Evaluation of the Linkage Disequilibrium Method for Estimating Effective Population Size

Part of the Environmental and Ecological Statistics book series (ENES, volume 3)


Data on linkage disequilibrium at unlinked loci provide an estimate of the inbreeding effective population size of the parental generation of the sampled cohort. The inbreeding effective population size, N e , is the reciprocal of the probability that two gametes, selected at random without replacement from those that produced the sampled cohort, derive from the same parent. Effective population size is an important parameter for measuring the rate of inbreeding in a population. We detail the construction of the linkage disequilibrium estimator of N e , and evaluate its performance by simulation. We simulate populations which are dioecious and non-selfing. We use the simulations to examine the effects of several types of deviation from ideal population conditions, and of sample size, genotyping errors, number of loci typed, and polymorphic loci. We find substantial bias in the N e estimator when there have been recent fluctuations in census population size, when the index of breeding variability is greater than one, and when the ratio of sample size to effective population size differs substantially from one. Due to high variability, estimators that have low bias for the reciprocal of N e can present substantial bias when used as estimators of N e itself. We consider a recent small sample size bias correction proposed for the method, and find that it improves bias in the reciprocal, but at the expense of increased bias for N e . The improvements in the bias of the reciprocal are usually small, but are substantial when sample size is much less than N e , while the increase in bias for N e is often substantial. We test the method on two exhaustively sampled rat populations, and find it performs as expected from simulation. For practitioners, we recommend that resources are spent first in ensuring that the sample size is likely to be greater than the effective population size, and only then that the number of loci is increased to improve the precision of the estimate.


Burrow’s composite disequilibrium measure Effective population size Non-ideal populations Rats Rattus Squared correlation coefficient 


