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Counting Rankings of Tree-Child Networks
1Biomathematics Research Center, School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand.
Bulletin of Mathematical Biology
|February 21, 2026
Summary
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.
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.
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