Coalescence times and FST values in subdivided populations with symmetric structure

Advances in Applied Probability

Volumn 35, Issue 3, 2003, Pages 665-690

  Wilkinson Herbots, Hilde M ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

F statistics; Genealogy; Graph theory; Markov chain; Structured coalescent; Subpopulation differentiation

Indexed keywords

GRAPH THEORY; MATHEMATICAL MODELS; POPULATION STATISTICS; SAMPLING;

GENEALOGY; SUBPOPULATION DIFFERENTIATION;

MARKOV PROCESSES;

EID: 0041878887     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1059486823     Document Type: Article

References (44)

1. Adel'son-Velskii, G. M. (1969). Example of a graph without a transitive automorphism group. Soviet Math. Dokl. 10, 440-441.
2. Bahlo, M. and Griffiths, R. C. (2001). Coalescence time for two genes from a subdivided population. J. Math. Biol. 43, 397-410.
3. Barton, N. H. and Wilson, I. (1995). Genealogies and geography. Phil. Trans. R. Soc. London B 349, 49-59.
4. Barton, N. H. and Wilson, I. (1996). Genealogies and geography. In New Uses for New Phylogenies, eds P. H. Harvey et al., Oxford University Press, pp. 23-56.
5. Barton, N. H., Depaulis, F. and Etheridge, A. M. (2002). Neutral evolution in spatially continuous populations. Theoret. Pop. Biol. 61, 31-48.
6. Biggs, N. (1974). Algebraic Graph Theory. Cambridge University Press.
7. Bollobás, B. (1979). Graph Theory. An Introductory Course (Graduate Texts Math. 63). Springer, New York.
8. Cannings, C. (1974). The latent roots of certain Markov chains arising in genetics: a new approach. I. Haploid models. Adv. Appl. Prob. 6, 260-290.
9. Crow, J. F. and Maruyama, T. (1971). The number of neutral alleles maintained in a finite, geographically structured population. Theoret. Pop. Biol. 2, 437-453.
10. Donnelly, P. and Tavaré S. (1995). Coalescents and genealogical structure under neutrality. Annual Rev. Genet. 29, 401-421.
11. Fu, Y. X. and Li, W. H. (1999). Minireview: coalescing into the 21st century: an overview and prospects of coalescent theory. Theoret. Pop. Biol. 56, 1-10.
12. Godsii, C. and Royle, G. (2001). Algebraic Graph Theory. Springer, New York.
13. Griffiths, R. C. and Tavaré, S. (1994a). Ancestral inference in population genetics. Statist. Sci. 9, 307-319.
14. Griffiths, R. C. and Tavaré, S. (1994b). Sampling theory for neutral alleles in a varying environment. Phil. Trans. R. Soc. London B 344, 403-410.
15. Griffiths, R. C. and Tavaré, S. (1994c). Simulating probability distributions in the coalescent. Theoret. Pop. Biol. 46, 131-159.
16. Herbots, H. M. (1994). Stochastic models in population genetics: genealogy and genetic differentiation in structured populations. Doctoral Thesis, University of London.
17. Herbots, H. M. (1997). The structured coalescent. In Progress in Population Genetics and Human Evolution (IMA Vol. Math. Appl. 87), eds P. Donnelly and S. Tavaré, Springer, New York, pp. 231-255.
18. Hudson, R. R. (1990). Gene genealogies and the coalescent process. In Oxford Surveys in Evolutionary Biology, eds D. J. Futuyama and J. Antonovics, Oxford University Press, pp. 1-44.
19. Kingman, J. F. C. (1982a). Exchangeability and the evolution of large populations. In Exchangeability in Probability and Statitics, eds G. Koch and F. Spizzichino, North-Holland, Amsterdam, pp. 97-112.
20. Kingman, J. F. C. (1982b). On the genealogy of large populations. In Essays in Statistical Science (J. Appl. Prob. Spec. Vol. 19A), eds. J. Gani and E. J. Hannan, Applied Probability Trust, Sheffield, pp. 27-43.
21. Kingman, J. F. C. (1982c). The coalescent. Stoch. Process. Appl. 13, 235-248.
22. Li, W.-H. (1976). Distribution of nucleotide differences between two randomly chosen cistrons in a subdivided population: the finite island model. Theoret. Pop. Biol. 10, 303-308.
23. Nagylaki, T. (1980). The strong-migration limit in geographically structured populations. J. Math. Biol. 9, 101-114.
24. Nagylaki, T. (1982). Geographical invariance in population genetics. J. Theoret. Biol. 99, 159-172.
25. Nagylaki, T. (1998). The expected number of heterozygous sites in a subdivided population. Genetics 149, 1599-1604.
26. Nagylaki, T. (2000). Geographical invariance and the strong-migration limit in subdivided populations. J. Math. Biol. 41, 123-142.
27. Nath, H. B. and Griffiths, R. C. (1993). The coalescent in two colonies with symmetric migration. J. Math. Biol. 31, 841-852.
28. Nei, M. (1973). Analysis of gene diversity in subdivided populations. Proc. Nat. Acad. Sci. USA 70, 3321-3323.
29. Notohara, M. (1990). The coalescent and the genealogical process in geographically structured population. J. Math. Biol. 29, 59-75.
30. Notohara, M. (1993). The strong-migration limit for the genealogical process in geographically structured populations. J. Math. Biol. 31, 115-122.
31. Rousset, F. (1996). Equilibrium values of measures of population subdivision for stepwise mutation processes. Genetics 142, 1357-1362.
32. Slatkin, M. (1985). Gene flow in natural populations. Annual Rev. Ecol. Systems 16, 393-430.
33. Slatkin, M. (1987). The average number of sites separating DNA sequences drawn from a subdivided population. Theoret. Pop. Biol. 32, 42-49.
34. Slatkin, M. (1991). Inbreeding coefficients and coalescence times. Genetical Res. 58, 167-175.
35. Slatkin, M. (1993). Isolation by distance in equilibrium and non-equilibrium population. Evolution 47, 264-279.
36. Slatkin, M. and Barton, N. H. (1989). A comparison of three indirect methods for estimating average levels of gene flow. Evolution 43, 1349-1368.
37. Stephens, M. (2001). Inference under the coalescent. In Handbook of Statistical Genetics, eds D. J. Balding, M. Bishop and C. Cannings, John Wiley, Chichester, p. 213-238.
38. Strobeck, C. (1987). Average number of nucleotide differences in a sample from a single subpopulation: a test for population subdivision. Genetics 117, 149-153.
39. Takahata, N. (1988). The coalescent in two partially isolated diffusion populations. Genetical Res. 52, 213-222.
40. ST ≠ 1/(4Nm + 1). Heredity 82, 117-125.
41. Wilkins, J. F. and Wakeley, J. (2002). The coalescent in a continuous, finite, linear population. Genetics 161, 873-888.
42. Wilkinson-Herbots, H. M. (1998). Genealogy and subpopulation differentiation under various models of population structure. J. Math. Biol. 37, 535-585.
43. Wright, S. (1931). Evolution in Mendelian populations. Genetics 16, 97-159.
44. Wright, S. (1951). The genetical structure of populations. Ann. Eugenics 15, 323-354.