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Monte Carlo algorithms for Brownian phylogenetic models.

Benjamin Horvilleur1, Nicolas Lartillot1

  • 1Université de Lyon, Université Lyon 1, CNRS; UMR 5558, Laboratoire de Biométrie, Biologie Évolutive, F-69622 Villeurbanne, France.

Bioinformatics (Oxford, England)
|July 24, 2014
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Summary

This study introduces a novel Monte Carlo method for Brownian models in phylogenetics, improving accuracy in analyzing substitution rate variation over time. The approach enhances molecular dating and comparative analyses by precisely tracking evolutionary rate changes.

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Area of Science:

  • Phylogenetics
  • Computational Biology
  • Evolutionary Biology

Background:

  • Brownian models are used in phylogenetics to model time-varying substitution rates.
  • Current Monte Carlo methods use approximations, sampling Brownian processes only at nodes or midpoints.
  • This leads to simplified branchwise average substitution rates, limiting accuracy.

Purpose of the Study:

  • To develop a more accurate Monte Carlo approach for Brownian models in phylogenetics.
  • To improve the analysis of time-varying substitution rates and their impact on evolutionary studies.
  • To enable precise modeling of substitution patterns across lineages and over time.

Main Methods:

  • Introduced a Monte Carlo approach that samples a fine-grained discretization of the Brownian process trajectory along the phylogeny.
  • Developed generic Monte Carlo resampling algorithms for updating Brownian paths.
  • Created specific computational strategies for integrating finite-time substitution probabilities.

Main Results:

  • The new method provides a more accurate representation of the Brownian process trajectory.
  • Markov chain Monte Carlo sampler shows reasonable scaling of mixing properties and computational complexity with discretization.
  • The approach allows practical applications with significant discretization levels.

Conclusions:

  • The developed method offers enhanced precision for time-dependent substitution models in phylogenetics.
  • It generalizes to other Markovian stochastic processes, broadening applicability.
  • The program is freely available, facilitating wider use in evolutionary research.