# Calculations and Comparisons

## Simple Calculations Based on PD

Many possible calculations can be based on counting-up features within the PD framework. As examples, complementarity, endemism, and dissimilarities between objects all can be calculated. In principle, every index conventionally defined in ecology at the species level has its counterpart for other biodiversity units. Counting-up the total number of features (as units) represented by a set of taxa

**Fig. 1 For each tree, the tick marks correspond to loss in PD if each species from area B is lost. The tick marks show how much PD is uniquely represented by that area. PD endemism sees the scenario on the left as implying greater endemism of area B, compared to the scenario on the right. The We method cannot distinguish between the two scenarios because it ignores a critical aspect of phylogenetic context, called complementarity**

remains the core measure of “diversity”, but the other calculations capture other aspects – for example, expected change in biodiversity as a result of extinction.

Useful PD calculations for biodiversity comparisons among geographic localities include PD-dissimilarities between places or samples (see Lozupone and Knight 2005) and PD-endemism (Faith et al. 2004; illustrated in Fig. 1). Another useful calculation is “expected PD”, based on estimated probabilities of extinction. Here, species' estimated extinction probabilities indicate amounts of “expected PD loss” (discussed further below; see also Faith 2008, 2013). All these calculations operate as if we are applying the standard species-based measures at the features level. Thus, these newer calculations make sense, given the interpretation of PD as counting-up features.

This interpretation has helped to justify other recent proposed extensions of PD. One important case is the integration of abundance information. Faith and Richards (2012) noted that a PD-based Hill numbers framework (Chao et al. 2010; see also Chao et al. chapter “Phylogenetic Diversity Measures and Their Decomposition: A Framework Based on Hill Numbers”) can be interpreted as an application of the standard species-level Hill numbers calculation, but with evolutionary features (as indicated by PD) substituted for species. Thus, the basic PD evolutionary model provides a simple justification for a phylogenetic measure integrating abundance information.