Optimal core definitions for the APY model with an example in large-scale pig dataset

Genetic evaluation databases accumulated vast amounts of genomic information that are skyrocketing computational needs for standard genomic evaluation models due to their cubic computational complexity. Several scalable approaches have been proposed, such as the Algorithm for Proven and Young (APY), where genotyped animals are usually randomly partitioned into core and noncore subsets to obtain sparse approximation of the inverse of genomic relationship matrix. Here we show a deterministic optimisation of the core set using a sequential sampling approach. We test this optimisation on a large pig dataset. Our results confirm that the APY is robust and that the size of the core set is critical. Our results further show that the stability of APY can be enhanced with an optimal spread of core animals across a given domain of genotyped animals. We discuss possibilities of an alternative optimisation based on the Nearest Neighbours Gaussian Process that also results in a sparse inverse.