The space of equidistant phylogenetic cactuses

Huber, Katharina T., Moulton, Vincent ORCID:, 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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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
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Depositing User: LivePure Connector
Date Deposited: 25 May 2023 10:32
Last Modified: 18 Mar 2024 09:30
DOI: 10.1007/s00026-023-00656-0


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