Statistics and partitioning of species diversity, and similarity among multiple communities

Species richness, Shannon information, and Simpson diversity are the three most commonly used nonparametric measures of species diversity. The sampling bias and variance of these measures differ greatly. Species richness may be seriously underestimated for even very large samples from a speciose community. The bias in species richness and Shannon information depend on unknown parameters of the species abundance distribution. An unbiased estimator exists only for Simpson diversity. Each of these measures is concave, so that the total diversity in a pooled set of communities exceeds (or equals) the average diversity within communities. The total diversity in a set of communities can therefore be partitioned into positive, additive components within and among communities, corresponding to alpha- and beta-diversity. Partitioning Simpson diversity corresponds to an analysis of variance. The proportion of the total diversity found within communities provides a natural measure of similarity among multiple communities. The expected similarity among multiple random samples from the same community depends on the number of samples and on the underlying measure of diversity.