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Bridging Wright-Fisher and Moran models.

Arthur Alexandre1, Alia Abbara1, Cecilia Fruet1

  • 1Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, CH-1015, Switzerland; SIB Swiss Institute of Bioinformatics, Lausanne, CH-1015, Switzerland.

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Summary
This summary is machine-generated.

We introduce a new population genetics model that unifies the Wright-Fisher and Moran models. This model helps calculate allele fixation probabilities and coalescent properties in evolving populations.

Keywords:
Diffusion approximationGenetic driftMoran modelPartial updatePopulation geneticsWright–Fisher model

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Area of Science:

  • Population Genetics
  • Mathematical Biology
  • Evolutionary Dynamics

Background:

  • The Wright-Fisher and Moran models are foundational in population genetics, describing allele frequency changes in fixed-size populations.
  • These models are crucial for understanding genetic drift and evolution but offer distinct perspectives.

Purpose of the Study:

  • To propose a novel, tractable population genetics model that bridges the gap between the Wright-Fisher and Moran models.
  • To analyze the fixation probability, fixation times, and extinction times of alleles within this new framework.
  • To investigate the associated coalescent process and effective population sizes.

Main Methods:

  • Developing a discrete-time model where a fixed fraction of the population is updated at each step.
  • Employing diffusion approximation to derive key population genetic parameters.
  • Analyzing the convergence of the model's coalescent process to Kingman's coalescent.
  • Generalizing the model to include fluctuating update fractions, variable lifetimes, and selection.

Main Results:

  • The proposed model successfully unifies aspects of both Wright-Fisher and Moran models.
  • Analytical results for fixation probability and fixation/extinction times were obtained under diffusion approximation.
  • The coalescent process associated with the model was shown to converge to Kingman's coalescent.
  • Effective population sizes were calculated, providing insights into population structure.

Conclusions:

  • The new model offers a flexible and unified approach to studying allele frequency dynamics.
  • It provides a valuable tool for analyzing genetic drift, fixation probabilities, and coalescent behavior.
  • Generalizations allow for more realistic scenarios incorporating selection and demographic fluctuations.