Abstract
The Fair Proportion of a species in a phylogenetic tree is a very simple measure that has been used to assess its genetic value relative to the overall phylogenetic diversity represented by the tree. It has recently been proved by Fuchs and Jin to be equal to the Shapley Value of the coalitional game that sends each subset of species to its rooted Phylogenetic Diversity in the tree. We prove in this paper that this result extends to the natural translations of the Fair Proportion and the rooted Phylogenetic Diversity to rooted phylogenetic networks. We also generalize to rooted phylogenetic networks the expression for the Shapley Value of the unrooted Phylogenetic Diversity game on a phylogenetic tree established by Haake, Kashiwada and Su.
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Acknowledgements
This research was partially supported by the Spanish Ministry of Economy and Competitiveness and the ERDF through project DPI2015-67082-P (MINECO/FEDER). We thank I. García and the reviewers for their helpful suggestions on several aspects of this paper.
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Coronado, T.M., Riera, G., Rosselló, F. (2018). The Fair Proportion Is a Shapley Value on Phylogenetic Networks Too. In: Graciani, C., Riscos-Núñez, A., Păun, G., Rozenberg, G., Salomaa, A. (eds) Enjoying Natural Computing. Lecture Notes in Computer Science(), vol 11270. Springer, Cham. https://doi.org/10.1007/978-3-030-00265-7_7
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