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Exact Markov chain and approximate diffusion solution for haploid genetic drift with one-way mutation
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 3
2016 (English)In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 272, 100-112 p.Article in journal (Refereed) Published
Abstract [en]

The classical Kimura solution of the diffusion equation is investigated for a haploid random mating (Wright-Fisher) model, with one-way mutations and initial-value specified by the founder population. The validity of the transient diffusion solution is checked by exact Markov chain computations, using a. Jordan decomposition of the transition matrix. The conclusion is that the one-way diffusion model mostly works well, although the rate of convergence depends on the initial allele frequency and the mutation rate. The diffusion approximation is poor for mutation rates so low that the non-fixation boundary is regular. When this happens we perturb the diffusion solution around the non-fixation boundary and obtain a more accurate approximation that takes quasi-fixation of the mutant allele into account. The main application is to quantify how fast a specific genetic variant of the infinite alleles model is lost. We also discuss extensions of the quasi-fixation approach to other models with small mutation rates.

Place, publisher, year, edition, pages
2016. Vol. 272, 100-112 p.
Keyword [en]
Diffusion, Jordan decomposition, Markov chain, Mutation, Quasi-fixation, Wright-Fisher model
National Category
Biological Sciences Mathematics
URN: urn:nbn:se:su:diva-127358DOI: 10.1016/j.mbs.2015.12.006ISI: 000369456200012PubMedID: 26724565OAI: diva2:910910
Available from: 2016-03-10 Created: 2016-03-02 Last updated: 2016-03-10Bibliographically approved

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Hössjer, Ola
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