Chapter

Biodiversity Conservation and Phylogenetic Systematics

Volume 14 of the series Topics in Biodiversity and Conservation pp 141-172

Open Access This content is freely available online to anyone, anywhere at any time.

Phylogenetic Diversity Measures and Their Decomposition: A Framework Based on Hill Numbers

  • Anne ChaoAffiliated withInstitute of Statistics, National Tsing Hua University Email author 
  • , Chun-Huo ChiuAffiliated withInstitute of Statistics, National Tsing Hua University
  • , Lou JostAffiliated withEcoMinga Foundation

Abstract

Conservation biologists need robust, intuitive mathematical tools to quantify and assess patterns and changes in biodiversity. Here we review some commonly used abundance-based species diversity measures and their phylogenetic generalizations. Most of the previous abundance-sensitive measures and their phylogenetic generalizations lack an essential property, the replication principle or doubling property. This often leads to inconsistent or counter-intuitive interpretations, especially in conservation applications. Hill numbers or the “effective number of species” obey the replication principle and thus resolve many of the interpretational problems. Hill numbers were recently extended to incorporate phylogeny; the resulting measures take into account phylogenetic differences between species while still satisfying the replication principle. We review the framework of phylogenetic diversity measures based on Hill numbers and their decomposition into independent alpha and beta components. Both additive and multiplicative decompositions lead to the same classes of normalized phylogenetic similarity or differentiation measures. These classes include multiple-assemblage phylogenetic generalizations of the Jaccard, Sørensen, Horn and Morisita-Horn measures. For two assemblages, these classes also include the commonly used UniFrac and PhyloSør indices as special cases. Our approach provides a mathematically rigorous, self-consistent, ecologically meaningful set of tools for conservationists who must assess the phylogenetic diversity and complementarity of potential protected areas. Our framework is applied to a real dataset to illustrate (i) how to use phylogenetic diversity profiles to completely convey species abundances and phylogenetic information among species in an assemblage; and (ii) how to use phylogenetic similarity (or differentiation) profiles to assess phylogenetic resemblance or difference among multiple assemblages.

Keywords

Diversity Diversity decomposition Hill numbers Phylogenetic diversity Replication principle Species diversity