Core-dependent changes in genomic predictions using the Algorithm for Proven and Young in single-step genomic best linear unbiased prediction

Single-step genomic best linear unbiased prediction with the Algorithm for Proven and Young (APY) is a popular method for large-scale genomic evaluations. With the APY algorithm, animals are designated as core or noncore, and the computing resources to create the inverse of the genomic relationship matrix (GRM) are reduced by inverting only a portion of that matrix for core animals. However, using different core sets of the same size causes fluctuations in genomic estimated breeding values (GEBVs) up to one additive standard deviation without affecting prediction accuracy. About 2% of the variation in the GRM is noise. In the recursion formula for APY, the error term modeling the noise is different for every set of core animals, creating changes in breeding values. While average changes are small, and correlations between breeding values estimated with different core animals are close to 1.0, based on the normal distribution theory, outliers can be several times bigger than the average. Tests included commercial datasets from beef and dairy cattle and from pigs. Beyond a certain number of core animals, the prediction accuracy did not improve, but fluctuations decreased with more animals. Fluctuations were much smaller than the possible changes based on prediction error variance. GEBVs change over time even for animals with no new data as genomic relationships ties all the genotyped animals, causing reranking of top animals. In contrast, changes in nongenomic models without new data are small. Also, GEBV can change due to details in the model, such as redefinition of contemporary groups or unknown parent groups. In particular, increasing the fraction of blending of the GRM with a pedigree relationship matrix from 5% to 20% caused changes in GEBV up to 0.45 SD, with a correlation of GEBV > 0.99. Fluctuations in genomic predictions are part of genomic evaluation models and are also present without the APY algorithm when genomic evaluations are computed with updated data. The best approach to reduce the impact of fluctuations in genomic evaluations is to make selection decisions not on individual animals with limited individual accuracy but on groups of animals with high average accuracy.

Current status of genomic evaluation

Early application of genomic selection relied on SNP estimation with phenotypes or de-regressed proofs (DRP). Chips of 50k SNP seemed sufficient for an accurate estimation of SNP effects. Genomic estimated breeding values (GEBV) were composed of an index with parent average, direct genomic value, and deduction of a parental index to eliminate double counting. Use of SNP selection or weighting increased accuracy with small data sets but had minimal to no impact with large data sets. Efforts to include potentially causative SNP derived from sequence data or high-density chips showed limited or no gain in accuracy. After the implementation of genomic selection, EBV by BLUP became biased because of genomic preselection and DRP computed based on EBV required adjustments, and the creation of DRP for females is hard and subject to double counting. Genomic selection was greatly simplified by single-step genomic BLUP (ssGBLUP). This method based on combining genomic and pedigree relationships automatically creates an index with all sources of information, can use any combination of male and female genotypes, and accounts for preselection. To avoid biases, especially under strong selection, ssGBLUP requires that pedigree and genomic relationships are compatible. Because the inversion of the genomic relationship matrix (G) becomes costly with more than 100k genotyped animals, large data computations in ssGBLUP were solved by exploiting limited dimensionality of genomic data due to limited effective population size. With such dimensionality ranging from 4k in chickens to about 15k in cattle, the inverse of G can be created directly (e.g., by the algorithm for proven and young) at a linear cost. Due to its simplicity and accuracy, ssGBLUP is routinely used for genomic selection by the major chicken, pig, and beef industries. Single step can be used to derive SNP effects for indirect prediction and for genome-wide association studies, including computations of the P-values. Alternative single-step formulations exist that use SNP effects for genotyped or for all animals. Although genomics is the new standard in breeding and genetics, there are still some problems that need to be solved. This involves new validation procedures that are unaffected by selection, parameter estimation that accounts for all the genomic data used in selection, and strategies to address reduction in genetic variances after genomic selection was implemented.