A decomposition of a phylogenetically-informed distance between species assemblages into basal and terminal components

Ecologists seeking to quantify differences between species assemblages often rely on dissimilarity measures that incorporate both species composition and the phylogenetic relatedness among species. Although many variants of such distances are available, their statistical properties remain poorly understood. For instance, an analyst comparing species abundances in two types of sites might apply PERMANOVA with UniFrac as the dissimilarity measure and obtain one result, but using PERMANOVA with Rao’s dissimilarity coefficient could yield a different conclusion. In other contexts, the pattern of significance might be reversed. While such discrepancies are well documented empirically, the mathematical underpinnings of this phenomenon are not well understood. We analyze a phylogenetically-informed distance that has been described many times in the literature under different names. Specifically, it corresponds to Rao’s DISC (Radhakrishna, 1982) with a certain choice of distance between species, has also been referred to as H (Jérôme et al., 2007), δCO (Sandrine et al., 2004), and is related to PST (Olivier and Bruno, 2007). We show that we can decompose this distance into pieces that describe basal and terminal phylogenetic structure and show that it places an overwhelming amount of weight on the basal phylogenetic structure. We show that a related class of distances used in other contexts can be interpreted as modulating the influence of the basal structure, demonstrate how this modification can increase power for detecting phylogenetically-structured effects at different scales, and present examples using both simulated and real datasets.