  1. Barrowclough GF, Rockwell RF (1993) Variance of lifetime reproductive success: estimation based on demographic data. American Naturalist 141:281–295CrossRefGoogle Scholar
  2. Bartley D, Bagley M, Gall G, Bentley B (1992) Use of linkage disequilibrium data to estimate effective size of hatchery and natural fish populations. Conservation Biology 6:365–375.CrossRefGoogle Scholar
  3. Berthier P, Beaumont MA, Cornuet J-M, Luikart G (2002) Likelihood-based estimation of the effective population size using temporal changes in allele frequencies: a genealogical approach. Genetics 160:741–751.Google Scholar
  4. Borchers DL, Buckland ST, Zucchini W (2002) Estimating animal abundance: closed populations. Springer, London.CrossRefGoogle Scholar
  5. Buckland ST, Newman KB, Thomas L, Koesters NB (2004) State-space models for the dynamics of wild animal populations. Ecological Modelling 171:157–175.CrossRefGoogle Scholar
  6. Caballero A, Hill WG (1992) A note on the inbreeding effective population size. Evolution 46:1969–1972.CrossRefGoogle Scholar
  7. Caballero A (1994) Developments in the prediction of effective population size. Heredity 73: 657–679.CrossRefGoogle Scholar
  8. Campton DE (1987) Natural hybridization and introgression in fishes. In: Ryman N, Utter F (eds) Population genetics and fishery management. University of Washington Press, Seattle, pp 161–192.Google Scholar
  9. Caswell H (2001) Matrix population models: construction, analysis, and interpretation. Sinauer Associates, Sunderland.Google Scholar
  10. Cockerham CC, Weir BS (1977) Digenic descent measures for finite populations. Genetical Research 30:121–147.CrossRefGoogle Scholar
  11. Crandall KA, Posada D, Vasco D (1999) Effective population sizes: missing measures and missing concepts. Animal Conservation 2:17–319.CrossRefGoogle Scholar
  12. Crow JF, Kimura M (1970) An introduction to population genetics theory. Burgess, Minneapolis.Google Scholar
  13. Crow JF, Denniston C (1988) Inbreeding and variance effective population numbers. Evolution 42:482–495.CrossRefGoogle Scholar
  14. England PR, Cornuet J-M, Berthier P, Tallmon DA, Luikart G (2006) Estimating effective population size from linkage disequilibrium: severe bias in small samples. Conservation Genetics 7:303–308.CrossRefGoogle Scholar
  15. Frankham R (1995) Effective population size / adult population size ratios in wildlife: a review. Genetical Research 66:95–107.CrossRefGoogle Scholar
  16. Garza JC, Williamson EG (2001) Detection of reduction in population size using data from microsatellite loci. Molecular Ecology 10:305–318.CrossRefGoogle Scholar
  17. Hayes BJ, Visscher PM, McPartlan HC, Goddard ME (2003) Novel multilocus measure of linkage disequilibrium to estimate past effective population size. Genome Research 13:635–643.CrossRefGoogle Scholar
  18. Heiberg A-C, Leirs H, Siegismund HR (2006) Reproductive success of bromadiolone-resistant rats in absence of anticoagulant pressure. Pest Management Science 62:862–871.CrossRefGoogle Scholar
  19. Hill WG (1981) Estimation of effective population size from data on linkage disequilibrium. Genetical Research 38:209–216.CrossRefGoogle Scholar
  20. Hoffman JI, Amos W (2005) Microsatellite genotyping errors: detection approaches, common sources and consequences for paternal exclusion. Molecular Ecology 14:599–612.CrossRefGoogle Scholar
  21. Holland BS (2000) Genetics of marine bioinvasions. Hydrobiologia 420:63–71.CrossRefGoogle Scholar
  22. Innes JG (2005a) Ship rat. In: King CM (ed) The handbook of New Zealand mammals. Oxford University Press, Melbourne, pp 187–203.Google Scholar
  23. Innes JG (2005b) Norway rat. In: King CM (ed) The handbook of New Zealand mammals. Oxford University Press, Melbourne, pp 174–187.Google Scholar
  24. Lande R, Barrowclough GF (1987) Effective population size, genetic variation, and their use in population management. In: Soulé M (ed) Viable populations for conservation. Cambridge University Press, Cambridge, pp 87–123.CrossRefGoogle Scholar
  25. Laurie-Ahlberg CC, Weir BS (1979) Allozymic variation and linkage disequilibrium in some laboratory populations of Drosophila melanogaster. Genetics 92:1295–1314.Google Scholar
  26. Leberg P (2005) Genetic approaches for estimating the effective population size of populations. Journal of Wildlife Management 69:1385–1399.CrossRefGoogle Scholar
  27. Lippé C, Dumont P, Bernatchez L (2006) High genetic diversity and no inbreeding in the endangered copper redhorse, Moxostoma hubbsi (Catostomidae, Pisces): the positive side of a long generation time. Molecular Ecology 15:1769–1780.CrossRefGoogle Scholar
  28. Lynch M, Lande R (1998) The critical effective size for a genetically secure population. Animal Conservation 1:69–73.CrossRefGoogle Scholar
  29. Marshall TC, Slate J, Kruuke LEB, Pemberton JM (1998) Statistical confidence for likelihood-based paternity inference in natural populations. Molecular Ecology 7:639–655.CrossRefGoogle Scholar
