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. 2003 Jul;164(3):1043–1053. doi: 10.1093/genetics/164.3.1043

Theory of the effects of population structure and sampling on patterns of linkage disequilibrium applied to genomic data from humans.

John Wakeley 1, Sabin Lessard 1
PMCID: PMC1462626  PMID: 12871914

Abstract

We develop predictions for the correlation of heterozygosity and for linkage disequilibrium between two loci using a simple model of population structure that includes migration among local populations, or demes. We compare the results for a sample of size two from the same deme (a single-deme sample) to those for a sample of size two from two different demes (a scattered sample). The correlation in heterozygosity for a scattered sample is surprisingly insensitive to both the migration rate and the number of demes. In contrast, the correlation in heterozygosity for a single-deme sample is sensitive to both, and the effect of an increase in the number of demes is qualitatively similar to that of a decrease in the migration rate: both increase the correlation in heterozygosity. These same conclusions hold for a commonly used measure of linkage disequilibrium (r(2)). We compare the predictions of the theory to genomic data from humans and show that subdivision might account for a substantial portion of the genetic associations observed within the human genome, even though migration rates among local populations of humans are relatively large. Because correlations due to subdivision rather than to physical linkage can be large even in a single-deme sample, then if long-term migration has been important in shaping patterns of human polymorphism, the common practice of disease mapping using linkage disequilibrium in "isolated" local populations may be subject to error.

