On a Continuum Model for Random Genetic Drift: A Dynamic Boundary Condition Approach

TL;DR

This paper introduces a new continuum model for genetic drift using dynamic boundary conditions, providing a regularized Kimura equation that accurately captures gene fixation and moment conservation.

Contribution

It presents a novel regularized continuum model with proven existence and uniqueness of solutions, advancing the mathematical understanding of genetic drift dynamics.

Findings

Model captures gene fixation phenomena.

Ensures conservation of the first moment.

Numerical results validate the model's accuracy.

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 the 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.