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Algebraic Invariants for Inferring 4-Leaf Semi-Directed Phylogenetic Networks.

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Title: Algebraic Invariants for Inferring 4-Leaf Semi-Directed Phylogenetic Networks.
Authors: Martin, Samuel1 (AUTHOR), Holtgrefe, Niels2 (AUTHOR), Moulton, Vincent3 (AUTHOR), Leggett, Richard M4 (AUTHOR)
Source: Systematic Biology. Jul2026, Vol. 75 Issue 4, p657-672. 16p.
Subjects: Phylogeny, Nucleotide sequencing, Biological evolution, Computational biology, Invariant theory, Molecular phylogeny
Abstract: A core goal of phylogenomics is to determine the evolutionary history of a set of species from biological sequence data. Phylogenetic networks are able to describe more complex evolutionary phenomena than phylogenetic trees but are more difficult to accurately reconstruct. Recently, there has been growing interest in developing methods to infer semi-directed phylogenetic networks. As computing such networks can be computationally intensive, one approach to building such networks is to puzzle together smaller networks. Thus, it is essential to have robust methods for inferring semi-directed phylogenetic networks on small numbers of taxa. In this paper, we investigate an algebraic method for performing phylogenetic network inference from nucleotide sequence data on 4-leaf semi-directed phylogenetic networks by analyzing the distribution of leaf-pattern probabilities. On simulated data, we found that we can correctly identify with high accuracy the undirected phylogenetic network for sequences of length at least 10 kbp. We found that identifying the semi-directed network is more challenging and requires sequences of length approaching 10 Mbp. We are also able to use our approach to identify treelike evolution and determine the underlying tree. Finally, we employ our method on a real data set from Xiphophorus species and use the results to build a phylogenetic network. [ABSTRACT FROM AUTHOR]
Copyright of Systematic Biology is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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An: 194674268
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  Data: Algebraic Invariants for Inferring 4-Leaf Semi-Directed Phylogenetic Networks.
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  Data: <searchLink fieldCode="AR" term="%22Martin%2C+Samuel%22">Martin, Samuel</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Holtgrefe%2C+Niels%22">Holtgrefe, Niels</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Moulton%2C+Vincent%22">Moulton, Vincent</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Leggett%2C+Richard+M%22">Leggett, Richard M</searchLink><relatesTo>4</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Systematic+Biology%22">Systematic Biology</searchLink>. Jul2026, Vol. 75 Issue 4, p657-672. 16p.
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  Data: <searchLink fieldCode="DE" term="%22Phylogeny%22">Phylogeny</searchLink><br /><searchLink fieldCode="DE" term="%22Nucleotide+sequencing%22">Nucleotide sequencing</searchLink><br /><searchLink fieldCode="DE" term="%22Biological+evolution%22">Biological evolution</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+biology%22">Computational biology</searchLink><br /><searchLink fieldCode="DE" term="%22Invariant+theory%22">Invariant theory</searchLink><br /><searchLink fieldCode="DE" term="%22Molecular+phylogeny%22">Molecular phylogeny</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: A core goal of phylogenomics is to determine the evolutionary history of a set of species from biological sequence data. Phylogenetic networks are able to describe more complex evolutionary phenomena than phylogenetic trees but are more difficult to accurately reconstruct. Recently, there has been growing interest in developing methods to infer semi-directed phylogenetic networks. As computing such networks can be computationally intensive, one approach to building such networks is to puzzle together smaller networks. Thus, it is essential to have robust methods for inferring semi-directed phylogenetic networks on small numbers of taxa. In this paper, we investigate an algebraic method for performing phylogenetic network inference from nucleotide sequence data on 4-leaf semi-directed phylogenetic networks by analyzing the distribution of leaf-pattern probabilities. On simulated data, we found that we can correctly identify with high accuracy the undirected phylogenetic network for sequences of length at least 10 kbp. We found that identifying the semi-directed network is more challenging and requires sequences of length approaching 10 Mbp. We are also able to use our approach to identify treelike evolution and determine the underlying tree. Finally, we employ our method on a real data set from Xiphophorus species and use the results to build a phylogenetic network. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Systematic Biology is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1093/sysbio/syaf071
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 16
        StartPage: 657
    Subjects:
      – SubjectFull: Phylogeny
        Type: general
      – SubjectFull: Nucleotide sequencing
        Type: general
      – SubjectFull: Biological evolution
        Type: general
      – SubjectFull: Computational biology
        Type: general
      – SubjectFull: Invariant theory
        Type: general
      – SubjectFull: Molecular phylogeny
        Type: general
    Titles:
      – TitleFull: Algebraic Invariants for Inferring 4-Leaf Semi-Directed Phylogenetic Networks.
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            NameFull: Martin, Samuel
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            NameFull: Holtgrefe, Niels
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            NameFull: Moulton, Vincent
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            NameFull: Leggett, Richard M
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            – D: 01
              M: 07
              Text: Jul2026
              Type: published
              Y: 2026
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              Value: 75
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            – TitleFull: Systematic Biology
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