Abstract
Base population allele frequencies (AF) should be used in genomic evaluations. A program named Bpop was implemented to estimate base population AF using a generalized least squares (GLS) method when the base population individuals can be assigned to groups. The required dense matrix products involving (A22 )-1v were implemented efficiently using sparse submatrices of A-1, where A and A22 are pedigree relationship matrices for all and genotyped animals, respectively. Three approaches were implemented: iteration on pedigree (IOP), iteration in memory (IM), and direct inversion by sparsity preserving Cholesky decomposition (CHM). The test data had 1.5 million animals genotyped using 50240 markers. Total computing time (the product (A22)-11) was 53 min (1.2 min) by IOP, 51 min (0.3 min) by IM, and 56 min (4.6 min) by CHM. Peak computer core memory use was 0.67 GB by IOP, 0.80 GB by IM, and 7.53 GB by CHM. Thus, the IOP and IM approaches can be recommended for large data sets because of their low memory use and computing time.
Highlights
Base population allele frequencies (AF) are recommended to be used in computation of the genomic relationship matrix used in the genomic evaluation (VanRaden 2008) and estimation of the genomic compliant relationship matrix among metafounders (Garcia-Baccino et al 2017)
In two of the presented three methods, i.e., generalized least squares (GLS) and maximum likelihood (ML), computationally the most challenging step is the product v = (A22)-1s where vector s is a function of marker genotypes and A22 is the pedigree based relationship matrix between the genotyped animals
The Cholesky decomposition (CHM) approach was the slowest because the extra computing time due to making the factorization took all the computing time benefits attained by fast solving of the c vector
Summary
Base population allele frequencies (AF) are recommended to be used in computation of the genomic relationship matrix used in the genomic evaluation (VanRaden 2008) and estimation of the genomic compliant relationship matrix among metafounders (Garcia-Baccino et al 2017). In two of the presented three methods, i.e., generalized least squares (GLS) and maximum likelihood (ML), computationally the most challenging step is the product v = (A22)-1s where vector s is a function of marker genotypes and A22 is the pedigree based relationship matrix between the genotyped animals. Strandén et al (2017) presented an alternative computational approach for the GLS method (McPeek et al 2006) where explicit calculation of (A22)-1 is avoided. They used equality (A22)-1s = (A22 –A21(A11)-1A12)s where Aij, i,j = 1,2,are submatrices of A-1 which are often sparse, and numbers 1 and 2 refer to the non-genotyped and the genotyped animals, respectively. This product requires using either an iterative or a sparse matrix solver (Strandén et al 2017)
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