The Rarefaction of Phylogenetic Diversity: Formulation, Extension and Application

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Like other measures of diversity, Phylogenetic Diversity (PD) increases monotonically and asymptotically with increasing sample size. This relationship can be described by a rarefaction curve tracing the expected PD for a given number of accumulation units. Accumulation units represent individual organisms, collections of organisms (e.g. sites), or even species (or equivalent), giving individual-based, sample-based and species-based curves respectively. The formulation for the exact analytical solution for the rarefaction of PD is given in an expanded form to demonstrate congruence with the classic formulation for the rarefaction of species richness. Rarefaction is commonly applied as a standardisation for diversity values derived from differing numbers of sampling units. However, the solution can be simply extended to create measures of phylogenetic evenness, phylogenetic beta-diversity and phylogenetic dispersion, derived from individual-based, sample-based and species-based curves respectively. This extension, termed ∆PD, is simply the initial slope of the rarefaction curve and is related to entropy measures such as PIE (Probability of Interspecific Encounter) and Gini-Simpson entropy. The application of rarefaction of PD to sample standardisation and measurement of phylogenetic evenness, phylogenetic beta-diversity and phylogenetic dispersion is demonstrated. Future prospects for PD rarefaction include the recognition of evolutionary hotspots (independent of species richness), the basis for ecological theory such as phylogeny-area relationships, and the prediction of unseen biodiversity.