Change search
ReferencesLink to record
Permanent link

Direct link
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
Identifiers
URN: urn:nbn:se:su:diva-127358DOI: 10.1016/j.mbs.2015.12.006ISI: 000369456200012PubMedID: 26724565OAI: oai:DiVA.org:su-127358DiVA: diva2:910910
Available from: 2016-03-10 Created: 2016-03-02 Last updated: 2016-03-10Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textPubMed

Search in DiVA

By author/editor
Hössjer, Ola
By organisation
Department of Mathematics
In the same journal
Mathematical Biosciences
Biological SciencesMathematics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 10 hits
ReferencesLink to record
Permanent link

Direct link