  30. McKay JK, Bishop JG, Lin J-Z, Richards JH, Sala A, Mitchell-Olds T (2001) Local adaptation across a climatic gradient despite small effective population size in the rare sapphire rockcress. Proceedings of the Royal Society of London B 268:1715–1721.CrossRefGoogle Scholar
  31. Nunney L, Campbell KA (1993) Assessing minimum viable population size: demography meets population genetics. Trends in Ecology & Evolution 8:234–239.CrossRefGoogle Scholar
  32. Nunney L, Elam DR (1994) Estimating the effective population size of conserved populations. Conservation Biology 8:175–184.CrossRefGoogle Scholar
  33. Peel D, Ovenden JR, Peel SL (2004) NeEstimator: software for estimating effective population size (version 1.3). Queensland Government, Department of Primary Industries and Fisheries, Brisbane.Google Scholar
  34. Rockwell RF, Barrowclough GF (1995) Effective population size and lifetime reproductive success. Conservation Biology 9:1225–1233.CrossRefGoogle Scholar
  35. Sax DF, Brown JH (2000) The paradox of invasion. Global Ecology & Biogeography 9:363–371.CrossRefGoogle Scholar
  36. Schmeller DS, Merilä J (2007) Demographic and genetic estimates of effective population and breeding size in the amphibian Rana temporaria. Conservation Biology 21:142–151.CrossRefGoogle Scholar
  37. Schwartz MK, Tallmon DA, Luikart G (1998) Review of DNA-based census and effective population size estimators. Animal Conservation 1:293–299.CrossRefGoogle Scholar
  38. Seber GAF (1982) The estimation of animal abundance and related parameters. The Blackburn Press, Caldwell.Google Scholar
  39. Selkoe KA, Toonen RJ (2006) Microsatellites for ecologists: a practical guide to using and evaluating microsatellite markers. Ecology Letters 9:615–629.CrossRefGoogle Scholar
  40. Sugg DW, Chesser RK (1994) Effective population sizes with multiple paternity. Genetics 137:1147–1155.Google Scholar
  41. Sved JA (1971) Linkage disequilibrium and homozygosity of chromosome segments in finite populations. Theoretical Population Biology 2:125–141.CrossRefGoogle Scholar
  42. Van Oosterhout C, Hutchinson WF, Wills DPM, Shipley P (2004) MICRO-CHECKER: software for identifying and correcting genotyping errors in microsatellite data. Molecular Ecology Notes 4:535–538.CrossRefGoogle Scholar
  43. Vitalis R, Couvet D (2001) Two-locus identity probabilities and identity disequilibrium in a partially selfing subdivided population. Genetical Research 77:67–81.CrossRefGoogle Scholar
  44. Wang J (2001) A pseudo-likelihood method for estimating effective population size from temporally spaced samples. Genetical Research 78:243–257.CrossRefGoogle Scholar
  45. Wang J (2005) Estimation of effective population sizes from data on genetic markers. Philosophical Transactions of the Royal Society B 360:1395–1409.CrossRefGoogle Scholar
  46. Wang J, Caballero A (1999) Developments in predicting the effective size of subdivided populations. Heredity 82:212–226.CrossRefGoogle Scholar
  47. Wang J, Whitlock MC (2003) Estimating effective population size and migration rates from genetic samples over space and time. Genetics 163:429–446.Google Scholar
  48. Waples RS (1989) A generalized approach for estimating effective population size from temporal changes in allele frequency. Genetics 121:379–391.Google Scholar
  49. Waples RS (1991) Genetic methods for estimating the effective size of cetacean populations. Reports of the International Whaling Commission Special Issue 13:279–300.Google Scholar
  50. Waples RS (2005) Genetic estimates of contemporary effective population size: to what time periods do the estimates apply? Molecular Ecology 14:3335–3352.CrossRefGoogle Scholar
  51. Waples RS (2006) A bias correction for estimates of effective population size based on linkage disequilibrium at unlinked loci. Conservation Genetics 7:167–184.CrossRefGoogle Scholar
  52. Waples RS, Do C (in press) LDNE: a program for estimating effective population size from data on linkage disequilibrium. Molecular Ecology Resources.Google Scholar
  53. Weir BS (1979) Inferences about linkage disequilibrium. Biometrics 35:235–254.CrossRefMATHGoogle Scholar
  54. Weir BS, Hill WG (1980) Effect of mating structure on variation in linkage disequilibrium. Genetics 95:477–488.MathSciNetGoogle Scholar
  55. Weir BS, Avery PJ, Hill WG (1980) Effect of mating structure on variation in inbreeding. Theoretical Population Biology 18:396–429.CrossRefMATHMathSciNetGoogle Scholar
  56. Weir BS (1996) Genetic Data Analysis II: methods for discrete population genetic data. Sinauer Associates, Sunderland.Google Scholar
  57. Williamson EG, Slatkin M (1999) Using maximum likelihood to estimate population size from temporal changes in allele frequencies. Genetics 152:755–761.Google Scholar
  58. Wright S (1931) Evolution in mendelian populations. Genetics 16:97–159.Google Scholar

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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of AucklandNew Zealand

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