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The Wright-Fisher Fokker-Planck equation describes the stochastic dynamics ofself-reproducing, competing variants at fixed population size. We use Fisher'sangular transformation, which defines a natural length for this stochasticprocess, to remove the co-ordinate dependence of it's diffusive dynamics,resulting in simple Brownian motion in an unstable potential, driving variantsto extinction or fixation. This insight allows calculation of very accurateasymptotic formula for the Green's function under neutrality and selection,using a novel heuristic Gaussian approximation.

Asymptotic Green's function for the stochastic reproduction of competing variants via Fisher's angular transformation