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Selected References

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  1. Eaves I. A., Merriman T. R., Barber R. A., Nutland S., Tuomilehto-Wolf E., Tuomilehto J., Cucca F., Todd J. A. The genetically isolated populations of Finland and sardinia may not be a panacea for linkage disequilibrium mapping of common disease genes. Nat Genet. 2000 Jul;25(3):320–323. doi: 10.1038/77091. [DOI] [PubMed] [Google Scholar]
  2. Ewens W. J., Spielman R. S. The transmission/disequilibrium test: history, subdivision, and admixture. Am J Hum Genet. 1995 Aug;57(2):455–464. [PMC free article] [PubMed] [Google Scholar]
  3. Gabriel Stacey B., Schaffner Stephen F., Nguyen Huy, Moore Jamie M., Roy Jessica, Blumenstiel Brendan, Higgins John, DeFelice Matthew, Lochner Amy, Faggart Maura. The structure of haplotype blocks in the human genome. Science. 2002 May 23;296(5576):2225–2229. doi: 10.1126/science.1069424. [DOI] [PubMed] [Google Scholar]
  4. Harpending H. C., Batzer M. A., Gurven M., Jorde L. B., Rogers A. R., Sherry S. T. Genetic traces of ancient demography. Proc Natl Acad Sci U S A. 1998 Feb 17;95(4):1961–1967. doi: 10.1073/pnas.95.4.1961. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Hawks J., Hunley K., Lee S. H., Wolpoff M. Population bottlenecks and Pleistocene human evolution. Mol Biol Evol. 2000 Jan;17(1):2–22. doi: 10.1093/oxfordjournals.molbev.a026233. [DOI] [PubMed] [Google Scholar]
  6. Helweg-Larsen J., Benfield T. L., Eugen-Olsen J., Lundgren J. D., Lundgren B. Effects of mutations in Pneumocystis carinii dihydropteroate synthase gene on outcome of AIDS-associated P. carinii pneumonia. Lancet. 1999 Oct 16;354(9187):1347–1351. doi: 10.1016/S0140-6736(99)03320-6. [DOI] [PubMed] [Google Scholar]
  7. Hey J. A multi-dimensional coalescent process applied to multi-allelic selection models and migration models. Theor Popul Biol. 1991 Feb;39(1):30–48. doi: 10.1016/0040-5809(91)90039-i. [DOI] [PubMed] [Google Scholar]
  8. Hudson R. R. Estimating the recombination parameter of a finite population model without selection. Genet Res. 1987 Dec;50(3):245–250. doi: 10.1017/s0016672300023776. [DOI] [PubMed] [Google Scholar]
  9. Hudson R. R. The sampling distribution of linkage disequilibrium under an infinite allele model without selection. Genetics. 1985 Mar;109(3):611–631. doi: 10.1093/genetics/109.3.611. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Hudson R. R. Two-locus sampling distributions and their application. Genetics. 2001 Dec;159(4):1805–1817. doi: 10.1093/genetics/159.4.1805. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Jorde L. B. Linkage disequilibrium as a gene-mapping tool. Am J Hum Genet. 1995 Jan;56(1):11–14. [PMC free article] [PubMed] [Google Scholar]
  12. Jorgensen Tove H., Degn Birte, Wang August G., Vang Maria, Gurling Hugh, Kalsi Gursharan, McQuillin Andrew, Kruse Torben A., Mors Ole, Ewald Henrik. Linkage disequilibrium and demographic history of the isolated population of the Faroe Islands. Eur J Hum Genet. 2002 Jun;10(6):381–387. doi: 10.1038/sj.ejhg.5200816. [DOI] [PubMed] [Google Scholar]
  13. Kaplan N. L., Hill W. G., Weir B. S. Likelihood methods for locating disease genes in nonequilibrium populations. Am J Hum Genet. 1995 Jan;56(1):18–32. [PMC free article] [PubMed] [Google Scholar]
  14. Kaplan N., Hudson R. R. The use of sample genealogies for studying a selectively neutral m-loci model with recombination. Theor Popul Biol. 1985 Dec;28(3):382–396. doi: 10.1016/0040-5809(85)90036-x. [DOI] [PubMed] [Google Scholar]
  15. Kong Augustine, Gudbjartsson Daniel F., Sainz Jesus, Jonsdottir Gudrun M., Gudjonsson Sigurjon A., Richardsson Bjorgvin, Sigurdardottir Sigrun, Barnard John, Hallbeck Bjorn, Masson Gisli. A high-resolution recombination map of the human genome. Nat Genet. 2002 Jun 10;31(3):241–247. doi: 10.1038/ng917. [DOI] [PubMed] [Google Scholar]
  16. Kruglyak L. Prospects for whole-genome linkage disequilibrium mapping of common disease genes. Nat Genet. 1999 Jun;22(2):139–144. doi: 10.1038/9642. [DOI] [PubMed] [Google Scholar]
  17. Lander E. S., Schork N. J. Genetic dissection of complex traits. Science. 1994 Sep 30;265(5181):2037–2048. doi: 10.1126/science.8091226. [DOI] [PubMed] [Google Scholar]
  18. Lander E. S. The new genomics: global views of biology. Science. 1996 Oct 25;274(5287):536–539. doi: 10.1126/science.274.5287.536. [DOI] [PubMed] [Google Scholar]
  19. Lewontin R C. The Interaction of Selection and Linkage. I. General Considerations; Heterotic Models. Genetics. 1964 Jan;49(1):49–67. doi: 10.1093/genetics/49.1.49. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Maruyama T. A simple proof that certain quantities are independent of the geographical structure of population. Theor Popul Biol. 1974 Apr;5(2):148–154. doi: 10.1016/0040-5809(74)90037-9. [DOI] [PubMed] [Google Scholar]
