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

Ecologists needing to quantify differences between communities of organisms often use measures of dissimilarity that incorporate both differences in species composition and information about the phylogenetic relatedness of the species. Many variants on these distances are available to analysts, but their properties are not well developed. We analyze a phylogenetically-informed distance that has been described many times in the literature under different names. 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 can be interpreted as modulating the influence of the basal structure, how this modification can give more power for identifying different scales of phylogenetically-structured effects, and show examples in simulated and real datasets.