Theoretical basis to extend single-step genomic prediction of dominance in a pig population

Single-step methods predict implicitly unknown gene content information of non-genotyped from known gene content for genotyped animals. This theory is well derived in an additive setting. There are reasons not to ignore the dominance context when working with partially genotyped populations. This study addressed several outstanding issues in this context. First, it presented the theoretical basis for dominance single-step genomic best linear unbiased prediction theory. A specific and important issue in all dominance setting is the handling of inbreeding. A total of five dominance single-step inverse matrices were tested and described as C1 to C5 by considering different parameterization (e.g. different ways to account for inbreeding) for pedigree-based and genomic relationships matrices. We simulated genotypes for real crossbred pig population (n=11,943 animals). The SNP effects were assumed to be equal to calculate true dominance values. We added random noise and used them as phenotypes. Accuracy was defined as correlation between true and predicted dominance breeding values. We applied five replicates and estimated accuracies between three situations: all (S1); non-genotyped (S2) and inbred non-genotyped animals (S3). Potential bias of predicted dominance values was assessed by regressing the true dominance values on predicted values. Accuracies of each tested matrix (C1 to C5) were 0.75, 0.33 and 0.35 in average, for S1, S2 and S3, respectively. The matrix C5 better performed and breeding values from C1 and C2 were more biased than those obtained by using C3, C4 and C5. We showed a useful approach to predict dominance gene contents for nongenotyped from genotyped animals. Better matrix compatibility can be obtained by re-scaling the pedigree-based and the genomic relationship matrices to obtain standardized diagonal elements equal to 1 minus the inbreeding
coefficient, i.e. the C5 matrix.