%0 Journal Article
%T A hierarchical extension scheme for solutions of the Wright-Fisher model
%A Julian Hofrichter
%A Tat Dat Tran
%A Jščrgen Jost
%J Mathematics
%D 2014
%I arXiv
%X We develop a global and hierarchical scheme for the forward Kolmogorov (Fokker-Planck) equation of the diffusion approximation of the Wright-Fisher model of population genetics. That model describes the random genetic drift of several alleles at the same locus in a population. The key of our scheme is to connect the solutions before and after the loss of an allele. Whereas in an approach via stochastic processes or partial differential equations, such a loss of an allele leads to a boundary singularity, from a biological or geometric perspective, this is a natural process that can be analyzed in detail. Our method depends on evolution equations for the moments of the process and a careful analysis of the boundary flux.
%U http://arxiv.org/abs/1406.5152v3