An Optimal Mass Transport Method for Random Genetic Drift

We propose and analyze an optimal mass transport method for a random genetic drift problem driven by Moran process under weak-selection. The continuum limit, formulated as reaction-advection-diffusion equation known the Kimura equation, inherits degenerate diffusion from discrete stochastic that conveys to blow-up into Dirac-delta singularities hence brings great challenges both analytical numerical studies. proposed can quantitatively capture fullest possible extent development of segregation on one hand, preserves several sets biologically relevant computationally favored properties other. Moreover, scheme exponentially converges unique stationary state in time at rate independent mesh size up error. Numerical evidence is given illustrate support these properties, demonstrate spatio-temporal dynamics generic drift.