Advertisement

Theoretical and Applied Genetics

, Volume 129, Issue 5, pp 963–976 | Cite as

Epistasis and covariance: how gene interaction translates into genomic relationship

  • Johannes W. R. MartiniEmail author
  • Valentin Wimmer
  • Malena Erbe
  • Henner Simianer
Original Article

Abstract

Key message

Models based on additive marker effects and on epistatic interactions can be translated into genomic relationship models. This equivalence allows to perform predictions based on complex gene interaction models and reduces computational effort significantly.

Abstract

In the theory of genome-assisted prediction, the equivalence of a linear model based on independent and identically normally distributed marker effects and a model based on multivariate Gaussian distributed breeding values with genomic relationship as covariance matrix is well known. In this work, we demonstrate equivalences of marker effect models incorporating epistatic interactions and corresponding mixed models based on relationship matrices and show how to exploit these equivalences computationally for genome-assisted prediction. In particular, we show how models with epistatic interactions of higher order (e.g., three-factor interactions) translate into linear models with certain covariance matrices and demonstrate how to construct epistatic relationship matrices for the linear mixed model, if we restrict the model to interactions defined a priori. We illustrate the practical relevance of our results with a publicly available data set on grain yield of wheat lines growing in four different environments. For this purpose, we select important interactions in one environment and use this knowledge on the network of interactions to increase predictive ability of grain yield under other environmental conditions. Our results provide a guide for building relationship matrices based on knowledge on the structure of trait-related gene networks.

Keywords

Predictive Ability Epistatic Interaction Relationship Matrix Pairwise Interaction DArT Marker 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The authors thank Daniel Gianola and another unknown reviewer for helpful suggestions. The comments helped to improve the manuscript immensely. JWRM thanks KWS SAAT SE for financial support and Camila Fabre Sehnem for helpful discussions.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical standards

This manuscript constitutes a first submission to a scientific journal and neither the entire manuscript nor any part of its content has been published or has been accepted by another journal.

