Technical note: Automatic scaling in single-step genomic BLUP

摘要

Single-step genomic BLUP (ssGBLUP) requirescompatibility between genomic and pedigree relationshipsfor unbiased and accurate predictions. Scaling thegenomic relationship matrix (G) to have the same averagesas the pedigree relationship matrix (i.e., scalingby averages) is one way to ensure compatibility. Thisrequires computing both relationship matrices, calculatingaverages, and changing G, whereas only the inversesof those matrices are needed in the mixed modelequations. Therefore, the compatibility process can addextra computing burden. In the single-step Bayesianregression, the scaling is done by including a mean (μg)as a fixed effect in the model. The parameter μg canbe interpreted as the average of the breeding valuesof the genotyped animals. In this study, such scaling,called automatic, was implemented in ssGBLUP viaQuaas-Pollak transformation of the inverse of the relationshipmatrix used in ssGBLUP (H), which combinesthe inverses of the pedigree and genomic relationshipmatrices. Comparisons involved a simulated data set,and the genomic relationship matrix was computedusing different allele frequencies either from the currentpopulation (i.e., realized allele frequencies), equalamong all the loci, or from the base population. For allof the scenarios, we computed bias [defined as the averagedifference between true breeding values (TBV) andgenomic estimated breeding values (GEBV)], accuracy(defined as the correlation between TBV and GEBV),and dispersion (defined as the regression coefficient ofGEBV on TBV). With no scaling, the bias expressedin terms of genetic standard deviations was 0.86, 0.64,and 0.58 with realized, equal, and base population allelefrequencies, respectively. With scaling by averages,which is currently used in ssGBLUP, bias was 0.07,0.08, and 0.03, respectively. With automatic scaling,bias was 0.18 regardless of allele frequencies. Accuracieswere similar among scaling methods, but about0.1 lower in the scenario without scaling. The GEBVwere more inflated without any scaling, whereas theautomatic scaling performed similarly to the scaling byaverages. The average dispersion for those methods was0.94. When μ_g was treated as random, with the varianceequal to differences between pedigree and genomicrelationships, the bias was the same as with the scalingby averages. The automatic scaling is biased, especiallywhen μ_g is treated as a fixed effect. The bias may besmall in real data with fewer generations, when traitsare undergoing weak selection, or when the number ofgenotyped animals is large.