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Phase-type distributions in mathematical population genetics: An emerging framework.

Asger Hobolth1, Iker Rivas-González2, Mogens Bladt3

  • 1Department of Mathematics, Aarhus University, Denmark.

Theoretical Population Biology
|March 9, 2024
PubMed
Summary
This summary is machine-generated.

Phase-type distributions offer a powerful mathematical framework for analyzing coalescent models in population genetics. This review explains phase-type theory and its application to derive key properties of ancestral processes for statistical inference.

Keywords:
CoalescentLaplace transformLikelihood inferencePhase-type theoryPopulation geneticsReward transformation

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Area of Science:

  • Population genetics
  • Mathematical biology
  • Probability theory

Background:

  • Phase-type distributions model time to absorption in Markov chains.
  • They provide a general framework for calculating properties of coalescent models.
  • Key coalescent process times and spectra are phase-type distributed.

Purpose of the Study:

  • To explain phase-type distribution theory.
  • To demonstrate its application in deriving coalescent model properties.
  • To provide tools for statistical inference in population genetics.

Main Methods:

  • Utilizing matrix manipulations for analytical tractability of phase-type distributions.
  • Connecting first-step analysis of coalescent models to phase-type calculations.
  • Applying reward transformations for calculating covariances and correlations.

Main Results:

  • Phase-type distributions simplify calculations for coalescent model properties.
  • Derivation of likelihoods for small coalescent trees using phase-type theory.
  • Demonstration of phase-type framework's versatility with R-code.

Conclusions:

  • Phase-type distributions offer a convenient and versatile framework for understanding coalescent models.
  • This approach facilitates statistical inference and provides insights into ancestral processes.
  • The presented methods and R-code enable reproducible analysis.