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

2015/08/06 by Bhavin S. Khatri, Khatri, Bhavin S.
Computer Science · #Evolutionary Algorithms and Applications #FOS: Biological sciences #Populations and Evolution (q-bio.PE)

paper · pdf · doi:10.48550/arxiv.1508.01453

openalex publication_date 2015/08/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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

Citations

• The Neutral Theory of Molecular Evolution

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