Source: Daniel Faith, Catherine Lozupone, David Nipperess, Rob Knight, The Cladistic Basis for the Phylogenetic Diversity (PD) Measure Links Evolutionary Features to Environmental Gradients and Supports Broad Applications of Microbial Ecology’s “Phylogenetic Beta Diversity” Framework International Journal of Molecular Sciences 2009, Vol. 10, Pages 4723-4741 www.mdpi.com/1422-0067/10/11/4723 Figure 2. A hypothetical phylogenetic tree, and the distribution of taxa in two localities, illustrates the link to distributions of features along environmental gradients. For details, see text following the figure.(a) The portion of a hypothetical phylogenetic tree showing 5 taxa, and two localities, j and k, from Figure 1. We now interpret the branch lengths as counting derivation of evolutionary features, according to the PD model [1,2], and we graphically indicate these features with tick marks in accord with the original PD studies [1,2]. The blue branches indicate features only represented in j; red branches indicate features only represented in k; green branches indicate features represented in both; the gray branch indicates features in neither. The PD-dissimilarity, analogous to the presence-absence version of Bray-Curtis dissimilarity , counts the number of features in j, not k (length of blue branches) plus the number of features in k, not j (length of red branches), divided by the sum of the total number of features found in each (length of blue plus length of green branches, plus length of red plus length of green branches). (b) Because each branch represents new evolutionary features arising along that branch, showing the set of sites (along a hypothetical underlying environmental gradient) that represent a given branch also shows the set of sites that have the corresponding features. This gradients diagram illustrates unimodal responses for such evolutionary features. The hollow-line arrow is a hypothetical gradient with localities i, j, k, and l. Under the unimodal response model, the features in both j and k (green branches in (a)) form the green line segment, with a black line graphically indicating the identical distribution of the corresponding features along the gradient. Blue and red branches from (a) similarly correspond to line segments along the gradient, representing the distribution of the corresponding features along the gradient. Line segments are stacked above the gradient in order to show individual coloured distribution extents. These line segments reflect the simple presence-absence case of unimodality (“binary” case , see also ). Abundance information would transform the segment into a single-peaked curve, where some point along the segment corresponds to maximum abundance. Under the assumptions of the unimodal model, Bray-Curtis type PD-dissimilarities (including that in UniFrac), applied to observations on the presence/abundance of features (branches) in localities, can be used in robust ordination methods to recover key gradients.