Solving efficiently large single ‐step genomic best linear unbiased prediction models

Summary Single‐step genomic BLUP (ssGBLUP) requires a dense matrix of the size equal to the number of genotyped animals in the coefficient matrix of mixed model equations (MME). When the number of genotyped animals is high, solving time of MME will be dominated by this matrix. The matrix is the difference of two inverse relationship matrices: genomic (G) and pedigree (A22). Different approaches were used to ease computations, reduce computing time and improve numerical stability. Inverse of A22 can be computed as where Aij, i, j = 1,2, are sparse sub‐matrices of A−1, and numbers 1 and 2 refer to non‐genotyped and genotyped animals, respectively. Inversion of A11 was avoided by three alternative approaches: iteration on pedigree (IOP), matrix iteration in memory (IM), and Cholesky decomposition by CHOLMOD library (CM). For the inverse of G, the APY (algorithm for proven and young) approach using Cholesky decomposition was formulated. Different approaches to choose the APY core were compared. These approaches were tested on a joint genetic evaluation of the Nordic Holstein cattle for fertility traits and had 81,031 genotyped animals. Computing time per iteration was 1.19 min by regular ssGBLUP, 1.49 min by IOP, 1.32 min by IM, and 1.21 min by CM. In comparison with the regular ssGBLUP, the total computing time decreased due to omitting the inversion of the relationship matrix A22. When APY used 10,000 (20,000) animals in the core, the computing time per iteration ...
Source: Journal of Animal Breeding and Genetics - Category: Genetics & Stem Cells Authors: Tags: ORIGINAL ARTICLE Source Type: research