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Correction: "Distinguishing Phylogenetic Level-2 Networks with Quartets and Inter-Taxon Quartet Distances".

Bulletin of mathematical biology·2026
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Distinguishing Phylogenetic Level-2 Networks with Quartets and Inter-Taxon Quartet Distances.

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Updated: Jan 9, 2026

Using Phylogenetic Analysis to Investigate Eukaryotic Gene Origin
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Characterizing semi-directed phylogenetic networks and their multi-rootable variants.

Niels Holtgrefe1, Katharina T Huber2, Leo van Iersel1

  • 1Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands.

Theory in Biosciences = Theorie in Den Biowissenschaften
|December 10, 2025
PubMed
Summary

This study introduces explicit mathematical definitions for semi-directed phylogenetic networks, improving the analysis of complex evolutionary histories involving reticulate events. These new characterizations aid in understanding evolutionary relationships beyond simple trees.

Keywords:
Mixed graphOrchard networkPath partitionsSemi-directed phylogenetic networkTree-based networkTree-child network

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Area of Science:

  • Evolutionary Biology
  • Graph Theory
  • Computational Biology

Background:

  • Phylogenetic networks model complex evolutionary histories with reticulate events.
  • Semi-directed networks are a specialized class of phylogenetic networks.
  • Existing definitions of semi-directed networks are implicit and lack clear characterization.

Purpose of the Study:

  • To introduce novel, explicit mathematical characterizations for semi-directed and multi-semi-directed networks.
  • To extend foundational tools from rooted network theory to the semi-directed setting.
  • To determine when (multi-)semi-directed networks can be derived from specific classes of rooted networks.

Main Methods:

  • Developing explicit mathematical characterizations for semi-directed networks.
  • Extending concepts like cherry picking sequences, omnians, and path partitions.
  • Analyzing the relationship between semi-directed networks and established network classes (tree-child, orchard, tree-based, forest-based).

Main Results:

  • Novel explicit mathematical characterizations for semi-directed and multi-semi-directed networks are presented.
  • Foundational tools are successfully extended to the semi-directed setting.
  • Conditions are established for deriving (multi-)semi-directed networks from specific rooted network classes.

Conclusions:

  • The study provides explicit mathematical frameworks for analyzing semi-directed phylogenetic networks.
  • These results enhance the theoretical and computational understanding of complex evolutionary histories.
  • The findings facilitate advancements in algebraic evolutionary models based on phylogenetic networks.