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The equivalence of two phylogenetic biodiversity measures: the Shapley value and Fair Proportion index
Citation
Hartmann, K, The equivalence of two phylogenetic biodiversity measures: the Shapley value and Fair Proportion index, Journal of Mathematical Biology, 67, (5) pp. 1163-1170. ISSN 1432-1416 (2013) [Refereed Article]
Copyright Statement
Copyright 2012 Springer-Verlag
DOI: doi:10.1007/s00285-012-0585-y
Abstract
Most biodiversity conservation programs are forced to prioritise species
in order to allocate their funding. This paper contains a mathematical proof that provides
biological support for one common approach based on phylogenetic indices.
Phylogenetic trees describe the evolutionary relationships between a group of taxa.
Two indices for computing the distinctiveness of each taxon in a phylogenetic tree
are considered here—the Shapley value and the Fair Proportion index. These indices
provide a measure of the importance of each taxon for overall biodiversity and have
been used to prioritise taxa for conservation. The Shapley value is the biodiversity contribution
a taxon is expected to make if all taxa are equally likely to become extinct.
This interpretation makes it appealing to use the Shapley value in biodiversity conservation
applications. The Fair Proportion index lacks a convenient interpretation,
however it is significantly easier to calculate and understand. It has been empirically
observed that there is a high correlation between the two indices. This paper shows the
mathematical basis for this correlation and proves that as the number of taxa increases,
the indices become equivalent. Consequently in biodiversity prioritisation the simpler
Fair Proportion index can be used whilst retaining the appealing interpretation of the
Shapley value.
Item Details
Item Type: | Refereed Article |
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Keywords: | phylogenetic diversity, biodiversity, conservation, Shapley fair proportion |
Research Division: | Mathematical Sciences |
Research Group: | Applied Mathematics |
Research Field: | Biological Mathematics |
Objective Division: | Environment |
Objective Group: | Flora, Fauna and Biodiversity |
Objective Field: | Flora, Fauna and Biodiversity at Regional or Larger Scales |
UTAS Author: | Hartmann, K (Dr Klaas Hartmann) |
ID Code: | 80830 |
Year Published: | 2013 (online first 2012) |
Web of Science® Times Cited: | 15 |
Deposited By: | Sustainable Marine Research Collaboration |
Deposited On: | 2012-11-13 |
Last Modified: | 2016-12-08 |
Downloads: | 297 View Download Statistics |
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