Right-Hand-Side Updating Enables Genomic Prediction with Millions of SNPs

There is a growing interest to include whole genome sequence information in genomic prediction. This requires algorithms that explicitly perform regression on all SNP genotypes, and employ variable selection. Current algorithms use residual updating, and computing time may prohibit fitting several million SNPs simultaneously. Residual updating computes conditional phenotypes, that are used to estimate the effect of a particular SNP in a Gibbs sampling scheme. Conditional phenotypes are computed as the sum of current residuals and the estimated effect of the evaluated SNP in the previous iteration. Efficient implementations of residual updating require updating all residuals once for each SNP, which is the most expensive operation in this algorithm. The recently developed right-hand-side updating algorithm requires updating each residual once, when computing effects for 3-6 SNPs, depending on the number of animals in the analysis. This postponed updating takes advantage of the property that each SNP has only three genotypes, and therefore the updating of residuals is based on changes in multiple SNP effects, while between residual updating steps the right-hand-sides of the equations to estimate SNP effects are computed as sums of non-updated residuals and combinations of changes in estimated SNP effects. Applying the right-hand-side updating algorithm was shown to reduce computation time by 35-43% and memory use by 74-93%. This enables genomic prediction with whole genome sequence data, as recently shown in applications including analyses of 5,503 Holstein dairy bulls with imputed genotypes for 12,590,056 SNPs, and of 1,244 white laying hens with imputed genotypes for 3,936,039 SNPs.