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On the Partitioning of Genetic Variance with Epistasis

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Epistasis

Part of the book series: Methods in Molecular Biology ((MIMB,volume 1253))

Abstract

The decomposition of genetic variance into additive, dominance, and epistatic components is a common procedure in quantitative genetics. Yet, the interpretation of this variance partition is not trivial, especially concerning nonadditive components. In this chapter, we compile various uses of variance partitioning from published analyses, new simulations, and theoretical examples. We show ways in which advanced genetic modeling facilitates the analysis of data through variance partitioning, focusing on the natural and orthogonal interactions (NOIA) model. We also discuss how epistasis and epistatic variance may influence the outcome of selection, a topic that is still a matter of debate among quantitative and evolutionary geneticists.

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References

  1. Fisher RA (1918) The correlation between relatives on the supposition of Mendelian inheritance. Trans R Soc Edinburgh 52:339–433

    Google Scholar 

  2. Falconer DS, MacKay TFC (1996) Introduction to quantitative genetics, 4th edn. Prentice Hall, Harlow

    Google Scholar 

  3. Galton F (1886) Regression towards mediocrity in hereditary stature. J R Anthropol Inst Great Brit Ireland 15:246–263

    Article  Google Scholar 

  4. Avery OT, MacLeod CM, McCarty M (1944) Studies on the chemical nature of the substance inducing transformation of pneumococcal types induction of transformation by a desoxyribonucleic acid fraction isolated from pneumococcus type ii. J Exp Med 79:137–158

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  5. Franklin R, Gosling RG (1953) Molecular configuration in sodium thymonucleate. Nature 171:740–741

    Article  CAS  PubMed  Google Scholar 

  6. Watson JD, Crick FHC (1953) A structure for deoxyribose nucleic acid. Nature 171:737–738

    Article  CAS  PubMed  Google Scholar 

  7. Thoday JM (1961) Location of polygenes. Nature 191:368–370

    Article  Google Scholar 

  8. Lander ES, Botstein D (1989) Mapping mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics 121(1):185–199

    CAS  PubMed Central  PubMed  Google Scholar 

  9. Travisano M, Shaw RG (2013) Lost in the map. Evolution 67(2):305–314

    Article  CAS  PubMed  Google Scholar 

  10. Cheverud JM (2000) Detecting epistasis among quantitative trait loci. In: Wolf JB, Brodie ED, Wade MJ (eds) Epistasis and the evolutionary process. Oxford University Press, Oxford, pp 58–81

    Google Scholar 

  11. Cheverud JM, Routman EJ (1995) Epistasis and its contribution to genetic variance components. Genetics 139(3):1455–1461

    CAS  PubMed Central  PubMed  Google Scholar 

  12. Hansen TF, Wagner GP (2001) Modeling genetic architecture: a multilinear theory of gene interaction. Theor Popul Biol 59(1):61–86

    Article  CAS  PubMed  Google Scholar 

  13. Kao CH, Zeng ZB (2002) Modeling epistasis of quantitative trait loci using Cockerham's model. Genetics 160(3):1243–1261

    PubMed Central  PubMed  Google Scholar 

  14. Mao Y, London NR, Ma L, Dvorkin D, Da Y (2006) Detection of SNP epistasis effects of quantitative traits using an extended Kempthorne model. Physiol Genomics 28(1):46–52

    Article  CAS  PubMed  Google Scholar 

  15. Yang R-C (2004) Epistasis of quantitative trait loci under different gene action models. Genetics 167(3):1493–1505

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  16. Kempthorne O (1954) The correlation between relatives in a random mating population. Proc R Soc Lond B Biol Sci 143(910):102–113

    Article  CAS  PubMed  Google Scholar 

  17. Cockerham CC (1954) An extension of the concept of partitioning hereditary variance for analysis of covariances among relatives when epistasis is present. Genetics 39:859–882

    CAS  PubMed Central  PubMed  Google Scholar 

  18. Álvarez-Castro JM, Carlborg Ö (2007) A unified model for functional and statistical epistasis and its application in quantitative trait loci analysis. Genetics 176(2):1151–1167

