Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-23T05:14:50.011Z Has data issue: false hasContentIssue false
  • English
  • Français

Distribution of the number of alleles in multigene families

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, VIC 3168, Australia.
Get access Rights & Permissions [Opens in a new window]

Abstract

The distribution of the number of alleles in samples from r chromosomes is studied. The stochastic model used includes gene conversion within chromosomes and mutation at loci on the chromosomes. A method is described for simulating the distribution of alleles and an algorithm given for computing lower bounds for the mean number of alleles.

A formula is derived for the expected number of samples from r chromosomes which contain the allele type of a locus chosen at random.

Keywords

CHROMOSOMESGENE CONVERSIONPOPULATION GENETICS

MSC classification

Primary: 92D10: Genetics
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 4 , December 1992 , pp. 759 - 769
Copyright
Copyright © Applied Probability Trust 1992 

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

Ewens, W. J. (1972) The sampling theory of selectively neutral alleles. Theoret. Popn Biol. 3, 87–112.CrossRefGoogle ScholarPubMed
Griffiths, R. C. (1991) Two chromosomes with multigene families. Theoret. Popn Biol. 39, 263–273.CrossRefGoogle ScholarPubMed
Griffiths, R. C. and Watterson, G. A. (1990) The number of alleles in multigene families. Theoret. Popn Biol. 37, 110–123.CrossRefGoogle ScholarPubMed
Kimura, M. and Crow, J. F. (1964) The number of alleles that can be maintained in a finite population. Genetics 49, 763–771.CrossRefGoogle Scholar
Kingman, J. F. C. (1982) The coalescent. Stoch. Proc. Appl. 13, 235–248.CrossRefGoogle Scholar
Ohta, T. (1983) On the evolution of multigene families. Theor. Popn Biol. 23, 216–240.CrossRefGoogle ScholarPubMed
Ohta, T. (1986) Actual number of alleles contained in a multigene family. Genet. Res. 48, 119–123.CrossRefGoogle Scholar
Shimizu, A. (1987) Stationary distribution of a diffusion process taking values in probability distributions on the partitions. In Stochastic Models in Biology, ed. Kimura, M., Kallianpur, G. and Hida, T., Springer-Verlag, Berlin.Google Scholar
Watterson, G. A. (1989a) Allele frequencies in multigene families. I. Diffusion equation approach. Theoret. Popn Biol. 35, 142–160.CrossRefGoogle ScholarPubMed
Watterson, G. A. (1989b) Allele frequencies in multigene families. II. Coalescent approach. Theoret. Popn Biol. 35, 161–179.CrossRefGoogle ScholarPubMed
Watterson, G. A. (1992) The mean number of alleles in a multigene family. Adv. Appl. Prob. 24, 1–19.CrossRefGoogle Scholar