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Coalescent patterns in diploid exchangeable population models.

Martin Möhle1, Serik Sagitov

  • 1Eberhard Karls University of Tübingen, Mathematics Institute, 72076 Tübingen, Germany. martin.moehle@uni-tuebingen.de

Journal of Mathematical Biology
|October 3, 2003
PubMed
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This study models two-sex populations, analyzing reproduction through mating, exchangeable reproduction, and sex assignment. It proves convergence for the diploid ancestral process, identifying conditions for the Kingman coalescent and multiple mergers.

Area of Science:

  • Population Genetics
  • Mathematical Biology

Background:

  • Two-sex population models are fundamental in evolutionary biology.
  • Understanding the genetic ancestry of populations requires robust modeling techniques.

Purpose of the Study:

  • To analyze a class of two-sex population models with N females and N males.
  • To introduce and study the diploid ancestral process for sampled genes.
  • To determine conditions under which the ancestral process converges to a coalescent.

Main Methods:

  • Modeling reproduction in three stages: random mating, exchangeable reproduction, and random sex assignment.
  • Developing the diploid ancestral process for n genes sampled from the current generation.
  • Proving a convergence criterion for the diploid ancestral process as N approaches infinity.

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Main Results:

  • Established a convergence criterion for the diploid ancestral process with unchanged n as N tends to infinity.
  • Specified conditions for the limiting process to be the Kingman coalescent.
  • Discussed scenarios where the coalescent allows for multiple mergers of ancestral lines.

Conclusions:

  • The study provides a theoretical framework for understanding the genetic ancestry in two-sex populations.
  • Identified key conditions determining the behavior of ancestral lines, including convergence to the Kingman coalescent.
  • The findings contribute to the mathematical theory of population genetics and coalescent processes.