Recent publications indicate that single-step models are suitable to estimate breeding values, dominance deviations and total genetic values with acceptable quality. Additive single-step methods implicitly extend known number of allele information from genotyped to non-genotyped animals. This theory is well derived in an additive setting. It was recently shown, at least empirically, that this basic strategy can be extended to dominance with reasonable prediction quality. Our study addressed two additional issues. It illustrated the theoretical basis for extension and validated genomic predictions to dominance based on single-step genomic best linear unbiased prediction theory. This development was then extended to include inbreeding into dominance relationships, which is a currently not yet solved issue. Different parametrizations of dominance relationship matrices were proposed. Five dominance single-step inverse matrices were tested and described as C1 , C2 , C3 , C4 and C5 . Genotypes were simulated for a real pig population (n = 11,943 animals). In order to avoid any confounding issues with additive effects, pseudo-records including only dominance deviations and residuals were simulated. SNP effects of heterozygous genotypes were summed up to generate true dominance deviations. We added random noise to those values and used them as phenotypes. Accuracy was defined as correlation between true and predicted dominance deviations. We conducted five replicates and estimated accuracies in three sets: between all (S1 ), non-genotyped (S2 ) and inbred non-genotyped (S3 ) animals. Potential bias was assessed by regressing true dominance deviations on predicted values. Matrices accounting for inbreeding (C3 , C4 and C5 ) best fit. Accuracies were on average 0.77, 0.40 and 0.46 in S1 , S2 and S3 , respectively. In addition, C3 , C4 and C5 scenarios have shown better accuracies than C1 and C2 , and dominance deviations were less biased. Better matrix compatibility (accuracy and bias) was observed by re-scaling diagonal elements to 1 minus the inbreeding coefficient (C5 ).
Keywords: bias; dominance relationships; matrix compatibility; prediction accuracy.
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