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Quantitative approximation of the discrete Moran process by a Wright-Fisher diffusion.

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This study quantifies the error in using diffusion approximations for population genetics models with weak selection and immigration. It provides a robust method for analyzing these dynamics in large populations.

Keywords:
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Area of Science:

  • Population genetics
  • Mathematical biology
  • Evolutionary dynamics

Background:

  • The Moran discrete process and Wright-Fisher model are foundational in population genetics.
  • Diffusion approximations, like the Wright-Fisher diffusion, are widely used to study population genetics model dynamics.
  • Understanding the accuracy of these approximations is crucial for reliable analysis.

Purpose of the Study:

  • To quantitatively assess the error introduced by using diffusion approximations for population genetics models.
  • To analyze the large-population limit of errors under weak selection and weak immigration in one dimension.
  • To develop a robust approach applicable to Markovian selection and immigration processes.

Main Methods:

  • Analysis of the large-population limit of discrete population genetics models.
  • Quantitative error estimation for diffusion approximations.
  • Consideration of weak selection and weak immigration dynamics.
  • Extension to Markovian processes with finite state jump or diffusion limits.

Main Results:

  • A quantitative bound on the error of the Wright-Fisher diffusion approximation was derived.
  • The approach successfully handles weak selection and weak immigration.
  • The method's robustness was demonstrated for Markovian processes.

Conclusions:

  • The study provides a rigorous error analysis for diffusion approximations in population genetics.
  • The findings enhance the reliability of using diffusion models for studying evolutionary dynamics.
  • The developed approach offers a flexible framework for analyzing complex population processes.