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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 …