Decomposing phylogenetic entropy into α, β and γ components

Abstract

Measuring the phylogenetic diversity of communities has become a key issue for biogeography and conservation. However, most diversity indices that rely on interspecies phylogenetic distances may increase with species loss and thus violate the principle of weak monotonicity. Moreover, most published phylogenetic diversity indices ignore the abundance distribution along phylogenetic trees, even though lineage abundances are crucial components of biodiversity. The recently introduced concept of phylogenetic entropy overcomes these limitations, but has not been decomposed across scales, i.e. into α, β and γ components. A full understanding of mechanisms sustaining biological diversity within and between communities needs such decomposition. Here, we propose an additive decomposition framework for estimating α, β and γ components of phylogenetic entropy. Based on simulated trees, we demonstrate its robustness to phylogenetic tree shape and species richness. Our decomposition fulfils the requirements of both independence between components and weak monotonicity. Finally, our decomposition can also be adapted to the partitioning of functional diversity across different scales with the same desirable properties.

Figure 1.

A hypothetical case study illustrating the calculation of α-, β- and γ-phylogenetic diversities. (a) Phylogenetic relationships among three species in a regional pool. Phylogenetic distances (branch lengths) among pairs of species are indicated on the dendrogram. (b) Local abundances of species A, B and C in two hypothetical regions, each divided into two communities (C1 and C2). The total abundance per species and per site is indicated. (c) α, β and γ components estimated for each regional pool and each local community. H_αCx: local phylogenetic diversity; H_γ: regional phylogenetic diversity; : mean local phylogenetic diversity estimated on local communities; H_βst: phylogenetic turnover.

Figure 2.

α-, β- and γ-diversity values estimated on communities sampled among (a) 50-species or (b) 100-species trees generated under the Yule (closed circles) or PDA (open circles) model. α- (based on average local diversity values ()), β- and γ-diversity values were calculated on pairs of communities composed of one 20-species community and one n-community (n ranging from 1 to 50 or 1 to 100 species depending on the regional tree size). β-diversity is expressed as the proportion of biological turnover (i.e. H_βst = 1 − [/H_γ]).