The two-locus ancestral graph in a subdivided population: Convergence as the number of demes grows in the island model

Journal of Mathematical Biology

Volumn 48, Issue 3, 2004, Pages 275-292

  Lessard, Sabin ^a   Wakeley, John ^b  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b HARVARD UNIVERSITY   (United States)

Author keywords

Coalescent; Island model; Migration; Recombination

Indexed keywords

GOES;

ALGORITHM; ANIMAL; ARTICLE; BIOLOGICAL MODEL; COMPUTER SIMULATION; DIPLOIDY; GENETIC POLYMORPHISM; GENETIC RECOMBINATION; GENETICS; HUMAN; METHODOLOGY; MUTATION; PEDIGREE; POPULATION GENETICS; PROBABILITY;

ALGORITHMS; ANIMALS; COMPUTER SIMULATION; DIPLOIDY; GENETICS, POPULATION; HUMANS; MARKOV CHAINS; MODELS, GENETIC; MUTATION; PEDIGREE; POLYMORPHISM, GENETIC; RECOMBINATION, GENETIC;

EID: 4143067531     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00285-003-0230-x     Document Type: Article

References (40)

1. Begun, D.J., Aquadro, C.F.: Levels of naturally occurring polymorphism correlate with recombination rate in Drosophila melanogaster. Nature 356, 519-520 (1992)
2. Fearnhead, P., Donnelly, P.: Estimating recombination rates from population genetic data. Genetics 159, 1299-1318 (2001)
3. Fisher, R.A.: The Genetical Theory of Natural Selection. Clarendon, Oxford, 1930
4. Golding, G.B., Strobeck, C.: Linkage disequilibrium in a finite population that is partially selfing. Genetics 94, 777-789 (1980)
5. Griffiths, R.C., Marjoram, P.: Ancestral inference from samples of DNA sequences with recombination. J. Comp. Biol. 3, 479-502 (1996)
6. Hey, J., Wakeley, J.: A coalescent estimator of the population recombination rate. Genetics 145, 833-846 (1997)
7. Hill, W.G., Robertson, A.R.: Linkage disequilibrium in finite populations. Theoret. Appl. Genet. 38, 226-231 (1968)
8. Hudson, R.R.: Properties of a neutral allele model with intragenic recombination. Theoret. Pop. Biol. 23, 183-201 (1983)
9. Hudson, R.R.: Estimating the recombination parameter of a finite population model without selection. Genet. Res. Camb. 50, 245-250 (1987)
10. Hudson, R.R.: Two-locus sampling distributions and their application. Genetics 159, 1805-1817 (2001)
11. Hudson, R.R., Kaplan, N.L.: Statistical properties of the number of recombination events in the history of a sample of DNA sequences. Genetics 111, 147-164 (1985)
12. Hudson, R.R., Kaplan, N.L.: The coalescent process in models with selection and recombination. Genetics 120, 831-840 (1988)
13. Hudson, R.R., Slatkin, M., Maddison, W.P.: Estimation of levels of gene flow from DNA sequence data. Genetics 132, 583-589 (1992)
14. Jorde, L.B.: Linkage disequilibrium as a gene mapping tool. Am. J. Hum. Genet. 56, 11-14 (1995)
15. Kaplan, N.L., Darden, T., Hudson, R.R.: Coalescent process in models with selection. Genetics 120, 819-829 (1988)
16. Kaplan, N.L., Hudson, R.R., Iizuka, M.: Coalescent processes in models with selection, recombination and geographic subdivision. Genet. Res. Camb. 57, 83-91 (1991)
17. Kingman, J.F.C.: The coalescent. Stochastic Process. Appl. 13, 235-248 (1982)
18. Kruglyak, L.: Prospects for whole genome linkage disequilibrium mapping of common diseases. Nature Genetics 22, 139-144 (1999)
19. Lander, E.S.: The new genomics: global views of biology. Sci. 274, 536-539 (1996)
20. Latter, B.D.H.: The island model of population differentiation: a general solution. Genetics 73, 147-157 (1973)
21. Lewontin, R.C., Kojima, K.: The evolutionary dynamics of complex polymorphisms. Evolution 14, 450-472 (1960)
22. Maruyama, T.: Effective number of alleles in a subdivided population. Theoret. Pop. Biol. 1, 273-306 (1970)
23. Möhle, M.: A convergence theorem for Markov chains arising in population genetics and the coalescent with partial selfing. Adv. Appl. Prob. 30, 493-512 (1998)
24. Moran, P.A.P.: The theory of some genetical effects of population subdivision. Austr. J. Biol. Sci. 12, 109-116 (1959)
25. Nachman, M.W.: Single nucleotide polymorphisms and recombination rate in humans. Trends in Genetics 17, 481-485 (2001)
26. Nordborg, M.: Linkage disequilibrium, gene trees and selfing: an ancestral recombination graph with partial selfing. Genetics 154, 923-929 (2000)
27. Nordborg, M.: Coalescent theory. In: Handbook of Statistical Genetics, D. J. Balding, M. J. Bishop, C. Cannings, (eds.), John Wiley & Sons, Chichester, England, 2001
28. Nordborg, M., Donnelly, P.: The coalescent process with selfing. Genetics 146, 1185-1195 (1997)
29. Nordborg, M., Krone, S.M.: Separation of time scales and convergence to the coalescent in structured populations. In: Modern Developments in Theoretical Population Genetics, M. Slatkin, M. Veuille, (eds.), Oxford University Press, Oxford, UK, 2002
30. Pollack, E.: On the theory of partially inbreeding finite populations. I. Partial selfing. Genetics 117, 353-360 (1987)
31. Reich, D.E., Cargill, M., Bolk, S., Ireland, J., Sabeti, P.C., Richter, D.J., Lavery, T., Farhadian, S.F., Ward, R., Lander, E.S.: Linkage disequilibrium in the human genome. Nature 411, 199-204 (2001)
32. Risch, N., Merikangas, K.: The future of genetic studies of complex human diseases. Sci. 273, 1516-1517 (1996)
33. Wakeley, J.: Segregating sites in Wright's island model. Theoret. Pop. Biol. 53, 166-175 (1998)
34. Wakeley, J.: Non-equilibrium migration in human history. Genetics 153, 1863-1871 (1999)
35. Wakeley, J.: The coalescent in an island model of population subdivision with variation among demes. Theoret. Pop. Biol. 59, 133-144 (2001)
36. Wakeley, J., Lessard, S.: Theory of the effects of population structure and sampling on patterns of linkage disequilibrium applied to genomic data from humans. Genetics 164, 1043-1053 (2003)
37. Wall, J.D.: A comparison of estimators of the population recombination rate. Mol. Biol. Evol. 17, 156-163 (1999)
38. Wilkinson-Herbots, H.M.: Genealogy and subpopulation differentiation under various models of population structure. J. Math. Biol. 37, 535-585 (1998)
39. Wright, S.: Evolution in Mendelian populations. Genetics 16, 97-159 (1931)
40. Wright, S.: Isolation by distance. Genetics 28, 114-138 (1943)