Theoretical and Applied Genetics

, Volume 126, Issue 6, pp 1457–1472 | Cite as

Contribution of an additive locus to genetic variance when inheritance is multi-factorial with implications on interpretation of GWAS

  • Daniel Gianola
  • Frederic Hospital
  • Etienne Verrier
Original Paper


Although the effects of linkage disequilibrium (LD) on partition of genetic variance have received attention in quantitative genetics, there has been little discussion on how this phenomenon affects attribution of variance to a given locus. This paper reinforces the point that standard metrics used for assessing the contribution of a locus to variance can be misleading when there is linkage LD and that factors such as distribution of effects and of allelic frequencies over loci, or existence of frequency-dependent effects, play a role as well. An apparently new metric is proposed for measuring how much of the variability is contributed by a locus when LD exists. Effects of intervening factors, such as type and extent of LD, number of loci, distribution of effects, and of allelic frequencies over loci, as well as a model for generating frequency-dependent effects, are illustrated via hypothetical simulation scenarios. Implications on the interpretation of genome-wide association studies (GWAS), as typically carried out in human genetics, where single marker regression and the assumption of a sole quantitative trait locus (QTL) are common, are discussed. It is concluded that the standard attributions to variance contributed by a single QTL from a GWAS analysis may be misleading, conceptually and statistically, when a trait is complex and affected by sets of many genes in linkage disequilibrium. Yet another factor to consider in the “missing heritability” saga?.


