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Updated: Jan 9, 2026

Using Phylogenetic Analysis to Investigate Eukaryotic Gene Origin

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Published on: August 14, 2018

Convergence-Divergence Models: Generalizations of Phylogenetic Trees Modeling Gene Flow Over Time.

Jonathan D Mitchell^1,2, Barbara R Holland^3,4

¹School of Natural Sciences (Mathematics), University of Tasmania, Hobart, TAS, Australia. jonathanmitchell88@gmail.com.

Bulletin of Mathematical Biology

|December 2, 2025

Summary

This study introduces new algorithms for inferring convergence-divergence models, which better represent evolutionary processes like gene flow than traditional phylogenetic trees. These methods accurately recover complex evolutionary histories from data.

Keywords:

Convergence Convergence-divergence models Gene flow Phylogenetic networks Phylogenetics Replicated evolution

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Last Updated: Jan 9, 2026

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Area of Science:

Evolutionary biology
Phylogenetics
Computational biology

Background:

Phylogenetic trees model divergent evolution but struggle with gene flow processes like introgressive hybridization.
Phylogenetic networks offer generalization but often assume instantaneous hybridization events.
Convergence-divergence models provide a flexible framework by retaining a principal tree and allowing gene flow over time.

Purpose of the Study:

To develop novel maximum likelihood algorithms for inferring N-taxon convergence-divergence models.
To address limitations of existing phylogenetic models in representing complex evolutionary scenarios.
To enable the study of processes like gene flow and replicated evolution within a unified framework.

Main Methods:

Development of quartet-based maximum likelihood algorithms for inferring convergence-divergence models.
Utilizing 4-taxon convergence-divergence models inferred via model selection for subsets of taxa.
Algorithms designed to infer the principal tree, sets of converging taxa, and model parameters (root probabilities, edge lengths, convergence parameters).

Main Results:

Successful inference of key aspects of N-taxon convergence-divergence models, including the principal tree and convergence parameters.
Demonstration of accurate recovery of convergence-divergence models from simulated data.
Algorithms are applicable to various data types, including multiple sequence alignments and gene presence/absence datasets.

Conclusions:

The developed algorithms provide a robust computational framework for inferring complex evolutionary histories beyond simple tree models.
Convergence-divergence models offer a more biologically realistic representation of evolutionary processes involving gene flow and convergence.
This work advances phylogenetic inference by enabling the analysis of more nuanced evolutionary dynamics.