    Article  PubMed Central  PubMed  Google Scholar 

  19. Álvarez-Castro JM, Carlborg O, Ronnegard L (2012) Estimation and interpretation of genetic effects with epistasis using the NOIA model. Methods Mol Biol 871:191–204

    Article  PubMed  Google Scholar 

  20. Álvarez-Castro JM, Yang R-C (2011) Multiallelic models of genetic effects and variance decomposition in non-equilibrium populations. Genetica 139(9):1119–1134

    Google Scholar 

  21. Le Rouzic A, Álvarez-Castro JM (2008) Estimation of genetic effects and genotype-phenotype maps. Evol Bioinform 4:225–235

    Google Scholar 

  22. Kempthorne O (1957) An introduction to genetic statistics. Wiley, New York

    Google Scholar 

  23. Lynch M, Walsh B (1998) Genetic analysis of quantitative traits. Sinauer, Sunderland

    Google Scholar 

  24. Yang R-C, Álvarez-Castro JM (2008) Functional and statistical genetic effects with miltiple alleles. Curr Top Genet 3:49–62

    Google Scholar 

  25. Álvarez-Castro JM (2012) Current applications of models of genetic effects with interactions across the genome. Curr Genomics 13(2):163–175

    Article  PubMed Central  PubMed  Google Scholar 

  26. Burke JM, Arnold ML (2001) Genetics and the fitness of hybrids. Annu Rev Genet 35:31–52

    Article  CAS  PubMed  Google Scholar 

  27. Dobzhansky T (1936) Studies on hybrid sterility. II. Location of sterility factors in Drosophila pseudoobscura hybrids. Genetics 21:113–135

    CAS  PubMed Central  PubMed  Google Scholar 

  28. Wilder JA, Hammer MF (2004) European ACP1*C allele has recessive deleterious effects on early life viability. Hum Biol 76(6):817–835

    Article  PubMed Central  PubMed  Google Scholar 

  29. Brinkmann B, Hoppe HH, Hennig W, Koops E (1971) Red cell enzyme polymorphisms in a northern German population. Gene frequencies and population genetics of the acid phosphatase (AP), phosphoglucomutase (PGM), adenylate kinase (AK), adenosine deaminase (ADA) and 6-phosphogluconate dehydrogenase (6-PGD). Hum Hered 21(3):278–288

    Article  CAS  PubMed  Google Scholar 

  30. Greene LS, Bottini N, Borgiani P, Gloria-Bottini F (2000) Acid phosphatase locus 1 (ACP1): possible relationship of allelic variation to body size and human population adaptation to thermal stress – a theoretical perspective. Am J Hum Biol 12(5):688–701

    Article  PubMed  Google Scholar 

  31. Álvarez-Castro JM, Le Rouzic A, Andersson L, Siegel PB, Carlborg O (2012) Modelling of genetic interactions improves prediction of hybrid patterns – a case study in domestic fowl. Genet Res (Camb) 94(5):255–266

    Article  Google Scholar 

  32. Marquez GC, Siegel PB, Lewis RM (2010) Genetic diversity and population structure in lines of chickens divergently selected for high and low 8-week body weight. Poult Sci 89(12):2580–2588

    Article  CAS  PubMed  Google Scholar 

  33. Kerje S, Carlborg Ö, Jacobsson L, Schutz K, Hartmann C, Jensen P, Andersson L (2003) The twofold difference in adult size between the red junglefowl and White Leghorn chickens is largely explained by a limited number of QTLs. Anim Genet 34(4):264–274

    Article  CAS  PubMed  Google Scholar 

  34. Zuk O, Hechter E, Sunyaev SR, Lander ES (2012) The mystery of missing heritability: genetic interactions create phantom heritability. Proc Natl Acad Sci U S A 109(4):1193–1198

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  35. Kimura M, Crow JF (1978) Effect of overall phenotypic selection on genetic change at individual loci. Proc Natl Acad Sci U S A 75(12):6168–6171

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  36. Barton NH, Turelli M (2004) Effects of genetic drift on variance components under a general model of epistasis. Evolution 58(10):2111–2132

    Article  CAS  PubMed  Google Scholar 

  37. Turelli M, Barton NH (2006) Will population bottlenecks and multilocus epistasis increase additive genetic variance? Evolution 60(9):1763–1776

