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Research Article | Open Access

On a continuum model for random genetic drift: a dynamic boundary condition approach

Chun Liu1, Jan-Eric Sulzbach2, Yiwei Wang3( )
Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL, USA
Department of Mathematics, Technical University Munich, Munich, Germany
Department of Mathematics, University of California, Riverside, Riverside, CA, USA
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Abstract

We propose a new continuum model for random genetic drift by employing a dynamic boundary condition approach. The model can be viewed as a regularized version of the Kimura equation and admits a continuous solution. We establish existence and uniqueness of a strong solution to the regularized system. Numerical experiments illustrate that, for sufficiently small regularization parameters, the model can capture key phenomena of the original Kimura equation, such as gene fixation and conservation of the first moment.

Keywords

genetic driftKimura equationWright–Fisher modeldynamic boundary conditionfixation probabilityenergetic variational approach
CLC number: 35K65, 35K20, 92D10, 76M30

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Communications in Analysis and Mechanics
Volume 17 Issue 3,
September 2025
Pages 829-848
DOI: 10.3934/cam.2025033

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Cite this article:
Liu C, Sulzbach J-E, Wang Y. On a continuum model for random genetic drift: a dynamic boundary condition approach. Communications in Analysis and Mechanics, 2025, 17(3): 829-848. https://doi.org/10.3934/cam.2025033

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Received: 31 December 2024
Revised: 17 June 2025
Accepted: 06 August 2025
Published: 15 September 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)