Deregression formula for single-step genomic BLUP
The objective of this study was to describe an algorithm to deregress GEBV in single-step genomic BLUP (ssGBLUP). The iterative method suggested by Jairath et al. (1998), which was for the pedigree-based EBV, was extended to support GEBV. The inverse of the unified relationship matrix (H-1), which is a function of the inverse of genomic relationship matrix (G-1) and the inverse of the additive relationship matrix (A-1), was considered in the deregression method. With more genotypes, G-1 can be replaced with a sparser inverse by the Algorithm of Proven and Young (APY) or a transformed matrix (single-step GTBLUP). The deregression algorithm consists of a series of matrix-vector multiplications, and the number of iterations is expected to be limited. Therefore, the total computing cost should be lower than PCG to solve the mixed model equations in the original single-step genomic evaluation. A validation study using real data is needed to confirm this method works as expected.
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