On a Multilocus Wright-Fisher Model with Mutation and a Svirezhev-Shahshahani Gradient-like Selection Dynamics

Erik Aurell; Magnus Ekeberg; Timo Koski

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arXiv · 1906.00716

On a Multilocus Wright-Fisher Model with Mutation and a Svirezhev-Shahshahani Gradient-like Selection Dynamics

Erik Aurell·Magnus Ekeberg·Timo Koski

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Abstract

In this paper we introduce a multilocus diffusion model of a population of $N$ 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.

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Erik Aurell, Magnus Ekeberg, Timo Koski. 2019-06-03. On a Multilocus Wright-Fisher Model with Mutation and a Svirezhev-Shahshahani Gradient-like Selection Dynamics. https://arxiv.org/abs/1906.00716

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