  In microbial ecology studies, the most commonly used ways of investigating
alpha (within-sample) diversity are either to apply count-only measures such as
Simpson's index to Operational Taxonomic Unit (OTU) groupings, or to use
classical phylogenetic diversity (PD), which is not abundance-weighted.
Although alpha diversity measures that use abundance information in a
phylogenetic framework do exist, but are not widely used within the microbial
ecology community. The performance of abundance-weighted phylogenetic diversity
measures compared to classical discrete measures has not been explored, and the
behavior of these measures under rarefaction (sub-sampling) is not yet clear.
In this paper we compare the ability of various alpha diversity measures to
distinguish between different community states in the human microbiome for
three different data sets. We also present and compare a novel one-parameter
family of alpha diversity measures, BWPD_\theta, that interpolates between
classical phylogenetic diversity (PD) and an abundance-weighted extension of
PD. Additionally, we examine the sensitivity of these phylogenetic diversity
measures to sampling, via computational experiments and by deriving a closed
form solution for the expectation of phylogenetic quadratic entropy under
re-sampling. In all three of the datasets considered, an abundance-weighted
measure is the best differentiator between community states. OTU-based
measures, on the other hand, are less effective in distinguishing community
types. In addition, abundance-weighted phylogenetic diversity measures are less
sensitive to differing sampling intensity than their unweighted counterparts.
Based on these results we encourage the use of abundance-weighted phylogenetic
diversity measures, especially for cases such as microbial ecology where
species delimitation is difficult.
