Statistical Models for the Prediction of Genetic Values

  • Chris-Carolin Schön
  • Valentin Wimmer


Agricultural and medical genetics are currently revolutionized by the technological developments in genomic research. The genetic analysis of quantitatively inherited traits and the prediction of the genetic predisposition of individuals based on molecular data are rapidly evolving fields of research. We ask how phenotypic variation for a quantitative trait can be linked to genetic variation at the DNA level. Advances in high-throughput genotyping technologies return data on thousands of loci per individual. We present linear models to identify molecular markers significantly associated with quantitative traits. We discuss the drawbacks arising from a large number of predictor variables and a high degree of collinearity between them. We illustrate how linear mixed models can overcome the limitations through shrinkage and allow the prediction of genetic values inferred from genome-wide marker data. With a small example from maize breeding, we present how the models can be applied to predict the risk of genetically diverse individuals to be damaged by insects and why predictions based on whole-genome marker profiles are likely to be more accurate than those based on pedigree information. The choice of appropriate methods for quantitative genetic analyses based on high-throughput genomic data for medical and agricultural genetics is discussed.


Quantitative genetics Genome-based prediction Linear mixed models Disease risk Genetic value 

Mathematics Subject Classification (2010)

62J05 62J07 62P10 



We thank Theresa Albrecht for help with the European corn borer example and Peter Westermeier for providing the corn borer photos. Valentin Wimmer acknowledges financial support by the German Federal Ministry of Education and Research (BMBF) within the AgroClustEr SynbreedSynergistic plant and animal breeding (FKZ 0315528A).


Selected Bibliography

  1. 1.
    D.S. Falconer, T.F.C. Mackay, Introduction to Quantitative Genetics (Longman Technical, Harlow, 1996) Google Scholar
  2. 2.
    A.J.F. Griffiths, S.R. Wessler, S.B. Carroll, J. Doebley, Introduction to Genetic Analysis, 10th edn. (Palgrave Macmillan, Basingstoke, 2012) Google Scholar
  3. 3.
    T. Hastie, R. Tibshirani, J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition. Springer Series in Statistics (Springer, Berlin, 2009) CrossRefGoogle Scholar
  4. 4.
    C.R. Henderson, Applications of Linear Models in Animal Breeding (University of Guelph, Guelph, 1984) Google Scholar
  5. 5.
    M. Lynch, B. Walsh, Genetics and Analysis of Quantitative Traits (Sinauer, Sunderland, 1998) Google Scholar
  6. 6.
    R.H. Myers, Classical and Modern Regression with Applications (Duxbury, Belmont, 1994) Google Scholar
  7. 7.
    S.R. Searle, G. Casella, C.E. McCulloch, Variance Components. Wiley Series in Probability and Statistics (Wiley-Interscience, Hoboken, 2006) zbMATHGoogle Scholar

Additional Literature

  1. 8.
    T. Albrecht, V. Wimmer, H.-J. Auinger, M. Erbe, C. Knaak, M. Ouzunova, H. Simianer, C.-C. Schön, Genome-based prediction of testcross values in maize. Theor. Appl. Genet. 123(2), 339–350 (2011) CrossRefGoogle Scholar
  2. 9.
    E.S. Buckler, J.B. Holland, P.J. Bradbury, C.B. Acharya, P.J. Brown, et al., The genetic architecture of maize flowering time. Science 325(5941), 714–718 (2009) CrossRefGoogle Scholar
  3. 10.
    G. de los Campos, D. Gianola, D.B. Allison, Predicting genetic predisposition in humans: the promise of whole-genome markers. Nat. Rev. Genet. 11(12), 880–886 (2010) CrossRefGoogle Scholar
  4. 11.
    D. Gianola, G. de los Campos, W.G. Hill, E. Manfredi, R.L. Fernando, Additive genetic variability and the Bayesian alphabet. Genetics 183(1), 347–363 (2009) CrossRefGoogle Scholar
  5. 12.
    D. Gianola, H. Okut, K.A. Weigel, G.J.J. Rosa, Predicting complex quantitative traits with Bayesian neural networks: a case study with Jersey cows and wheat. BMC Genet. (2011). doi: 10.1186/1471-2156-12-87 Google Scholar
  6. 13.
    M.E. Goddard, N.R. Wray, K. Verbyla, P.M. Visscher, Estimating effects and making predictions from genome-wide marker data. Stat. Sci. 24(4), 517–529 (2009) CrossRefMathSciNetGoogle Scholar
  7. 14.
    D.B. Goldstein, Growth of genome screening needs debate. Nature 476(7358), 27–28 (2011) CrossRefGoogle Scholar
  8. 15.
    D. Habier, R.L. Fernando, J.C.M. Dekkers, The impact of genetic relationship information on genome-assisted breeding values. Genetics 177(1), 2389–2397 (2007) Google Scholar
  9. 16.
    T.H.E. Meuwissen, B.J. Hayes, M.E. Goddard, Prediction of total genetic value using genome-wide dense marker maps. Genetics 157(4), 1819–1829 (2001) Google Scholar
  10. 17.
    E.C.G. Pimentel, M. Erbe, S. König, H. Simianer, Genome partitioning of genetic variation for milk production and composition traits in Holstein cattle. Front. Livest. Genomics 2, 19 (2011) Google Scholar
  11. 18.
    C.-C. Schön, H.F. Utz, S. Groh, B. Truberg, S. Openshaw, A.E. Melchinger, Quantitative trait locus mapping based on resampling in a vast maize testcross experiment and its relevance to quantitative genetics for complex traits. Genetics 167(1), 485–498 (2004) CrossRefGoogle Scholar
  12. 19.
    H.F. Utz, A.E. Melchinger, C.-C. Schön, Bias and sampling error of the estimated proportion of genotypic variance explained by quantitative trait loci determined from experimental data in maize using cross validation and validation with independent samples. Genetics 154(4), 1839–1849 (2000) Google Scholar
  13. 20.
    P.M. Visscher, Sizing up human height variation. Nat. Genet. 40(5), 489–490 (2008) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Chair of Plant Breeding, Center of Life and Food Sciences WeihenstephanTechnische Universität MünchenFreising-WeihenstephanGermany
  2. 2.Plant Breeding, Center of Life and Food Sciences WeihenstephanTechnische Universität MünchenFreising-WeihenstephanGermany

Personalised recommendations