  1. Avery PJ, Hill WG (1979) Variance in quantitative traits due to linked dominant genes and variance in heterozygosity in small populations. Genetics 91:817–844PubMedGoogle Scholar
  2. Barton NH (2000) Estimating multilocus linkage disequilibria. Heredity 84:373–389PubMedCrossRefGoogle Scholar
  3. Beavis WD (1998) QTL analysis: Power, precision, and accuracy. pp. 145–161. In: Paterson AH (ed.) Molecular dissection of complex traits. CRC Press, Boca RationGoogle Scholar
  4. Bulmer MG (1971) The effect of selection on genetic variability. Am Nat 105:201–211CrossRefGoogle Scholar
  5. Bulmer MG (1976) Regressions between relatives. Genet Res 28:199–203PubMedCrossRefGoogle Scholar
  6. Bulmer MG (1980) The Mathematical Theory of Quantitative Genetics. Oxford University Press, New YorkGoogle Scholar
  7. Comstock RE, Robinson HF (1952) Estimation of average dominance of genes. In JW Gowen (ed.) Heterosis, pp 494–516. Lowa State College Press, AmesGoogle Scholar
  8. Daetwyler, HD, Pong-Wong R, Villanueva B, Wooliams JA (2010) The impact of genetic architecture on genome-wide evaluation methods. Genetics 185:1021–1031PubMedCrossRefGoogle Scholar
  9. de los Campos G, Gianola D, Allison DAB (2010) Predicting genetic predisposition in humans: the promise of whole-genome markers. Nat Rev Genet 11:880–886CrossRefGoogle Scholar
  10. Emigh TH (1977) Partition of phenotypic variance under unknown dependent association of genotypes and environments. Biometrics 33:505–514CrossRefGoogle Scholar
  11. Falconer DS, Mackay TFC (1996) Introduction to Quantitative Genetics. 4th edn. Longman, New YorkGoogle Scholar
  12. Fisher RA (1918) The correlation between relatives on the suppostion of Mendelian inheritance. Trans Royal Soc Edinburgh 52:399–433CrossRefGoogle Scholar
  13. Gianola D, de los Campos G, Hill WG, Manfredi E, Fernando RL (2009) Additive genetic variability and the Bayesian alphabet. Genetics 183:347–363PubMedCrossRefGoogle Scholar
  14. Goldberger AS (1977) Models and methods in the IQ debate, Part I. Social Systems Research Institute Workshop Series, Number 7710. University of Wisconsin, MadisonGoogle Scholar
  15. Goddard ME, Hayes BJ (2009) Mapping genes for complex traits in domestic animals and their use in breeding programmes. Nat Rev Genet 10:381–391PubMedCrossRefGoogle Scholar
  16. Hayes JF, Hill WG (1981) Modification of estimates of parameters in the construction of genetic selection indices. Biometrics 37:483–493CrossRefGoogle Scholar
  17. Hedrick PW (1987) Gametic disequilibrium measures: proceed with caution. Genetics 117:331–341PubMedGoogle Scholar
  18. Henderson CR (1953) Estimation of variance and covariance components. Biometrics 9:226–252CrossRefGoogle Scholar
  19. Heslot N, Yang HP, Sorrells ME, Jannink JL (2012) Genomic selection in plant breeding: a comparison of models. Crop Sci 52:146–160Google Scholar
  20. Hill WG, Robertson A (1966) The effect of linkage on limits to artificial selection. Genet Res 8:269–294PubMedCrossRefGoogle Scholar
  21. Hill WG, Robertson, A (1968) Linkage disequilibrium in finite populations. Theor Appl Genet 38:226–231CrossRefGoogle Scholar
  22. Hospital F (1992) Effets de la liaison genique et des effectifs finis sur la variabilité des caracteres quantitatifs sous selection. These de Doctorat. Universite de Motpellier II, Academie de MontpellierGoogle Scholar
  23. Kathiresan S, Melander O, Guiducci O, Surti A, Burtt N, Rieder MJ, Cooper GM, Roos C, Voight BF, Havulinna AS, Wahlstrand B, Hedner T, Corella D, Shyong T, Ordovas JM, Berglund G, Vartiainen E, Jousilahti P, Hedblad B, Taskinen MR, Newton-Cheh C, Salomaa V, Peltonen L, Groop L, Altshuler DM, Orho-Melander M (2008) Six new loci associated with blood low-density lipoprotein cholesterol, high-density lipoprotein cholesterol or triglycerides in humans. Nat Genet 40:189–196PubMedCrossRefGoogle Scholar
  24. Kempthorne O (1978) Logical, epistemological and statistical aspects of nature-nurture data interpretation. Biometrics 34:1–23PubMedCrossRefGoogle Scholar
  25. Lewontin RC, Rose A, Kamin LJ (1984) Not in Our Genes: Biology, Ideology, and Human Nature. New York, PenguinGoogle Scholar
  26. Lewontin RC (1988) On measures of gametic disequilibrium. Genetics 120:849–852PubMedGoogle Scholar
  27. Lynch M, Walsh B (1998) Genetics and Analysis of Quantitative Traits. Sinauer, SunderlandGoogle Scholar
  28. Manolio TA, Collins FS, Cox NJ, Goldstein DB, Hindorff LA, Hunter DJ, McCarthy MI, Ramos EM, Cardon LR, Chakravarti A, Cho JH, Guttmacher AE, Kong A, Kruglyak L, Mardis E, Rotimi CN, Slatkin M, Valle D, Whittemore AS, Boehnke M, Clark AG, Eichler EE, Gibson G, Haines JL, Mackay TF, McCarroll SA, Visscher PM (2009) Finding the missing heritability of complex diseases. Nature 8. doi:10.1038/nature08494
  29. Marchetti GM, Drton M (2010) ggm: Graphical Gaussian Models. R package version 1.0.4.
  30. Marsaglia G, Olkin I (1984) Generating correlation matrices. SIAM J Sci Stat Comput 5:470–475CrossRefGoogle Scholar
  31. Meuwissen TH, Hayes BJ, Goddard ME (2001) Prediction of total genetic value using genome-wide dense marker maps. Genetics 157:1819–1829PubMedGoogle Scholar
  32. Ober U, Ayroles JF, Stone EA, Richards S, Zhu D, Gibbs RA, Stricker C, Gianola D, Schlather M, Mackay TFC, Simianer H (2012) Using whole-genome sequence data to predict quantitative trait phenotypes in Drosophila melanogaster. PLos Genet 8:e1002685PubMedCrossRefGoogle Scholar
  33. Powell JE, Kranis A, Floyd J, Dekkers JCM, Knott S, Haley CS (2011) Optimal use of regression models in genome-wide association studies. Anim Genet 43:133–143PubMedCrossRefGoogle Scholar
  34. Sabatti C, Risch N (2002) Homozygosity and linkage disequilibrium. Genetics 160:1707–1719PubMedGoogle Scholar
  35. Searle SR (1971) Linear Models. Wiley, New York Google Scholar
  36. Speliotes EK, Willer CJ, Berndt SI, Monda KL, Thorleifsson G et al (2010) Association analyses of 249,796 individuals reveal 18 new loci associated with body mass index. Nat Genet 42:937–948PubMedCrossRefGoogle Scholar
  37. Stranger BE, Stahl EA, Raj T (2011) Progress and promise of genome-wide association studies for human complex trait genetics. Genetics 187:367–383PubMedCrossRefGoogle Scholar
  38. Thompson R (1979) Sire evaluation. Biometrics 35:339–353CrossRefGoogle Scholar
  39. Turelli M, Barton NH (1990) Dinamycs of polygenic characters under selection. Theor Popul Biol 38:1–57CrossRefGoogle Scholar
  40. Weir B (2008) Linkage disequilibrium and association mapping. Annu Rev Genom Human Genet 9:129–142CrossRefGoogle Scholar
  41. Wu X, Ye Y, Rosell R, Amos CI et al (2011) Genome-wide association study of survival in non–small cell lung cancer patients receiving platinum-based chemotherapy. J Natl Cancer Inst 103:817–825PubMedCrossRefGoogle Scholar
  42. Xu S (2003) Theoretical basis of the Beavis effect. Genetics 165:2259–2268PubMedGoogle Scholar
  43. Zhang X-S, Wang J, Hill WG (2002) Pleiotropic model of maintenance of quantitative genetic variation at mutation–selection balance. Genetics 161:419–433PubMedGoogle Scholar
  44. Zhao H, Nettleton D, Soller M, Dekkers JCM (2005) Evaluation of linkage disequilibrium measures between multi-allelic markers as predictors of linkage disequilibrium between markers and QTL. Genet Res Camb 86:77–87CrossRefGoogle Scholar
  45. Zuk O, Hechter E, Sunyaev SR, Lander ES (2012) The mystery of missing heritability: genetic interactions create phantom heritability. Proc Natl Academy Sci 109:1193–1198CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Daniel Gianola
    • 1
    • 2
  • Frederic Hospital
    • 3
  • Etienne Verrier
    • 4
  1. 1.Department of Animal SciencesUniversity of Wisconsin-MadisonMadisonUSA
  2. 2.Department of Animal and Aquacultural SciencesNorwegian University of Life SciencesÅsNorway
  3. 3.INRA, UMR1313 Génétique animale et biologie intégrativeJouy-en-JosasFrance
  4. 4.AgroParisTechUMR1313 Génétique animale et biologie intégrativeParis 05France

Personalised recommendations