Combinatorial properties of phylogenetic diversity indices

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...

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Bibliographic Details
Published in:Journal of mathematical biology 2020-02, Vol.80 (3), p.687-715
Main Authors: Wicke, Kristina, Steel, Mike
Format: Article
Language:English
Subjects:
Applications of Mathematics
Biodiversity
Biological evolution
Combinatorial analysis
Diversity indices
Game Theory
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Phylogenetics
Phylogeny
Species diversity
Trees
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Summary: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.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-019-01438-0