Distinguishing phylogenetic level-2 networks with quartets and inter-taxon quartet distances

Holtgrefe, Niels, Allman, Elizabeth S., Baños, Hector, van Iersel, Leo, Moulton, Vincent, Rhodes, John A. and Wicke, Kristina (2025) Distinguishing phylogenetic level-2 networks with quartets and inter-taxon quartet distances. Bulletin of Mathematical Biology, 87. ISSN 0092-8240

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Abstract

The inference of phylogenetic networks, which model complex evolutionary processes including hybridization and gene flow, remains a central challenge in evolutionary biology. Until now, statistically consistent inference methods have been limited to phylogenetic level-1 networks, which allow no interdependence between reticulate events. In this work, we establish the theoretical foundations for a statistically consistent inference method for a much broader class: semi-directed level-2 networks that are outer-labeled planar and galled. We precisely characterize the features of these networks that are distinguishable from the topologies of their displayed quartet trees. Moreover, we prove that an inter-taxon distance derived from these quartets is circular decomposable, enabling future robust inference of these networks from quartet data, such as concordance factors obtained from gene tree distributions under the Network Multispecies Coalescent model. Our results also have novel identifiability implications across different data types and evolutionary models, applying to any setting in which displayed quartets can be distinguished.

Item Type:	Article
Additional Information:	Data Availability: No data are associated with this article. Funding information: This paper is based upon work supported by the National Science Foundation (NSF) under grant DMS-1929284 while all authors were in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, during the semester program on “Theory, Methods, and Applications of Quantitative Phylogenomics”. NH and LvI were partially supported by the Dutch Research Council (NWO) grant OCENW.M.21.306. ESA and JAR were partially supported by the National Science Foundation (NSF) grant DMS-205176, and HB by NSF grant DMS-2331660.
Uncontrolled Keywords:	phylogenetic network,semi-directed network,reticulate evolution,quartet,identifiability,circular split system,quartet,semi-directed network,circular split system,reticulate evolution,agricultural and biological sciences(all),environmental science(all),mathematics(all),biochemistry, genetics and molecular biology(all),neuroscience(all),pharmacology,computational theory and mathematics,immunology ,/dk/atira/pure/subjectarea/asjc/1100
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
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	29 Oct 2025 12:31
Last Modified:	10 Nov 2025 09:32
URI:	https://ueaeprints.uea.ac.uk/id/eprint/100829
DOI:	10.1007/s11538-025-01549-4

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