Correspondence on "Short Communication: Reduced GBLUP equations to core animals in the algorithm for proven and young (APY)"—Simplifications when non-core animals are non-phenotyped

The Algorithm for Proven and Young (APY) enables scalable genomic evaluation by approximating the inverse of the genomic relationship matrix through partitioning genotyped animals into core and non-core groups. A recently published short communication showed that, under APY, genomic BLUP (GBLUP) can be reduced to a system of equations involving only core animals, with solutions for non-core animals obtained by back-solving. In this correspondence, I demonstrate that when the non-core group contains no phenotyped animals, this reduced-equivalent GBLUP formulation can be further simplified. Under this condition, several matrix derivations and calculations become unnecessary, and the back-solving of non-core solutions is considerably simplified.