Combinatorial properties of phylogenetic diversity indices

Kristina Wicke, Mike Steel

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Phylogenetic diversity indices provide a formal way to apportion ‘evolutionary heritage’ across species. Two natural diversity indices are Fair Proportion (FP) and Equal Splits (ES). FP is also called ‘evolutionary distinctiveness’ and, for rooted trees, is identical to the Shapley Value (SV), which arises from cooperative game theory. In this paper, we investigate the extent to which FP and ES can differ, characterise tree shapes on which the indices are identical, and study the equivalence of FP and SV and its implications in more detail. We also define and investigate analogues of these indices on unrooted trees (where SV was originally defined), including an index that is closely related to the Pauplin representation of phylogenetic diversity.

Original languageEnglish (US)
Pages (from-to)687-715
Number of pages29
JournalJournal of Mathematical Biology
Issue number3
StatePublished - Feb 1 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


  • Biodiversity measures
  • Diversity index
  • Phylogenetic tree
  • Shapley value


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