The purpose of this study was to evaluate accuracy of genomic selection in single-step genomic BLUP (ssGBLUP) when the inverse of the genomic relationship matrix (G) is derived by the APY (algorithm for proven and young animals). This algorithm implements genomic recursions on a subset of “proven” animals. Only a matrix due to the subset needs to be inverted and extra costs of adding “young” animals are linear. Analyses involved 10,102,702 Holsteins with final scores on 6,930,618 cows. A total of 100k animals with genotypes included 23k sires (16k with more than 5 progenies), 27k cows, and 50k young animals. Genomic EBV (GEBV) were calculated with a regular inverse of G, and with the G inverse approximated by APY. Initially, animals in the “proven” subset included only sires or cows. Later, animals in the “proven” subset were randomly sampled from all genotyped animals in sets of 5k, 10k, and 20k; each sample was replicated 4 times. Genomic EBV with APY were accurate when the number of animals in the “proven” subset was ≥10k, with little difference between the ways of creating the subset. Numerical properties as shown by the number of rounds to convergence were best with random subsets. The ssGBLUP with APY can accommodate a large number of genotypes at low cost and with high accuracy. Table 1. Correlations (or range of correlations) between genomic EBV with regular and APY ssGBLUP for young genotyped animals and rounds to convergence for different subset of animals used in recursions

Definition of subset	Animals in subset	Correlation	Rounds to convergence
All	100,000	1.00	567
Sires	23,174	0.99	432
Cows	27,215	0.99	797
2k random	2,000	0.94	356
5k random	5,000	0.97	360
10k random	10,000	0.99	396
20k random	20,000	0.99	420