Decomposition of trait diversity among the nodes of a phylogenetic tree

Biodiversity studies aim to explain spatiotemporal patterns of species distributions. We propose a new methodology in which trait diversity is measured by the quadratic entropy index, with distances among species calculated from differences among trait states. We show how this index of trait diversity can be decomposed among the nodes of a phylogenetic tree. The contribution to trait diversity of a particular node is equal to the trait diversity among the n groups of species descending from it multiplied by an abundance weight (either proportional to the number of descendant species or to their relative abundance). We developed three tests to characterize the phylogenetic pattern of trait diversity and evaluated our methodology with seven evolutionary models. The power of the tests was high and increased with the number of extant taxa and the number of traits analyzed. The Type I error analyses (erroneous rejection of true null hypotheses) suggested that our tests are neither too liberal nor too conservative. Species abundances were found to modify the phylogenetic signal in trait diversity if only a few species were abundant and if species abundances were correlated to their phylogenetic relatedness and/or their trait states. By comparing phylogenetic signals in trait diversity from the local to the metacommunity level, we explored the factors that structure butterfly trait diversity in calcareous grasslands of northern France and southern Belgium. We show that partial phylogenetic signal in traits combined with habitat filtering determined which species and lineages were able to co‐occur locally. Interestingly, no phylogenetic signal was detected when measures of abundance were included in our analyses. For most species and clades, the abundance distribution among communities at the regional scale was random. Overall, studying trait diversity in a phylogenetic context allows the link between current local ecological processes and lineage‐dependent historical evolutionary factors to be thoroughly investigated.