    Article  PubMed  Google Scholar 

  38. Templeton AR (2006) Population genetics and microevolutionary theory. Wiley-Liss, Hoboken, NJ

    Book  Google Scholar 

  39. Hemani G, Knott S, Haley C (2013) An evolutionary perspective on epistasis and the missing heritability. PLoS Genet 9(2):e1003295

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  40. Shen X (2013) The curse of the missing heritability. Front Genet 4:225

    PubMed Central  PubMed  Google Scholar 

  41. Gjuvsland AB, Vik JO, Woolliams JA, Omholt SW (2011) Order-preserving principles underlying genotype-phenotype maps ensure high additive proportions of genetic variance. J Evol Biol 24(10):2269–2279

    Article  CAS  PubMed  Google Scholar 

  42. Hallander J, Waldmann P (2007) The effect of non-additive genetic interactions on selection in multi-locus genetic models. Heredity 98(6):349–359

    CAS  PubMed  Google Scholar 

  43. Sellis D, Callahan BJ, Petrov DA, Messer PW (2011) Heterozygote advantage as a natural consequence of adaptation in diploids. Proc Natl Acad Sci U S A 108(51):20666–20671

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  44. Hansen TF (2013) Why epistasis is important for selection and adaptation. Evolution 67(12):3501–3511

    Article  PubMed  Google Scholar 

  45. Weinreich DM, Watson RA, Chao L (2005) Perspective: sign epistasis and genetic constraint on evolutionary trajectories. Evolution 59(6):1165–1174

    Article  CAS  PubMed  Google Scholar 

  46. Carter AJ, Hermisson J, Hansen TF (2005) The role of epistatic gene interactions in the response to selection and the evolution of evolvability. Theor Popul Biol 68:179–196

    Article  PubMed  Google Scholar 

  47. Houle D, Pelabon C, Wagner GP, Hansen TF (2011) Measurement and meaning in biology. Q Rev Biol 86(1):3–34

    Article  PubMed  Google Scholar 

  48. Pavlicev M, Le Rouzic A, Cheverud JM, Wagner GP, Hansen TF (2010) Directionality of epistasis in a murine intercross population. Genetics 185(4):1489–1505

    Article  CAS  PubMed Central  PubMed  Google Scholar 

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Acknowledgements

We acknowledge funding from grants BFU2010-20003 and EM2014/024 from the now defunct Spanish Ministry of Science and Innovation and the autonomous administration Xunta de Galicia, respectively, to J.A.C. and by grant ERT 256507 from the European Research Council to A.L.R. We thank Estelle Rünneburger for helpful comments on the manuscript.

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Authors and Affiliations

  1. Department of Genetics, University of Santiago de Compostela, Avda. Carvalho Calero s/n, Lugo, Galiza, ES-27002, Spain

    José M. Álvarez-Castro

  2. Instituto Gulbenkian de Ciência, Oeiras, Portugal

    José M. Álvarez-Castro

  3. Laboratoire Évolution, Génomes, Spéciation, CNRS, UPR9034, CNRS, Avenue de la Terrasse, Bâtiment 13, Gyf-sur-Yvette, 91198, France

    Arnaud Le Rouzic

Authors
  1. José M. Álvarez-Castro
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  2. Arnaud Le Rouzic
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Corresponding author

Correspondence to José M. Álvarez-Castro .

Editor information

Editors and Affiliations

  1. Department of Genetics, Institute of Quantitative Biomedical Sciences, Geisel School of Medicine, Hanover, New Hampshire, USA

    Jason H. Moore

  2. Department of Genetics, Institute of Quantitative Biomedical Sciences, Geisel School of Medicine, Hanover, New Hampshire, USA

    Scott M. Williams

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Álvarez-Castro, J.M., Le Rouzic, A. (2015). On the Partitioning of Genetic Variance with Epistasis. In: Moore, J., Williams, S. (eds) Epistasis. Methods in Molecular Biology, vol 1253. Humana Press, New York, NY. https://doi.org/10.1007/978-1-4939-2155-3_6

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  • DOI: https://doi.org/10.1007/978-1-4939-2155-3_6

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  • Publisher Name: Humana Press, New York, NY

  • Print ISBN: 978-1-4939-2154-6

  • Online ISBN: 978-1-4939-2155-3

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