A perturbation method for the structured coalescent with strong migration

Journal of Applied Probability

Volumn 37, Issue 1, 2000, Pages 148-167

  Notohara, Morihiro ^a  

^a KYUSHU UNIVERSITY   (Japan)

Author keywords

Migration; Perturbation; Structured coalescent

Indexed keywords

EID: 0034341951     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1014842274     Document Type: Article

References (22)

1. Cann, R. L., STONEKING, M. and WILSON, A. C. (1987). Mitochondrial DNA andhuman evolution. Nature 325, 31-36.
2. Ewens, W. J. (1972). The sampling theory of selectively neutral alleles. Theor. Popul. Biol. 3, 87-112.
3. HERBOTS, H. M. (1995). Stochastic modelsinpopulationgenetics: genealogyand geneticdifferentiationin structured populations. Ph.D. thesis, University of London.
4. HERBOTS, H. M. (1997). The structured coalescent. In Progress in Population Genetics and Human Evolution, eds. P. Donnelly and S. Tavaré, pp. 231-255.
5. Horai, S. and Hayasaka, K. (1990). Intraspecific nucleotide sequence differences in the major noncodingregion of human mitochondrial DNA. Am. J. Hum. Genet. 46, 828-842.
6. HUDSON, R. R. (1990). Gene genealogies and the coalescentprocess. In Oxford Surveys in Evolutionary Biology 7, eds. D. J. Futuyma and J. Antonovics. Oxford University Press, Oxford, pp. 1-44.
7. KINGMAN, J. F. C. (1982a). On the genealogy of large populations. In Essays in Statistical Science, eds. J. Gari and E. J. Hannan (J. Appl. Prob. 19A). Applied Probability Trust, Sheffield, pp. 27-43.
8. Kingman, J. F. C. (1982b). The coalescent. Stoch. Proc. Appl. 13, 235-248.
9. Nagylaki, T. (1980). The strong-migrationlimitin geographicallystructuredpopulations. J. Math. Biol. 9,101-114.
10. NATH, H. B. and GRIFFITHS, R. C. (1993). The coalescentin two colonies with symmetric migration. J. Math. Biol. 31, 841-852.
11. NOTOHARA, M. (1990). The coalescentandthe genealogicalprocessin geographicallystructuredpopulation. J. Math. Biol. 29, 59-75.
12. NOTOHARA, M. (1993a). The strong-migration limit for the genealogical process in geographically structured populations. J. Math. Biol. 31, 115-122.
13. NOTOHARA, M. (1993b). The genealogical process of neutral genes with mutation in geographically structured populations. J. Math. Biol. 31,123-132.
14. 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.
15. SHIGA, T. (1980). An interacting systemin population genetics I, II. J. Math. Kyoto Univ. 20, 212-242, 723-733.
16. 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.
17. SLATKIN, M. (1991). Inbreeding coefficient and coalescenttimes. Genet. Res. 58,167-175.
18. TAKAHATA, N. (1988). The coalescentin two partially isolated diffusion populations. Genet. Res. 52, 213-222.
19. TAKAHATA, N.(1991). Genealogyof neutral genes and spreading of selected mutations in a geographicallystructured population. Genetics 129,585-595.
20. Tavare, S. (1984). Line-of-descentand genealogicalprocesses, and their application in population genetics models. Theor. Popul. Biol. 26, 119-164.
21. TILLIER, E. R. and GOLDING, G. B. (1988). A sampling theory of selectively neutral alleles in a subdivided population. Genetics 119, 721-729.
22. WATTERSON, G. A. (1984). Lines of descentand the coalescent. Theor. Popul. Biol. 26, 77-92.