Phylogenetic diversity indices from an affine and projective viewpoint

Moulton, Vincent ORCID: https://orcid.org/0000-0001-9371-6435, Spillner, Andreas and Wicke, Kristina (2024) Phylogenetic diversity indices from an affine and projective viewpoint. Bulletin of Mathematical Biology, 86. ISSN 0092-8240

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Abstract

Phylogenetic diversity indices are commonly used to rank the elements in a collection of species or populations for conservation purposes. The derivation of these indices is typically based on some quantitative description of the evolutionary history of the species in question, which is often given in terms of a phylogenetic tree. Both rooted and unrooted phylogenetic trees can be employed, and there are close connections between the indices that are derived in these two different ways. In this paper, we introduce more general phylogenetic diversity indices that can be derived from collections of subsets (clusters) and collections of bipartitions (splits) of the given set of species. Such indices could be useful, for example, in case there is some uncertainty in the topology of the tree being used to derive a phylogenetic diversity index. As well as characterizing some of the indices that we introduce in terms of their special properties, we provide a link between cluster-based and split-based phylogenetic diversity indices that uses a discrete analogue of the classical link between affine and projective geometry. This provides a unified framework for many of the various phylogenetic diversity indices used in the literature based on rooted and unrooted phylogenetic trees, generalizations and new proofs for previous results concerning tree-based indices, and a way to define some new phylogenetic diversity indices that naturally arise as affine or projective variants of each other or as generalizations of tree-based indices.

Item Type: Article
Faculty \ School: Faculty of Science > School of Computing Sciences
UEA Research Groups: Faculty of Science > Research Groups > Norwich Epidemiology Centre
Faculty of Medicine and Health Sciences > Research Groups > Norwich Epidemiology Centre
Faculty of Science > Research Groups > Computational Biology
Depositing User: LivePure Connector
Date Deposited: 01 Jul 2024 11:33
Last Modified: 14 Jul 2024 06:34
URI: https://ueaeprints.uea.ac.uk/id/eprint/95722
DOI: 10.1007/s11538-024-01332-x

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