Short Communication: Reduced GBLUP equations to core animals in the algorithm for proven and young (APY)

The number of animal genotypes is rapidly increasing, and a major challenge for animal models is inverting the genomic relationship matrix (G). Matrix G has a limited dimensionality, and the algorithm for proven and young (APY) makes inverting a large G possible via the inverse of a block diagonal of G with a size equivalent to the dimensionality of G. APY divides genotyped animals into core and non-core groups, and breeding values of non-core animals are conditioned on the breeding values of core animals. Therefore, there is the possibility of opting out equations for non-core animals from the model. A methodology was presented for a reduced APY genomic BLUP (GBLUP) to equations for core animals. Using a small example dataset, the method was validated by the equality of the full and the reduced model analysis results. Absorption of fixed effect equations into random effect equations was successful in reducing the number of equations to solve and producing the same random effect solutions. Extending the method to APY single-step GBLUP (ssGBLUP) was not computationally justifiable. Other reduction techniques exist for ssGBLUP (regardless of APY or non-APY) that work by reducing the number of equations for non-genotyped animals. The number of equations can further be reduced by data pruning.