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On joint subtree distributions under two evolutionary models.

Taoyang Wu1, Kwok Pui Choi2

  • 1School of Computing Sciences, University of East Anglia, Norwich, United Kingdom.

Theoretical Population Biology
|November 27, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces a dynamic method to compute tree shape distributions for evolutionary biology. It reveals unique properties of cherry and pitchfork distributions under Yule-Harding-Kingman and PDA models.

Keywords:
Joint distributionPDA modelPhylogenetic treeSubtree distributionTree indicesYule–Harding–Kingman model

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Area of Science:

  • Evolutionary biology
  • Population genetics
  • Phylogenetics

Background:

  • Hypotheses on micro- and macro-evolutionary processes are tested by comparing empirical evolutionary tree shapes with neutral models.
  • Accurate computation of tree shape index distributions under random models is crucial for this comparison.

Purpose of the Study:

  • To investigate the joint distribution of cherries and pitchforks (subtrees with 2 and 3 leaves) under the Yule-Harding-Kingman (YHK) and proportional to distinguishable arrangements (PDA) models.
  • To develop a numerical method for computing exact joint and marginal distributions of tree shapes for any tree size.

Main Methods:

  • Developed two novel recursive formulae for dynamic computation of tree shape distributions.
  • Analyzed the statistical properties of tree shapes generated by the YHK and PDA models.
  • Investigated the joint distribution of cherries and pitchforks.

Main Results:

  • Proposed a dynamic approach to numerically compute exact joint distributions of cherries and pitchforks for trees of any size.
  • Identified a constant correlation between cherry and pitchfork distributions under the YHK model.
  • Demonstrated log-concavity and unimodality of cherry distributions under both models, with a unique change point between them.

Conclusions:

  • The developed method enables precise computation of tree shape distributions, aiding evolutionary process inference.
  • The study provides novel insights into the statistical properties of evolutionary trees under common null models.
  • Understanding these distributions is key for distinguishing between different evolutionary models.