Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-25T06:01:40.875Z Has data issue: false hasContentIssue false
  • English
  • Français

A perturbation method for the structured coalescent with strong migration

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Morihiro Notohara
Morihiro Notohara*
Affiliation:
Kyushu University
*
∗Postal address: Department of Biology, Faculty of Science, Kyushu University, 33, Fukuoka 812, Japan. Email address: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

By applying a perturbation method to the structured coalescent process in population genetics theory, we obtain the approximate solutions of the moment generating functions for the total coalescence time, the number of segregating sites among sampled DNA sequences and the number of allele types in a sample in the case of strong migration.

Keywords

Structured coalescentmigrationperturbation

MSC classification

Primary: 92D10: Genetics
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 1 , March 2000 , pp. 148 - 167
Copyright
Copyright © 2000 by The 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.)

References

Cann, R. L., Stoneking, M., and Wilson, A. C. (1987). Mitochondrial DNA and human evolution. Nature 325, 31–36.CrossRefGoogle ScholarPubMed
Ewens, W. J. (1972). The sampling theory of selectively neutral alleles. Theor. Popul. Biol. 3, 87–112.Google Scholar
Herbots, H. M. (1995). Stochastic models in population genetics: genealogy and genetic differentiation in structured populations. Ph.D. thesis, University of London.Google Scholar
Herbots, H. M. (1997). The structured coalescent. In Progress in Population Genetics and Human Evolution, eds. Donnelly, P. and Tavaré, S., pp. 231–255.CrossRefGoogle Scholar
Horai, S., and Hayasaka, K. (1990). Intraspecific nucleotide sequence differences in the major noncoding region of human mitochondrial DNA. Am. J. Hum. Genet. 46, 828–842.Google Scholar
Hudson, R. R. (1990). Gene genealogies and the coalescent process. In Oxford Surveys in Evolutionary Biology 7, eds. Futuyma, D. J. and Antonovics, J. Oxford University Press, Oxford, pp. 1–44.Google Scholar
Kingman, J. F. C. (1982a). On the genealogy of large populations. In Essays in Statistical Science, eds. Gari, J. and Hannan, E. J. (J. Appl. Prob. 19A), Applied Probability Trust, Sheffield, pp. 27–43.Google Scholar
Kingman, J. F. C. (1982b). The coalescent. Stoch. Proc. Appl. 13, 235–248.Google Scholar
Nagylaki, T. (1980). The strong-migration limit in geographically structured populations. J. Math. Biol. 9, 101–114.CrossRefGoogle ScholarPubMed
Nath, H. B., and Griffiths, R. C. (1993). The coalescent in two colonies with symmetric migration. J. Math. Biol. 31, 841–852.Google Scholar
Notohara, M. (1990). The coalescent and the genealogical process in geographically structured population. J. Math. Biol. 29, 59–75.Google Scholar
Notohara, M. (1993a). The strong-migration limit for the genealogical process in geographically structured populations. J. Math. Biol. 31, 115–122.Google Scholar
Notohara, M. (1993b). The genealogical process of neutral genes with mutation in geographically structured populations. J. Math. Biol. 31, 123–132.Google Scholar
Notohara, M. (1997). The number of segregating sites in a sample of DNA sequences from a geographically structured population. J. Math. Biol. 36, 188–200.Google Scholar
Shiga, T. (1980). An interacting system in population genetics I, II. J. Math. Kyoto Univ. 20, 212–242, 723–733.Google Scholar
Shimizu, T., and Soshi, T. (1997). A stepping stone model with infinitely many alleles and the number of alleles in a sample of finite genes. Preprint.Google Scholar
Slatkin, M. (1991). Inbreeding coefficient and coalescent times. Genet. Res. 58, 167–175.Google Scholar
Takahata, N. (1988). The coalescent in two partially isolated diffusion populations. Genet. Res. 52, 213–222.Google Scholar
Takahata, N. (1991). Genealogy of neutral genes and spreading of selected mutations in a geographically structured population. Genetics 129, 585–595.CrossRefGoogle Scholar
Tavaré, S. (1984). Line-of-descent and genealogical processes, and their application in population genetics models. Theor. Popul. Biol. 26, 119–164.CrossRefGoogle ScholarPubMed
Tillier, E. R., and Golding, G. B. (1988). A sampling theory of selectively neutral alleles in a subdivided population. Genetics 119, 721–729.CrossRefGoogle Scholar
Watterson, G. A. (1984). Lines of descent and the coalescent. Theor. Popul. Biol. 26, 77–92.CrossRefGoogle Scholar