Efficient single-step genomic evaluation for a multibreed beef cattle population having many genotyped animals

An equivalent computational approach called ssGTBLUP was formulated for the original single-step GBLUP (ssGBLUP). In ssGTBLUP, the genomic relationship matrix has the form G = ZZʹ + C, where the (centered and scaled) Z marker matrix has size n x m (numbers of genotypes and markers), and the C matrix can be easily inverted. The inverse can be written as G-1 = C-1 − TʹT where T is an m by n matrix. When the preconditioned conjugate gradient (PCG) method is used to solve the mixed model equations, a matrix vector product G-1d needs to be computed. In ssGBLUP, this requires n2 multiplications, but in ssGTBLUP, the product TʹTd has 2nm multiplications and C-1d has cn multiplications with the constant c independent of n or m. In an approximate approach called ssGTBLUP(p), the eigendecomposition of ZʹC-1Z is used to reduce the number of rows in the T matrix. Here, p is the percentage of total variance explained by the accepted eigenvalues. The objective of this study was to compare the performance of ssGBLUP, ssGTBLUP, ssGTBLUP(p), and the APY (algorithm for proven and young) method. In APY, the core had 50,000 (APY50K), 30,000 (APY30K), or 10,000 (APY10K) animals. The approaches were tested on the Irish beef carcass conformation genetic evaluation which has a heterogeneous multibreed population. The pedigree had 13.3 million animals. There were m = 54,620 markers available from n = 163,277 genotyped animals. For genotyped animals, the correlations of breeding values between ssGBLUP and ssGTBLUP(p) for the 11 traits in the model ranged from 0.999–1.000 for p = 99, 0.998–1.000 for p = 98, and 0.992–0.998 for p = 95 but were 0.994–1.000 for APY50K, 0.969–0.997 for APY30K, and 0.899–0.967 for APY10K. Computing times per iteration were 4.43, 3.30, 2.69, 2.29, 1.55, 1.76, 1.27, and 0.55 min for ssGBLUP, ssGTBLUP, ssGTBLUP(99), ssGTBLUP(98), ssGTBLUP(95), APY50K, APY30K, and APY10K, respectively. The ssGTBLUP(p) approach allowed a well-defined approximation to ssGBLUP and fast computations