Assaf, M and Mobilia, M orcid.org/0000-0002-1424-567X (2011) Fixation of a deleterious allele under mutation pressure and finite selection intensity. Journal of Theoretical Biology, 275 (1). pp. 93-103. ISSN 0022-5193
Abstract
The mean fixation time of a deleterious mutant allele is studied beyond the diffusion approximation. As in Kimura's classical work [M. Kimura, Proc. Natl. Acad. Sci. USA. 77, 522 (1980)], that was motivated by the problem of fixation in the presence of amorphic or hypermorphic mutations, we consider a diallelic model at a single locus comprising a wild-type A and a mutant allele A' produced irreversibly from A at small uniform rate v. The relative fitnesses of the mutant homozygotes A'A', mutant heterozygotes A'A and wild-type homozygotes AA are 1-s, 1-h and 1, respectively, where it is assumed that v⪡s. Here, we employ a WKB theory and directly treat the underlying Markov chain (formulated as a birth-death process) obeyed by the allele frequency (whose dynamics is prescribed by the Moran model). Importantly, this approach allows to accurately account for effects of large fluctuations. After a general description of the theory, we focus on the case of a deleterious mutant allele (i.e. s>0) and discuss three situations: when the mutant is (i) completely dominant (s=h); (ii) completely recessive (h=0), and (iii) semi-dominant (h=s/2). Our theoretical predictions for the mean fixation time and the quasi-stationary distribution of the mutant population in the coexistence state, are shown to be in excellent agreement with numerical simulations. Furthermore, when s is finite, we demonstrate that our results are superior to those of the diffusion theory, while the latter is shown to be an accurate approximation only when N(e)s(2)⪡1, where N(e) is the effective population size.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | (c) 2011, Elsevier Ltd. All rights reserved. This is an author produced version of a paper published in Journal of Theoretical Biology. Uploaded in accordance with the publisher's self-archiving policy |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 08 Sep 2017 12:05 |
Last Modified: | 21 Jan 2018 19:05 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jtbi.2011.01.025 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:87676 |