Supplementary material

References

  1. Abdollahi-Arpanahi R, Pakdel A, Nejati-Javaremi A, Moradi Shahrbabak M, Morota G, Valente BD, Kranis A, Rosa GJM, Gianola D (2014) Dissection of additive genetic variability for quantitative traits in chickens using SNP markers. J Anim Breed Genet 131(3):183–193CrossRefPubMedGoogle Scholar
  2. Clifford D, McCullagh P (2006) The regress function. R News 6(2):10Google Scholar
  3. Clifford D, McCullagh P (2014) The regress package. R package version 1.3-14Google Scholar
  4. Cockerham CC (1954) An extension of the concept of partitioning hereditary variance for analysis of covariances among relatives when epistasis is present. Genetics 39(6):859–882PubMedPubMedCentralGoogle Scholar
  5. Crossa J, de Los Campos G, Pérez P, Gianola D, Burgueño J, Araus JL, Makumbi D, Singh RP, Dreisigacker S, Yan J, Arief V, Banziger M, Braun HJ (2010) Prediction of genetic values of quantitative traits in plant breeding using pedigree and molecular markers. Genetics 186(2):713–724CrossRefPubMedPubMedCentralGoogle Scholar
  6. de los Campos G, Perez-Rodriguez P (2014) BGLR: Bayesian Generalized Linear Regression. R package version 1.0.3. http://CRAN.R-project.org/package=BGLR
  7. Falconer DS, Mackay TFC (1996) Introduction to quantitative genetics, 4th edn. England, Benjamin CummingsGoogle Scholar
  8. Gianola D, Rosa GJM (2015) One hundred years of statistical developments in animal breeding. Annu Rev Anim Biosci 3:19–56CrossRefPubMedGoogle Scholar
  9. Gianola D, Morota G, Crossa J (2014) Genome-enabled prediction of complex traits with kernel methods: What have we learned?. In: Proceedings, 10th World Congress of Genetics Applied to Livestock ProductionGoogle Scholar
  10. Habier D, Fernando RL, Dekkers JCM (2007) The impact of genetic relationship information on genome-assisted breeding values. Genetics 177(4):2389–2397PubMedPubMedCentralGoogle Scholar
  11. Hallgrímsdóttir IB, Yuster DS (2008) A complete classification of epistatic two-locus models. BMC Genet 9(1):17CrossRefPubMedPubMedCentralGoogle Scholar
  12. Hayes BJ, Visscher PM, Goddard ME (2009) Increased accuracy of artificial selection by using the realized relationship matrix. Genet Res 91(1):47–60CrossRefGoogle Scholar
  13. He D, Wang Z, Parida L (2015) Data-driven encoding for quantitative genetic trait prediction. BMC Bioinform 16(Suppl 1):S10CrossRefGoogle Scholar
  14. Henderson CR (1984) Application of linear models in animal breeding. University of Guelph, GuelphGoogle Scholar
  15. Henderson CR (1985) Best linear unbiased prediction of nonadditive genetic merits in noninbred populations. J Anim Sci 60(1):111–117Google Scholar
  16. Henderson CR, Quaas RL (1976) Multiple trait evaluation using relatives records. J Anim Sci 43:1188Google Scholar
  17. Henderson CR (1975) Best linear unbiased estimation and prediction under a selection model. Biometrics 31(2):423–447CrossRefPubMedGoogle Scholar
  18. Hill WG, Goddard ME, Visscher PM (2008) Data and theory point to mainly additive genetic variance for complex traits. PLoS Genet 4(2):e1000008CrossRefPubMedPubMedCentralGoogle Scholar
  19. Hu Z, Li Y, Song X, Han Y, Cai X, Xu S, Li W (2011) Genomic value prediction for quantitative traits under the epistatic model. BMC Genet 12:15CrossRefPubMedPubMedCentralGoogle Scholar
  20. Jiang Y, Reif JC (2015) Modelling epistasis in genomic selection. Genetics 201:759–768. doi: 10.1534/genetics.115.177907 CrossRefPubMedGoogle Scholar
  21. Kempthorne O (1954) The correlation between relatives in a random mating population. In: Proceedings of the Royal Society of London. Series B-Biological Sciences 143, vol 910, pp 103–113Google Scholar
  22. Mackay TFC (2013) Epistasis and quantitative traits: using model organisms to study gene-gene interactions. Nat Rev Genet 15:22–33. doi: 10.1038/nrg3627 CrossRefPubMedPubMedCentralGoogle Scholar
  23. Meuwissen THE, Hayes BJ, Goddard ME (2001) Prediction of total genetic value using genome-wide dense marker maps. Genetics 157(4):1819–1829PubMedPubMedCentralGoogle Scholar
  24. Morota G, Gianola D (2014) Kernel-based whole-genome prediction of complex traits: a review. Front Genet 5:363. doi: 10.3389/fgene.2014.00363 PubMedPubMedCentralGoogle Scholar
  25. Morota G, Koyama M, Rosa GJM, Weigel KA, Gianola D (2013) Predicting complex traits using a diffusion kernel on genetic markers with an application to dairy cattle and wheat data. Genet Sel Evol 45:17CrossRefPubMedPubMedCentralGoogle Scholar
  26. Muñoz PR, Resende MFR, Gezan SA, Resende MDV, de los Campos G, Kirst M, Huber D, Peter GF (2014) Unraveling additive from nonadditive effects using genomic relationship matrices. Genetics 198(4):1759–1768CrossRefPubMedPubMedCentralGoogle Scholar
  27. Ober U, Huang W, Magwire M, Schlather M, Simianer H, Mackay TFC (2015) Accounting for genetic architecture improves sequence based genomic prediction for a Drosophila fitness trait. PLoS One 10(5):e0126880. doi: 10.1371/journal.pone.0126880 CrossRefPubMedPubMedCentralGoogle Scholar
  28. Piepho HP, Möhring J, Melchinger AE, Büchse A (2008) BLUP for phenotypic selection in plant breeding and variety testing. Euphytica 161:209–228CrossRefGoogle Scholar
  29. R Core Team (2014) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/
  30. Shawe-Taylor J, Cristianini N (2004) Kernel methods for pattern analysis. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  31. Strandén I, Christensen OF (2011) Allele coding in genomic evaluation. Genet Sel Evol 43:25CrossRefPubMedPubMedCentralGoogle Scholar
  32. Su G, Christensen OF, Ostersen T, Henryon M, Lund MS (2012) Estimating additive and non-additive genetic variances and predicting genetic merits using genome-wide dense single nucleotide polymorphism markers. PLOS One 7(9):e45293CrossRefPubMedPubMedCentralGoogle Scholar
  33. Technow F, Schrag TA, Schipprack W, Bauer E, Simianer H, Melchinger AE (2014) Genome properties and prospects of genomic prediction of hybrid performance in a breeding program of maize. Genetics 197(4):1343–1355CrossRefPubMedPubMedCentralGoogle Scholar
  34. VanRaden PM (2008) Efficient methods to compute genomic predictions. J Dairy Sci 91(11):4414–4423CrossRefPubMedGoogle Scholar
  35. Varona L, Vitezica ZG, Munilla S, Legarra A (2014) A general approach for calculation of genomic relationship matrices for epistatic effects. In: Proceedings, 10th World Congress of Genetics Applied to Livestock ProductionGoogle Scholar
  36. Wang D, El-Basyoni IS, Baenziger PS, Crossa J, Eskridge KM, Dweikat I (2012) Prediction of genetic values of quantitative traits with epistatic effects in plant breeding populations. Heredity 109(5):313–319CrossRefPubMedPubMedCentralGoogle Scholar
  37. Wittenburg D, Melzer N, Reinsch N (2011) Including non-additive genetic effects in Bayesian methods for the prediction of genetic values based on genome-wide markers. BMC Genet 12:74CrossRefPubMedPubMedCentralGoogle Scholar
  38. Zeng Z, Wang T, Zou W (2005) Modeling quantitative trait loci and interpretation of models. Genetics 169(3):1711–1725CrossRefPubMedPubMedCentralGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Johannes W. R. Martini
    • 1
    Email author
  • Valentin Wimmer
    • 2
  • Malena Erbe
    • 1
    • 3
  • Henner Simianer
    • 1
  1. 1.Department of Animal Sciences, Animal Breeding and Genetics GroupGeorg-August UniversityGöttingenGermany
  2. 2.KWS SAAT SEEinbeckGermany
  3. 3.Institute of Animal BreedingBavarian State Research Centre for AgricultureGrubGermany

Personalised recommendations