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. 2001 Feb;157(2):911–925. doi: 10.1093/genetics/157.2.911

Estimation of effective population size and migration rate from one- and two-locus identity measures.

R Vitalis 1, D Couvet 1
PMCID: PMC1461504  PMID: 11157007

Abstract

Standard methods for inferring demographic parameters from genetic data are based mainly on one-locus theory. However, the association of genes at different loci (e.g., two-locus identity disequilibrium) may also contain some information about demographic parameters of populations. In this article, we define one- and two-locus parameters of population structure as functions of one- and two-locus probabilities for the identity in state of genes. Since these parameters are known functions of demographic parameters in an infinite island model, we develop moment-based estimators of effective population size and immigration rate from one- and two-locus parameters. We evaluate this method through simulation. Although variance and bias may be quite large, increasing the number of loci on which the estimates are derived improves the method. We simulate an infinite allele model and a K allele model of mutation. Bias and variance are smaller with increasing numbers of alleles per locus. This is, to our knowledge, the first attempt of a joint estimation of local effective population size and immigration rate.

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Selected References

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  1. Avery P. J., Hill W. G. Variance in quantitative traits due to linked dominant genes and variance in heterozygosity in small populations. Genetics. 1979 Apr;91(4):817–844. doi: 10.1093/genetics/91.4.817. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Beerli P., Felsenstein J. Maximum-likelihood estimation of migration rates and effective population numbers in two populations using a coalescent approach. Genetics. 1999 Jun;152(2):763–773. doi: 10.1093/genetics/152.2.763. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Caballero A. Developments in the prediction of effective population size. Heredity (Edinb) 1994 Dec;73(Pt 6):657–679. doi: 10.1038/hdy.1994.174. [DOI] [PubMed] [Google Scholar]
  4. Cockerham C. C. Additive by additive variance with inbreeding and linkage. Genetics. 1984 Oct;108(2):487–500. doi: 10.1093/genetics/108.2.487. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Cockerham C. C., Weir B. S. Correlations, descent measures: drift with migration and mutation. Proc Natl Acad Sci U S A. 1987 Dec;84(23):8512–8514. doi: 10.1073/pnas.84.23.8512. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Crow J. F., Aoki K. Group selection for a polygenic behavioral trait: estimating the degree of population subdivision. Proc Natl Acad Sci U S A. 1984 Oct;81(19):6073–6077. doi: 10.1073/pnas.81.19.6073. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Hedrick P. W. Gametic disequilibrium measures: proceed with caution. Genetics. 1987 Oct;117(2):331–341. doi: 10.1093/genetics/117.2.331. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Hill W. G., Weir B. S. Maximum-likelihood estimation of gene location by linkage disequilibrium. Am J Hum Genet. 1994 Apr;54(4):705–714. [PMC free article] [PubMed] [Google Scholar]
  9. Lewontin R. C. On measures of gametic disequilibrium. Genetics. 1988 Nov;120(3):849–852. doi: 10.1093/genetics/120.3.849. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Luikart G., Cornuet J. M. Estimating the effective number of breeders from heterozygote excess in progeny. Genetics. 1999 Mar;151(3):1211–1216. doi: 10.1093/genetics/151.3.1211. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Nei M., Tajima F. Genetic drift and estimation of effective population size. Genetics. 1981 Jul;98(3):625–640. doi: 10.1093/genetics/98.3.625. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Ohta T. Linkage disequilibrium between amino acid sites in immunoglobulin genes and other multigene families. Genet Res. 1980 Oct;36(2):181–197. doi: 10.1017/s0016672300019790. [DOI] [PubMed] [Google Scholar]
  13. Ohta T. Linkage disequilibrium due to random genetic drift in finite subdivided populations. Proc Natl Acad Sci U S A. 1982 Mar;79(6):1940–1944. doi: 10.1073/pnas.79.6.1940. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. 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]
  15. Pudovkin A. I., Zaykin D. V., Hedgecock D. On the potential for estimating the effective number of breeders from heterozygote-excess in progeny. Genetics. 1996 Sep;144(1):383–387. doi: 10.1093/genetics/144.1.383. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Reynolds J., Weir B. S., Cockerham C. C. Estimation of the coancestry coefficient: basis for a short-term genetic distance. Genetics. 1983 Nov;105(3):767–779. doi: 10.1093/genetics/105.3.767. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Rousset F. Equilibrium values of measures of population subdivision for stepwise mutation processes. Genetics. 1996 Apr;142(4):1357–1362. doi: 10.1093/genetics/142.4.1357. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Slatkin M. Gene flow and the geographic structure of natural populations. Science. 1987 May 15;236(4803):787–792. doi: 10.1126/science.3576198. [DOI] [PubMed] [Google Scholar]
  19. Slatkin M. Inbreeding coefficients and coalescence times. Genet Res. 1991 Oct;58(2):167–175. doi: 10.1017/s0016672300029827. [DOI] [PubMed] [Google Scholar]
  20. Slatkin M., Maddison W. P. A cladistic measure of gene flow inferred from the phylogenies of alleles. Genetics. 1989 Nov;123(3):603–613. doi: 10.1093/genetics/123.3.603. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Smith J. M., Hoekstra R. Polymorphism in a varied environment: how robust are the models? Genet Res. 1980 Feb;35(1):45–57. doi: 10.1017/s0016672300013926. [DOI] [PubMed] [Google Scholar]
  22. Tachida H., Cockerham C. C. Analysis of linkage disequilibrium in an island model. Theor Popul Biol. 1986 Apr;29(2):161–197. doi: 10.1016/0040-5809(86)90008-0. [DOI] [PubMed] [Google Scholar]
  23. Tufto J., Engen S., Hindar K. Inferring patterns of migration from gene frequencies under equilibrium conditions. Genetics. 1996 Dec;144(4):1911–1921. doi: 10.1093/genetics/144.4.1911. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Weir B. S., Cockerham C. C. Group inbreeding with two linked loci. Genetics. 1969 Nov;63(3):711–742. doi: 10.1093/genetics/63.3.711. [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. Weir B. S., Hill W. G. Effect of mating structure on variation in linkage disequilibrium. Genetics. 1980 Jun;95(2):477–488. doi: 10.1093/genetics/95.2.477. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. Whitlock M. C., Barton N. H. The effective size of a subdivided population. Genetics. 1997 May;146(1):427–441. doi: 10.1093/genetics/146.1.427. [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. 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]
  28. van Noordwijk A. J. The interaction of inbreeding depression and environmental stochasticity in the risk of extinction of small populations. EXS. 1994;68:131–146. doi: 10.1007/978-3-0348-8510-2_12. [DOI] [PubMed] [Google Scholar]

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