  21. McVean Gilean A. T. A genealogical interpretation of linkage disequilibrium. Genetics. 2002 Oct;162(2):987–991. doi: 10.1093/genetics/162.2.987. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Nei M., Li W. H. Linkage disequilibrium in subdivided populations. Genetics. 1973 Sep;75(1):213–219. doi: 10.1093/genetics/75.1.213. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Nielsen R. Estimation of population parameters and recombination rates from single nucleotide polymorphisms. Genetics. 2000 Feb;154(2):931–942. doi: 10.1093/genetics/154.2.931. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Nordborg M. Linkage disequilibrium, gene trees and selfing: an ancestral recombination graph with partial self-fertilization. Genetics. 2000 Feb;154(2):923–929. doi: 10.1093/genetics/154.2.923. [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. Ohta T., Kimura M. Linkage disequilibrium between two segregating nucleotide sites under the steady flux of mutations in a finite population. Genetics. 1971 Aug;68(4):571–580. doi: 10.1093/genetics/68.4.571. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. Ohta T. Linkage disequilibrium with the island model. Genetics. 1982 May;101(1):139–155. doi: 10.1093/genetics/101.1.139. [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. Pluzhnikov A., Donnelly P. Optimal sequencing strategies for surveying molecular genetic diversity. Genetics. 1996 Nov;144(3):1247–1262. doi: 10.1093/genetics/144.3.1247. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. Pluzhnikov Anna, Di Rienzo Anna, Hudson Richard R. Inferences about human demography based on multilocus analyses of noncoding sequences. Genetics. 2002 Jul;161(3):1209–1218. doi: 10.1093/genetics/161.3.1209. [DOI] [PMC free article] [PubMed] [Google Scholar]
  29. Pritchard J. K., Przeworski M. Linkage disequilibrium in humans: models and data. Am J Hum Genet. 2001 Jun 14;69(1):1–14. doi: 10.1086/321275. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Przeworski M., Hudson R. R., Di Rienzo A. Adjusting the focus on human variation. Trends Genet. 2000 Jul;16(7):296–302. doi: 10.1016/s0168-9525(00)02030-8. [DOI] [PubMed] [Google Scholar]
  31. Reich D. E., Cargill M., Bolk S., Ireland J., Sabeti P. C., Richter D. J., Lavery T., Kouyoumjian R., Farhadian S. F., Ward R. Linkage disequilibrium in the human genome. Nature. 2001 May 10;411(6834):199–204. doi: 10.1038/35075590. [DOI] [PubMed] [Google Scholar]
  32. Reich David E., Schaffner Stephen F., Daly Mark J., McVean Gil, Mullikin James C., Higgins John M., Richter Daniel J., Lander Eric S., Altshuler David. Human genome sequence variation and the influence of gene history, mutation and recombination. Nat Genet. 2002 Aug 5;32(1):135–142. doi: 10.1038/ng947. [DOI] [PubMed] [Google Scholar]
  33. Risch N., Merikangas K. The future of genetic studies of complex human diseases. Science. 1996 Sep 13;273(5281):1516–1517. doi: 10.1126/science.273.5281.1516. [DOI] [PubMed] [Google Scholar]
  34. Slatkin M. Inbreeding coefficients and coalescence times. Genet Res. 1991 Oct;58(2):167–175. doi: 10.1017/s0016672300029827. [DOI] [PubMed] [Google Scholar]
  35. Slatkin M. Linkage disequilibrium in growing and stable populations. Genetics. 1994 May;137(1):331–336. doi: 10.1093/genetics/137.1.331. [DOI] [PMC free article] [PubMed] [Google Scholar]
  36. Strobeck C., Morgan K. The effect of intragenic recombination on the number of alleles in a finite population. Genetics. 1978 Apr;88(4):829–844. doi: 10.1093/genetics/88.4.829. [DOI] [PMC free article] [PubMed] [Google Scholar]
  37. Vitalis R., Couvet D. Estimation of effective population size and migration rate from one- and two-locus identity measures. Genetics. 2001 Feb;157(2):911–925. doi: 10.1093/genetics/157.2.911. [DOI] [PMC free article] [PubMed] [Google Scholar]
  38. Vitalis R., Couvet D. Two-locus identity probabilities and identity disequilibrium in a partially selfing subdivided population. Genet Res. 2001 Feb;77(1):67–81. doi: 10.1017/s0016672300004833. [DOI] [PubMed] [Google Scholar]
  39. Wakeley J., Aliacar N. Gene genealogies in a metapopulation. Genetics. 2001 Oct;159(2):893–905. doi: 10.1093/genetics/159.2.893. [DOI] [PMC free article] [PubMed] [Google Scholar]
  40. Wakeley J., Nielsen R., Liu-Cordero S. N., Ardlie K. The discovery of single-nucleotide polymorphisms--and inferences about human demographic history. Am J Hum Genet. 2001 Nov 6;69(6):1332–1347. doi: 10.1086/324521. [DOI] [PMC free article] [PubMed] [Google Scholar]
  41. Wakeley J. Nonequilibrium migration in human history. Genetics. 1999 Dec;153(4):1863–1871. doi: 10.1093/genetics/153.4.1863. [DOI] [PMC free article] [PubMed] [Google Scholar]
  42. Wakeley J. Segregating sites in Wright's island model. Theor Popul Biol. 1998 Apr;53(2):166–174. doi: 10.1006/tpbi.1997.1355. [DOI] [PubMed] [Google Scholar]
  43. Wakeley J. Using the variance of pairwise differences to estimate the recombination rate. Genet Res. 1997 Feb;69(1):45–48. doi: 10.1017/s0016672396002571. [DOI] [PubMed] [Google Scholar]
  44. Wright A. F., Carothers A. D., Pirastu M. Population choice in mapping genes for complex diseases. Nat Genet. 1999 Dec;23(4):397–404. doi: 10.1038/70501. [DOI] [PubMed] [Google Scholar]
  45. Wright S. Evolution in Mendelian Populations. Genetics. 1931 Mar;16(2):97–159. doi: 10.1093/genetics/16.2.97. [DOI] [PMC free article] [PubMed] [Google Scholar]

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