A general solution of the Wright-Fisher model of random genetic drift

Tat Dat Tran, Julian Hofrichter, and Jürgen Jost

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Submission date: 21. Mar. 2014
Pages: 28
published in: Differential equations and dynamical systems, 27 (2019) 4, p. 467-492 
DOI number (of the published article): 10.1007/s12591-016-0289-7
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Abstract:
We introduce a general solution concept for the Fokker-Planck (Kolmogorov) equation representing the diffusion limit of the Wright-Fisher model of random genetic drift for an arbitrary number of alleles at a single locus. This solution will continue beyond the transitions from the loss of alleles, that is, it will naturally extend to the boundary strata of the probability simplex on which the diffusion is defined. This also takes care of the degeneracy of the diffusion operator at the boundary. We shall then show the existence and uniqueness of a solution. From this solution, we can readily deduce information about the evolution of a Wright-Fisher population.