How Large-Scale Genomic Evaluations Are Possible: A Look into the Dimensionality of Genomic Information

When more than 100k animals are genotyped, the algorithm for proven and young (APY) enables computing the inverse of the genomic relationship matrix (GRM) and, therefore, genomic predictions using single-step genomic BLUP. This method is especially important for evaluation of cattle populations, which have the most genotyped animals: 1.4M for Holstein and 285k for Angus, and is implemented in US dairy and beef cattle evaluations. The APY uses recursions on a small subset of genotyped animals, called core, and its theory is based on the limited dimensionality of genomic information, relating to the effective population size. The dimensionality is computed as the number of the largest eigenvalues explaining 98% of the variation in the GRM. This dimension is the smallest of the numbers of genotyped animals, independent SNP, and independent chromosome segments. Field data studies estimated the dimensionality (effective population size) at 5k (44) for broiler chickens, 6k (48) for pigs, and 14k (113 to 148) for beef and dairy cattle. Given complete pedigrees for genotyped animals and sufficient core size, the choice of core animals in APY is not critical. If all causative SNP are identified from sequence data, the dimensionality of GRM equals the number of causative SNP. Using true SNP weights further reduces the dimensionality of the GRM, and weights for SNP are more important in small genotyped populations, because the independent segments are not fully represented. Although the amount of data is increasing rapidly, the limited dimensionality of genomic information enables inexpensive large-scale genomic evaluations.