The quality of the algorithm for proven and young with various sets of core animals in a multibreed sheep population1

Abstract

The inverses of the pedigree and genomic relationship matrices (A, G) are required for single-step GBLUP (ssGBLUP). While, inverting A is possible for millions of animals at a linear cost, inverting G has a cubic cost and feasible for at most 150,000 animals, using the current conventional algorithms. The algorithm for proven and young (APY) provides approximations of the regular ssGBLUP by splitting genotyped animals into core and noncore groups, with computational costs being cubic for core and linear for noncore animals. The data consisted of 9,406,096 animals in the pedigree, 6,243,753 weaning weight phenotypes, and 46,949 genotyped animals from 5 breeds, composites, and animals with missing breed information from New Zealand. Aiming to find a core sample for a multibreed sheep population that can provide evaluations similar to those from the regular ssGBLUP, different core types, and core sizes were studied. Core types random, composite, oldest, youngest, the most inbred animals in G (GINB), and in A (AINB) were studied in 5K, 10K, and 20K core sizes (K = 1,000). Romney core was studied in 5K and 10K, and Coopworth-Perendale core was studied in 5K. Correlation and regression coefficient (slope) between GEBV from the non-APY and the APY analyses, as indicators for consistency with non-APY and bias from non-APY, showed a large impact of APY on noncore and a small impact on nongenotyped animals. Breed-based 5K cores resulted in large bias from non-APY even for nongenotyped animals. Random and GINB at 20K core size resulted in the highest consistency with non-APY and the lowest bias from non-APY. However, GINB did not perform as well as Random at lower core sizes. The number of animals from a breed in the core sample was very important for the evaluation of that breed. We observed that cores without Texel or Highlander animals resulted in poor evaluations for those breeds. Solving the mixed model equations, within core type, the smallest core size, and within core size, Random core converged in the least number of iterations. However, APY per se did not necessarily reduce the solving time. Random cores performed the best, as they could give a good coverage on the generations and breeds, representative for the genotyped population. Core size 20K performed better than 5K and 10K, and the optimum core size was found to be 18.8K, according to the eigenvalue decomposition of G.

Optimisation of the core subset for the APY approximation of genomic relationships

“…Their approach with the QR decomposition of SNP genotype matrix choose a core subset that improved convergence, but it did not improve accuracy. Nilforooshan and Lee [15] used the diagonal construction based on G as well as based on A . They found that the diagonal construction based on G gave similar correlation between GEBVs from the full inverse and APY inverse, when the core subset was large, but worse with smaller core subsets.…”

“…During model fitting, phenotype information “flows” between both subsets of animals, hence both subsets contribute to the estimation. While APY is an approximation, it has been shown to be accurate and scalable for various populations of dairy and beef cattle [11, 12], pigs [13, 14], and sheep [15, 16].…”

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

“…Animals were sorted in genealogical order and then core animals were uniformly sampled across the pedigree. Since is a sparse representation of [ 14 , 16 , 17 ], sampling animals across generations has the potential to capture all (co)variation in .…”

“…In a seminal study, Misztal [ 11 ] hypothesized that the accuracy of APY depends on how well animals in the core group represent the independent chromosome segments (ICS) that are present in the population. Several studies have investigated the core definition in APY ssGBLUP [ 2 , 12 – 17 ]. Some have reported that, in cattle, using proven bulls as core led to nearly identical accuracy as using randomly selected core sets [ 2 , 13 , 18 ].…”

“…Some have reported that, in cattle, using proven bulls as core led to nearly identical accuracy as using randomly selected core sets [ 2 , 13 , 18 ]. However, in pigs and sheep, several studies have reported different EBV and accuracies of prediction by different core definitions [ 14 , 16 , 17 ]. In all these studies, the number of genotyped animals per breed was less than 22k, and none investigated the interplay between core size and definition, especially for larger genotyped populations.…”