Genomic Model with Correlation Between Additive and Dominance Effects.

Dominance genetic effects are rarely included in pedigree-based genetic evaluation. With the availability of single nucleotide polymorphism markers and the development of genomic evaluation, estimates of dominance genetic effects have become feasible using genomic best linear unbiased prediction (GBLUP). Usually, studies involving additive and dominance genetic effects ignore possible relationships between them. It has been often suggested that the magnitude of functional additive and dominance effects at the quantitative trait loci are related, but there is no existing GBLUP-like approach accounting for such correlation. Wellmann and Bennewitz (2012) showed two ways of considering directional relationships between additive and dominance effects, which they estimated in a Bayesian framework. However, these relationships cannot be fitted at the level of individuals instead of loci in a mixed model, and are not compatible with standard animal or plant breeding software. This comes from a fundamental ambiguity in assigning the reference allele at a given locus. We show that, if there has been selection, assigning the most frequent as the reference allele orients the correlation between functional additive and dominance effects. As a consequence, the most frequent reference allele is expected to have a positive value. We also demonstrate that selection creates negative covariance between genotypic additive and dominance genetic values. For parameter estimation, it is possible to use a combined additive and dominance relationship matrix computed from marker genotypes, and to use standard restricted maximum likelihood algorithms based on an equivalent model. Through a simulation study, we show that such correlations can easily be estimated by mixed model software and that the accuracy of prediction for genetic values is slightly improved if such correlations are used in GBLUP. However, a model assuming uncorrelated effects and fitting orthogonal breeding values and dominant deviations performed similarly for prediction.