A hierarchical extension scheme for solutions of the Wright-Fisher model
Analysis of PDEs
2015-09-21 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1406.5152,
title = {A hierarchical extension scheme for solutions of the Wright-Fisher model},
author = {Julian Hofrichter and Tat Dat Tran and Jürgen Jost},
journal= {arXiv preprint arXiv:1406.5152},
year = {2015}
}