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


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.


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.


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.



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


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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

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