Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T11:05:21.229Z Has data issue: false hasContentIssue false
  • English
  • Français

The common ancestor at a nonneutral locus

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Paul Fearnhead
Paul Fearnhead*
Affiliation:
University of Oxford
*
∗ Postal address: Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster LA1 4YW, UK. Email address: p.fearnhead@lancaster.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a nonneutral population genetics model with parent-independent mutations and two selective classes. We calculate the stationary distribution of the type of the common ancestor of a sample of genes from this model. The expected fitness of any ancestor (including the most recent common ancestor of any sample) is shown to be greater than the expected fitness of a randomly chosen gene from the population. The process of mutations to the common ancestor is also analysed. Our results are related to, but more general than, results obtained from diffusion theory.

Keywords

Ancestral selection graphcommon ancestorfitnessfixationparent-independent mutations

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces 92D10: Genetics
Secondary: 60G10: Stationary processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 1 , March 2002 , pp. 38 - 54
Copyright
Copyright © Applied Probability Trust 2002 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]. Bulmer, M. G. (1991). The selection–mutation–drift theory of synonymous codon usage. Genetics 129, 897–907.CrossRefGoogle ScholarPubMed
[2]. Donnelly, P. (1986). Dual processes in population genetics. In Stochastic Spatial Processes (Lecture Notes Math. 1212), ed. Tautu, P., Springer, Berlin, pp. 94–105.CrossRefGoogle Scholar
[3]. Donnelly, P., and Kurtz, T. (1999). Genealogical processes for Fleming–Viot models with selection and recombination. Ann. Appl. Prob. 9, 1091–1148.CrossRefGoogle Scholar
[4]. Donnelly, P., Nordberg, M., and Joyce, P. (2001). Likelihoods and simulation methods for a class of nonneutral population genetics models. Genetics 159, 853–867.CrossRefGoogle ScholarPubMed
[5]. Ewens, W. J. (1979). Mathematical Population Genetics. Springer, Berlin.Google Scholar
[6]. Fearnhead, P. (2001). Perfect simulation from population genetic models with selection. Theoret. Pop. Biol. 59, 263–279.CrossRefGoogle ScholarPubMed
[7]. Griffiths, R. C. (1980). Lines of descents in the diffusion approximation of neutral Wright–Fisher models. Theoret. Pop. Biol. 17, 37–50.CrossRefGoogle ScholarPubMed
[8]. Kimura, M. (1962). On the probability of fixation of mutant genes in a population. Genetics 47, 713–719.CrossRefGoogle ScholarPubMed
[9]. Krone, S. M., and Neuhauser, C. (1997). Ancestral processes with selection. Theoret. Pop. Biol. 51, 210–237.CrossRefGoogle ScholarPubMed
[10]. McVean, G. A. T., and Vieira, J. (2001). Inferring parameters of mutation, selection and demography from patterns of synonymous site evolution in drosophila. Genetics 157, 245–257.CrossRefGoogle ScholarPubMed
[11]. Neuhauser, C., and Krone, S. M. (1997). The genealogy of samples in models with selection. Genetics 145, 519–534.CrossRefGoogle ScholarPubMed
[12]. Norris, J. R. (1997). Markov Chains. Cambridge University Press.CrossRefGoogle Scholar
[13]. Parsons, T. J. et al. (1997). A high observed substitution rate in the human mitochondrial DNA control region. Nature Genet. 15, 363–368.CrossRefGoogle ScholarPubMed
[14]. Pritchard, J. K. (2001). Are rare variants responsible for susceptibility to complex diseases? Amer. J. Human Genet. 69, 124–137.CrossRefGoogle ScholarPubMed
[15]. Sigurŏardóttir, S. et al. (2000). The mutation rate in the human mitochondrial DNA control region. Amer. J. Human Genet. 66, 1599–1609.CrossRefGoogle Scholar
[16]. Slade, P. F. (2000). Most recent common ancestor probability distributions in gene genealogies under selection. Theoret. Pop. Biol. 58, 291–305.CrossRefGoogle ScholarPubMed
[17]. Slade, P. F. (2000). Simulation of selected genealogies. Theoret. Pop. Biol. 57, 35–49.CrossRefGoogle ScholarPubMed
[18]. Stephens, M. (2000). Times on trees and the age of an allele. Theoret. Pop. Biol. 57, 109–119.CrossRefGoogle ScholarPubMed
[19]. Stephens, M., and Donnelly, P. (2000). Inference in molecular population genetics (with discussion). J. R. Statist. Soc. B 62, 605–655.CrossRefGoogle Scholar
[20]. Stephens, M., and Donnelly, P. (2002). The age of a nonneutral mutation persisting in a finite population. In preparation.Google Scholar
[21]. Wright, S. (1949). Adaption and selection. In Genetics, Paleontology and Evolution, eds Jepson, G. L., Simpson, G. G. and Mayr, E., Princeton University Press, pp. 365–389.Google Scholar