Implication of the order of blending and tuning when computing the genomic relationship matrix in single-step GBLUP

Single-step genomic BLUP (ssGBLUP) relies on the combination of the genomic ( $$ ) and pedigree relationship matrices for all ( $$ ) and genotyped ( $$ ) animals. The procedure ensures $$ and $$ are compatible so that both matrices refer to the same genetic base ('tuning'). Then $$ is combined with a proportion of $$ ('blending') to avoid singularity problems and to account for the polygenic component not accounted for by markers. This computational procedure has been implemented in the reverse order (blending before tuning) following the sequential research developments. However, blending before tuning may result in less optimal tuning because the blended matrix already contains a proportion of $$ . In this study, the impact of 'tuning before blending' was compared with 'blending before tuning' on genomic estimated breeding values (GEBV), single nucleotide polymorphism (SNP) effects and indirect predictions (IP) from ssGBLUP using American Angus Association and Holstein Association USA, Inc. data. Two slightly different tuning methods were used; one that adjusts the mean diagonals and off-diagonals of $$ to be similar to those in $$ and another one that adjusts based on the average difference between all elements of $$ and $$ . Over 6 million Angus growth records and 5.9 million Holstein udder depth records were available. Genomic information was available on 51,478 Angus and 105,116 Holstein animals. Average realized relationship estimates among groups of animals were similar across scenarios. Scatterplots show that GEBV, SNP effects and IP did not noticeably change for all animals in the evaluation regardless of the order of computations and when using blending parameter of 0.05. Formulas were derived to determine the blending parameter that maximizes changes in the genomic relationship matrix and GEBV when changing the order of blending and tuning. Algebraically, the change is maximized when the blending parameter is equal to 0.5. Overall, tuning $$ before blending, regardless of blending parameter used, had a negligible impact on genomic predictions and SNP effects in this study.