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Counting Rankings of Tree-Child Networks.

Qiang Zhang1, Mike Steel2

  • 1Biomathematics Research Center, School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand.

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|February 21, 2026
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Summary
This summary is machine-generated.

This study counts temporal orderings of evolutionary events in tree-child networks, which model species evolution. We explored networks related to rankings and provided formulas for their expected number.

Keywords:
AlgorithmEnumerationPhylogenetic networkRankings

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Area of Science:

  • Evolutionary biology
  • Computational phylogenetics
  • Network theory

Background:

  • Rooted phylogenetic networks model species evolutionary history, including speciation and hybridization.
  • Tree-child networks are a well-studied class of phylogenetic networks.
  • Rankings represent temporal orderings of events in these networks.

Purpose of the Study:

  • To investigate methods for counting rankings on binary and semi-binary tree-child networks.
  • To explore the relationship between rankable and normal tree-child networks.
  • To derive an asymptotic expression for the expected number of rankings in randomly chosen tree-child networks.

Main Methods:

  • Combinatorial analysis of tree-child network structures.
  • Investigation of network properties related to event ordering.
  • Asymptotic analysis for random network ensembles.

Main Results:

  • A method for counting rankings on any given tree-child network.
  • Characterization of the relationship between rankable and normal networks.
  • An explicit asymptotic formula for the expected number of rankings.

Conclusions:

  • The study provides tools for quantifying evolutionary event orderings in complex phylogenetic networks.
  • Understanding network rankings offers insights into evolutionary processes.
  • The derived formulas facilitate theoretical analysis of phylogenetic network evolution.