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Dimensional Reduction for the General Markov Model on Phylogenetic Trees.

Jeremy G Sumner1

  • 1School of Physical Sciences, Mathematics, University of Tasmania, Private Bag 37, GPO, Hobart, TAS, 7001, Australia. Jeremy.Sumner@utas.edu.au.

Bulletin of Mathematical Biology
|February 12, 2017
PubMed
Summary

We developed a dimensionality reduction method for phylogenetic models. This technique simplifies complex evolutionary models, making it easier to analyze sequence data and identify evolutionary relationships on phylogenetic trees.

Keywords:
Affine groupMarkov chainsRepresentation theory

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Area of Science:

  • Computational Biology
  • Phylogenetics
  • Evolutionary Biology

Background:

  • Phylogenetic models describe sequence evolution on evolutionary trees.
  • Current models can be computationally intensive due to high dimensionality.
  • Analyzing sequence data to infer evolutionary history is crucial.

Purpose of the Study:

  • To present a dimensionality reduction method for the general Markov model of sequence evolution.
  • To simplify complex phylogenetic models for efficient analysis.
  • To retain the ability to statistically identify phylogenetic divergence events.

Main Methods:

  • Applying linear combinations to site pattern counts (random variables).
  • Identifying an invariant subspace dependent bilinearly on model parameters.
  • Reducing model dimensionality from exponential to quadratic with respect to the number of taxa.

Main Results:

  • Achieved dimensionality reduction from exponential to quadratic.
  • Developed a method to identify phylogenetic divergence events.
  • Identified an invariant subspace with bilinear parameter dependence.

Conclusions:

  • The method offers a computationally efficient approach to phylogenetic analysis.
  • Potential applications include calculating phylogenetic split (edge) weights from sequence data.
  • This work facilitates more tractable analysis of evolutionary processes on phylogenetic trees.