Quantifying the difference between phylogenetic diversity and diversity indices

Bordewich, Magnus; Semple, Charles

Abstract

Phylogenetic diversity is a popular measure for quantifying the biodiversity of a collection Y of species, while phylogenetic diversity indices provide a way to apportion phylogenetic diversity to individual species. Typically, for some specific diversity index, the phylogenetic diversity of Y is not equal to the sum of the diversity indices of the species in Y. In this paper, we investigate the extent of this difference for two commonly-used indices: Fair Proportion and Equal Splits. In particular, we determine the maximum value of this difference under various instances including when the associated rooted phylogenetic tree is allowed to vary across all rooted phylogenetic trees with the same leaf set and whose edge lengths are constrained by either their total sum or their maximum value.

Citation

Bordewich, M., & Semple, C. (2024). Quantifying the difference between phylogenetic diversity and diversity indices. Journal of Mathematical Biology, 88(4), Article 40. https://doi.org/10.1007/s00285-024-02059-y

• Journal Article Type: Article
• Acceptance Date: Feb 5, 2024
• Online Publication Date: Mar 6, 2024
• Publication Date: Apr 1, 2024
• Deposit Date: Mar 7, 2024
• Publicly Available Date: Mar 8, 2024
• Journal: Journal of Mathematical Biology
• Print ISSN: 0303-6812
• Electronic ISSN: 1432-1416
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 88
• Issue: 4
• Article Number: 40
• DOI: https://doi.org/10.1007/s00285-024-02059-y
• Keywords: Diversity indices, 05C85, 68R10, Equal Splits index, Phylogenetic tree, Fair Proportion index, Phylogenetic diversity
• Public URL: https://durham-repository.worktribe.com/output/2312322