When are quarnets sufficient to reconstruct semi-directed phylogenetic networks?

Huber, Katharina T., van Iersel, Leo, Jones, Mark, Moulton, Vincent and Veenema-Nipius, Leonie (2025) When are quarnets sufficient to reconstruct semi-directed phylogenetic networks? Bulletin of Mathematical Biology, 87. ISSN 0092-8240

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Abstract

Phylogenetic networks are graphs that are used to represent evolutionary relationships between different taxa. They generalize phylogenetic trees since for example, unlike trees, they permit lineages to combine. Recently, there has been rising interest in \emph{semi-directed} phylogenetic networks, which are mixed graphs in which certain lineage combination events are represented by directed edges coming together, whereas the remaining edges are left undirected. One reason to consider such networks is that it can be difficult to root a network using real data. In this paper, we consider the problem of when a semi-directed phylogenetic network is defined or \emph{encoded} by the smaller networks that it induces on the 4-leaf subsets of its leaf set. These smaller networks are called \emph{quarnets}. We prove that semi-directed binary level-$2$ phylogenetic networks are encoded by their quarnets, but that this is not the case for level-$3$. In addition, we prove that the so-called \emph{blob tree} of a semi-directed binary network, a tree that gives the coarse-grained structure of the network, is always encoded by the quarnets of the network. \rev{These results are relevant for proving the statistical consistency of programs that are currently being developed for reconstructing phylogenetic networks from practical data, such as the recently developed \textsc{Squirrel} software tool.}

Item Type:	Article
Additional Information:	Data Availability Statement: No data was used.
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
Depositing User:	LivePure Connector
Date Deposited:	12 May 2025 13:30
Last Modified:	30 Sep 2025 17:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/99242
DOI:	10.1007/s11538-025-01510-5

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