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

Abstract: We propose a new continuum model for a random genetic drift problem by employing a dynamical boundary condition approach. The new model, which can be viewed as a regularized Kimura equation, admits a continuous solution. The existence and uniqueness of the strong solution of the regularized system are shown. We present some numerical results for the regularized model, which indicate that the model can capture the main features of random genetic drift, such as gene fixation and conservation of the first moment.