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We propose and analyze an optimal mass transport method for a random geneticdrift problem driven by a Moran process under weak-selection. The continuumlimit, formulated as a reaction-advection-diffusion equation known as theKimura equation, inherits degenerate diffusion from the discrete stochasticprocess that conveys to the blow-up into Dirac-delta singularities hence bringsgreat challenges to both the analytical and numerical studies. The proposednumerical method can quantitatively capture to the fullest possible extent thedevelopment of Dirac-delta singularities for genetic segregation on one hand,and preserves several sets of biologically relevant and computationally favoredproperties of the random genetic drift on the other. Moreover, the numericalscheme exponentially converges to the unique numerical stationary state in timeat a rate independent of the mesh size up to a mesh error. Numerical evidenceis given to illustrate and support these properties, and to demonstrate thespatio-temporal dynamics of random generic drift.

An Optimal Mass Transport Method for Random Genetic Drift