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Using Phylogenetic Analysis to Investigate Eukaryotic Gene Origin
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On the Matrix Condition of Phylogenetic Tree.

Dwueng-Chwuan Jhwueng1, Brian C O'Meara2

  • 1Department of Statistics, Feng Chia University, Taichung, Taiwan R.O.C.

Evolutionary Bioinformatics Online
|February 29, 2020
PubMed
Summary

Phylogenetic comparative analyses can face instability issues when the phylogenetic covariance matrix becomes ill-conditioned. This study investigates this problem and proposes methods to improve the stability of evolutionary and ecological analyses.

Keywords:
Brownian motioncondition numbercovariance matrix inversionphylogenetic comparative analysisphylogenetic tree

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Area of Science:

  • Evolutionary biology
  • Ecology
  • Phylogenetics
  • Comparative methods

Background:

  • Phylogenetic comparative analyses utilize evolutionary trees to study species' evolution and ecology.
  • A phylogenetic tree transforms into a phylogenetic covariance matrix, crucial for comparative methods.
  • Matrix inversion for likelihood calculations can be unstable if the matrix is ill-conditioned.

Purpose of the Study:

  • To investigate potential numerical instability in phylogenetic comparative analyses.
  • To identify issues arising from ill-conditioned phylogenetic covariance matrices.
  • To propose and evaluate methods for remedying matrix ill-conditioning.

Main Methods:

  • Algebraic transformation of phylogenetic trees into covariance matrices.
  • Analysis of matrix conditioning using eigenvalue ratios.
  • Development and testing of numerical stability improvement techniques.

Main Results:

  • Ill-conditioned phylogenetic covariance matrices can lead to unstable likelihood calculations and parameter estimates.
  • The ratio of maximum to minimum eigenvalues quantifies matrix ill-conditioning.
  • Proposed methods aim to enhance the stability of comparative analyses.

Conclusions:

  • Numerical stability is a critical consideration in phylogenetic comparative analyses.
  • Addressing ill-conditioned covariance matrices is essential for reliable evolutionary and ecological inferences.
  • Further research into robust computational methods is warranted.