Encoding and ordering X-cactuses

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Francis, Andrew, Huber, Katharina T., Moulton, Vincent ORCID: https://orcid.org/0000-0001-9371-6435 and Wu, Taoyang ORCID: https://orcid.org/0000-0002-2663-2001 (2023) Encoding and ordering X-cactuses. Advances in Applied Mathematics, 142. ISSN 0196-8858

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Abstract

Phylogenetic networks are a generalization of evolutionary or phylogenetic trees that are commonly used to represent the evolution of species which cross with one another. A special type of phylogenetic network is an X-cactus, which is essentially a cactus graph in which all vertices with degree less than three are labelled by at least one element from a set X of species. In this paper, we present a way to encode X-cactuses in terms of certain collections of partitions of X that naturally arise from X-cactuses. Using this encoding, we also introduce a partial order on the set of X-cactuses (up to isomorphism), and derive some structural properties of the resulting partially ordered set. This includes an analysis of some properties of its least upper and greatest lower bounds. Our results not only extend some fundamental properties of phylogenetic trees to X-cactuses, but also provide a new approach to solving topical problems in phylogenetic network theory such as deriving consensus networks.

Item Type:	Article
Additional Information:	Funding Information: Francis, Huber and Moulton thank The Royal Society for its support. Huber and Moulton also thank Western Sydney University for its hospitality. The authors would like to thank the editor and the two anonymous referees for their valuable suggestions.
Uncontrolled Keywords:	consensus network,partition ordering,phylogenetic network,tree ordering,x-cactus,applied mathematics ,/dk/atira/pure/subjectarea/asjc/2600/2604
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 Faculty of Science > Research Centres > Centre for Ecology, Evolution and Conservation Faculty of Science > Research Groups > Data Science and AI
Related URLs:	http://www.scopus.com/inward/record.url?... http://arxiv.org/abs/2109.03183
Depositing User:	LivePure Connector
Date Deposited:	02 Aug 2022 13:30
Last Modified:	19 Dec 2024 01:07
URI:	https://ueaeprints.uea.ac.uk/id/eprint/87041
DOI:	10.1016/j.aam.2022.102414

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