Eigenvector estimation of phylogenetic and functional diversity

1. Although species richness is the most common metric for biodiversity, it is important to consider that among-species differences matter for many important processes such as ecosystem functioning and assembly patterns. Thus, alternative metrics have been proposed to measure phylogenetic (PD) and functional diversity (FD). 2. Here, we analysed the correlation structure and the geographic patterns of different phylogenetic and functional diversity metrics using 1000 Carnivora (mammals) assemblages distributed world-wide. We also proposed a general approach to estimate these metrics based on phylogenetic eigenvector regressions. 3. We showed that the cumulative variance of phylogenetic eigenvectors within assemblages converges to one metric of phylogenetic clustering, the phylogenetic species variability (PSV), which was recently proposed in the literature. Phylogenetic eigenvectors have also been used to model trait variation (i.e. body mass); therefore, the same reasoning allows us to decouple trait diversity (i.e. body mass) into phylogenetic [FD(P)] and specific [FD(S)] components. The cumulative variance of these components within assemblages, for a single trait or multiple traits, offers a direct estimate of the evolutionary and ecological components of functional variation. Our results indicated that the variance of the phylogenetic component of body mass [FD(P)] estimated within assemblages was highly correlated with a common measure of functional diversity (Rao's Q). 4. Our general approach based on phylogenetic eigenvectors provides similar results when compared to other metrics of FD and PD, but also has some important advantages. First, it allows a direct interpretation of at which hierarchical level in the phylogeny (expressed by different sets of eigenvectors) the patterns in PD and FD appear. Secondly, phylogenetic components of FD can be analysed directly because of the partition of functional diversity into FD(P) and FD(S), so it eliminates the need to generate 'a posteriori' phylogenetic correlations between PD and FD based on independently derived metrics, as well as of these metrics with other components of environmental variation.