ArticleJournal of mathematical biology2013
The equivalence of two phylogenetic biodiversity measures: the Shapley value and Fair Proportion index.
Article in Journal of mathematical biology, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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Who cites it
10 citing papers in PubMed.
- Normative assembly rule reveals fairness in microbial communities.PLoS biology · 2026Article
- Components of functional diversity revisited: A new classification and its theoretical and practical implications.Ecology and evolution · 2023Review
- The United States Swine Pathogen Database: integrating veterinary diagnostic laboratory sequence data to monitor emerging pathogens of swine.Database : the journal of biological databases and curation · 2021Article
- Mathematical indices for the influence of risk factors on the lethality of a disease.Journal of mathematical biology · 2021Article
- Correlation between Shapley values of rooted phylogenetic trees under the beta-splitting model.Journal of mathematical biology · 2020Article
- Biodiversity, Shapley value and phylogenetic trees: some remarks.Journal of mathematical biology · 2020Article
- I-HEDGE: determining the optimum complementary sets of taxa for conservation using evolutionary isolation.PeerJ · 2016Article
- Equality of Shapley value and fair proportion index in phylogenetic trees.Journal of mathematical biology · 2015Article
- Article
- Measuring Evolutionary Isolation for Conservation.PloS one · 2014Article
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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.
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