvements must be made in order to enhance its power and meet the required standards in comparative studies of diversity.