ArticleJournal of mathematical biology2015
Equality of Shapley value and fair proportion index in phylogenetic trees.
Article in Journal of mathematical biology, 2015. 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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10 citing papers in PubMed.
- Sackin indices for labeled and unlabeled classes of galled trees.Journal of mathematical biology · 2025Article
- Neutral phylogenetic models and their role in tree-based biodiversity measures.Philosophical transactions of the Royal Society of London. Series B, Biological sciences · 2025Review
- Phylogenetic Diversity Indices from an Affine and Projective Viewpoint.Bulletin of mathematical biology · 2024Article
- The robustness of phylogenetic diversity indices to extinctions.Journal of mathematical biology · 2024Article
- Predicting Long Pendant Edges in Model Phylogenies, with Applications to Biodiversity and Tree Inference.Systematic biology · 2023Article
- Mathematical indices for the influence of risk factors on the lethality of a disease.Journal of mathematical biology · 2021Article
- A simple derivation of the mean of the Sackin index of tree balance under the uniform model on rooted binary labeled trees.Mathematical biosciences · 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
- Combinatorial properties of phylogenetic diversity indices.Journal of mathematical biology · 2020Article
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2 authors.
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Abstract
The Shapley value and the fair proportion index of phylogenetic trees have been introduced recently for the purpose of making conservation decisions in genetics. Moreover, also very recently, Hartmann (J Math Biol 67:1163-1170, 2013) has presented data which shows that there is a strong correlation between a slightly modified version of the Shapley value (which we call the modified Shapley value) and the fair proportion index. He gave an explanation of this correlation by showing that the contribution of both indices to an edge of the tree becomes identical as the number of taxa tends to infinity. In this note, we show that the Shapley value and the fair proportion index are in fact the same. Moreover, we also consider the modified Shapley value and show that its covariance with the fair proportion index in random phylogenetic trees under the Yule-Harding model and uniform model is indeed close to one.
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