A comprehensive study on size and definition of the core group in the proven and young algorithm for single-step GBLUP

Abstract

Background The algorithm for proven and young (APY) has been suggested as a solution for recursively computing a sparse representation for the inverse of a large genomic relationship matrix (G). In APY, a subset of genotyped individuals is used as the core and the remaining genotyped individuals are used as noncore. Size and definition of the core are relevant research subjects for the application of APY, especially given the ever-increasing number of genotyped individuals. Methods The aim of this study was to investigate several core definitions, including the most popular animals (MPA) (i.e., animals with high contributions to the genetic pool), the least popular males (LPM), the least popular females (LPF), a random set (Rnd), animals evenly distributed across genealogical paths (Ped), unrelated individuals (Unrel), or based on within-family selection (Fam), or on decomposition of the gene content matrix (QR). Each definition was evaluated for six core sizes based on prediction accuracy of single-step genomic best linear unbiased prediction (ssGBLUP) with APY. Prediction accuracy of ssGBLUP with the full inverse of G was used as the baseline. The dataset consisted of 357k pedigreed Duroc pigs with 111k pigs with genotypes and ~ 220k phenotypic records. Results When the core size was equal to the number of largest eigenvalues explaining 50% of the variation of G (n = 160), MPA and Ped core definitions delivered the highest average prediction accuracies (~ 0.41−0.53). As the core size increased to the number of eigenvalues explaining 99% of the variation in G (n = 7320), prediction accuracy was nearly identical for all core types and correlations with genomic estimated breeding values (GEBV) from ssGBLUP with the full inversion of G were greater than 0.99 for all core definitions. Cores that represent all generations, such as Rnd, Ped, Fam, and Unrel, were grouped together in the hierarchical clustering of GEBV. Conclusions For small core sizes, the definition of the core matters; however, as the size of the core reaches an optimal value equal to the number of largest eigenvalues explaining 99% of the variation of G, the definition of the core becomes arbitrary.

Estimation of heritabilities and genetic correlations by time slices using predictivity in large genomic models

“…In a recent study (Abdollahi-Arpanahi et al 2022), accuracies by predictivity and Method LR (Legarra and Reverter 2018) considered resistant to selection bias were nearly identical, which indicates that selection biases with the predictivity formula are low with widespread genotyping. The formulas for the genetic correlations could possibly be incorporated into the LR method to take advantage of simpler computing and better statistics.…”

HIBLUP: an integration of statistical models on the BLUP framework for efficient genetic evaluation using big genomic data

“…Since the number of core animals is usually smaller than the number of all genotyped individuals, the APY strategy not only reduces the complexity of inverse computation significantly, but also helps to increase the sparsity of the coefficient matrix; thus, it should be beneficial for both computational efficiency and memory usage. Nevertheless, how to select the core animals and how large the number of core animals should be to obtain unbiased results are not that easy to determine for a non-expert or non-experienced beginner ( 32 ). On the other hand, recent research concluded that to ensure reliable estimation of variance components, it is required to consider a core size that corresponds to the number of the largest eigenvalues that explain ∼98% of the total variation in GRM.…”

Marker effect p-values for single-step GWAS with the algorithm for proven and young in large genotyped populations

“…The single-step genomic best linear unbiased prediction ( ssGBLUP ) has been successfully implemented in the routine genetic evaluation of several livestock species (Lourenco et al, 2015; Tsuruta et al, 2021; Abdollahi-Arpanahi et al, 2022). The vast adoption of ssGBLUP is associated with the straightforward, simultaneous evaluation of populations composed of genotyped and non-genotyped animals, the non-requirement of pseudo phenotypes, the decrease in biases attributed to double counting and genomic preselection, and reliable estimation of breeding values for complex genetic models (Misztal et al, 2020).…”