On a Multilocus Wright-Fisher Model with Mutation and a Svirezhev-Shahshahani Gradient-like Selection Dynamics
Abstract
In this paper we introduce a multilocus diffusion model of a population of haploid, asexually reproducing individuals. The model includes parent-dependent mutation and interlocus selection, the latter limited to pairwise relationships but among a large number of simultaneous loci. The diffusion is expressed as a system of stochastic differential equations (SDEs) that are coupled in the drift functions through a Shahshahani gradient-like structure for interlocus selection. The system of SDEs is derived from a sequence of Markov chains by weak convergence. We find the explicit stationary (invariant) density by solving the corresponding stationary Fokker-Planck equation under parent-independent mutation, i.e., Kingman's house-of-cards mutation. The density formula enables us to readily construct families of Wright-Fisher models corresponding to networks of loci.
Keywords
Cite
@article{arxiv.1906.00716,
title = {On a Multilocus Wright-Fisher Model with Mutation and a Svirezhev-Shahshahani Gradient-like Selection Dynamics},
author = {Erik Aurell and Magnus Ekeberg and Timo Koski},
journal= {arXiv preprint arXiv:1906.00716},
year = {2019}
}