The space of equidistant phylogenetic cactuses

Huber, Katharina T., Moulton, Vincent, Owen, Megan, Spillner, Andreas and St. John, Katherine (2024) The space of equidistant phylogenetic cactuses. Annals of Combinatorics, 28. pp. 1-32. ISSN 0218-0006

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Abstract

An equidistant X-cactus is a type of rooted, arc-weighted, directed acyclic graph with leaf set X, that is used in biology to represent the evolutionary history of a set X of species. In this paper, we introduce and investigate the space of equidistant X-cactuses. This space contains, as a subset, the space of ultrametric trees on X that was introduced by Gavryushkin and Drummond. We show that equidistant-cactus space is a CAT(0)-metric space which implies, for example, that there are unique geodesic paths between points. As a key step to proving this, we present a combinatorial result concerning ranked rooted X-cactuses. In particular, we show that such graphs can be encoded in terms of a pairwise compatibility condition arising from a poset of collections of pairs of subsets of X that satisfy certain set-theoretic properties. As a corollary, we also obtain an encoding of ranked, rooted X-trees in terms of partitions of X, which provides an alternative proof that the space of ultrametric trees on X is CAT(0). We expect that our results will provide the basis for novel ways to perform statistical analyses on collections of equidistant X-cactuses, as well as new directions for defining and understanding spaces of more general, arc-weighted phylogenetic networks.

Item Type:	Article
Additional Information:	Funding information: MO is partially supported by the US National Science Foundation (DMS 1847271). This work was supported by a grant from the Simons Foundation (#355824, Megan Owen). KAS thanks the Simons Foundation (#316124) and the US National Science Foundation (#1461094) for research and travel support.
Uncontrolled Keywords:	phylogenetic network,network space,combinatorial encoding,cat(0)-metric space,phylogenetic network,combinatorial encoding,network space,92d15,05c90,06a06,52b70,discrete mathematics and combinatorics ,/dk/atira/pure/subjectarea/asjc/2600/2607
Faculty \ School:	Faculty of Science > School of Computing Sciences
UEA Research Groups:	Faculty of Science > Research Groups > Computational Biology Faculty of Science > Research Groups > Norwich Epidemiology Centre Faculty of Medicine and Health Sciences > Research Groups > Norwich Epidemiology Centre
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	25 May 2023 10:32
Last Modified:	06 Feb 2025 11:27
URI:	https://ueaeprints.uea.ac.uk/id/eprint/92188
DOI:	10.1007/s00026-023-00656-0

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