Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-06-02T02:09:43.425Z Has data issue: false hasContentIssue false
  • English
  • Français

Transient distribution of the number of segregating sites in a neutral infinite-sites model with no recombination

Published online by Cambridge University Press:  14 July 2016

R. C. Griffiths
R. C. Griffiths*
Affiliation:
Monash University
*
∗Postal address: Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia.
Get access Rights & Permissions [Opens in a new window]

Abstract

The transient distribution of the number of segregating sites in a sample from a large population of 2N genes is found. Segregating sites are split into those in common with the sites segregating in the initial population and those segregating due to new mutations. The waiting time distribution for a population to lose all of its initial sites is also studied. A neutral infinite-sites model with no recombination is used. This paper extends the work of Watterson (1975), from the stationary case; and of Li (1977) from the transient distribution in a sample of 2.

Keywords

POPULATION GENETICSINFINITE-SITES MODELMOLECULAR POPULATION GENETICS
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 42 - 51
Copyright
Copyright © Applied Probability Trust 

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.)

Footnotes

Research carried out while the author was visiting the Center for Demographic and Population Genetics, University of Texas Health Science Center, Houston, Texas.

References

Ewens, W. J. (1979) Mathematical population genetics. In Biomathematics 9, Springer-Verlag, Berlin.Google Scholar
Griffiths, R. C. (1979a) A transition density expansion for a multiallele diffusion model. Adv. Appl. Prob. 11, 310–325.CrossRefGoogle Scholar
Griffiths, R. C. (1979b) Exact sampling distributions from the infinite neutral alleles model. Adv. Appl. Prob. 11, 326–354.CrossRefGoogle Scholar
Griffiths, R. C. (1980) Lines of descent in the diffusion approximation of neutral Wright-Fisher models. Theoret. Popn. Biol. CrossRefGoogle Scholar
Guess, H. A. (1973) On the weak convergence of Wright-Fisher models. Stoch. Proc. Appl. 1, 287–306.CrossRefGoogle Scholar
Kimura, M. and Crow, J. F. (1964) The number of alleles that can be maintained in a finite population. Genetics 49, 725–738.CrossRefGoogle Scholar
Li, W. H. (1977) Distribution of nucleotide differences between two randomly chosen cistrons in a finite population. Genetics 85, 331–337.CrossRefGoogle Scholar
Li, W. H. and Nei, M. (1977) Persistence of common alleles in two related populations or species. Genetics 86, 901–914.CrossRefGoogle ScholarPubMed
Littler, R. A. (1975) Loss of variability in a finite population. Math. Biosci. 25, 151–163.CrossRefGoogle Scholar
Norman, M. F. (1975) Diffusion approximation of non-markovian processes. Ann. Prob. 3, 358–364.CrossRefGoogle Scholar
Watterson, G. A. (1962) Some theoretical aspects of diffusion theory in population genetics. Ann. Math. Statist. 33, 939–957.CrossRefGoogle Scholar
Watterson, G. A. (1975) On the number of segregating sites in genetical models without recombination. Theoret. Popn. Biol. 7, 256–276.CrossRefGoogle ScholarPubMed