Estimating sample size for inference about the Shannon-Weaver and the Simpson Indices of species diversity

Abstract

A framework for a priori estimation of the expected sampling variances of the Shannon-Weaver and the Simpson indices of species diversity is developed by the introduction of the most probable relative species abundance distribution (MOPSAD). MOPSAD gives the prior probability of a species' relative abundance. The beta distribution is used here as the prior for MOPSAD. Sample sizes needed for efficient statistical inference and hypothesis testing about the two indices are provided for 16 distinct beta priors for MOPSAD. Shannon-Weaver and Simpson's diversity indices in plant communities expected to have a `U'-shaped or a J-shaped MOPSAD will have large sampling variances. For the same statistical resolution the Simpson index requires about nine times as many samples as the Shannon-Weaver index. The impact of a positive or negative spatial association among species on the variance of the diversity indices was also assessed. In general, spatial association had little impact on the variance of the indices; it suffices to increase the sample size by about 5% as a safeguard against variance inflation due to spatial associations.