Efficient and accurate computation of base generation allele frequencies

Allele frequencies are used for several aspects of genomic prediction, with the assumption that these are equal to the allele frequency in the base generation of the pedigree. The current standard method, however, calculates allele frequencies from the current genotyped population. We compared the current standard method with BLUP and general least squares (GLS) methods explicitly targeting the base population to determine whether there is a more accurate and still efficient method of calculating allele frequencies that better represents the base generation. A data set based on a typical dairy population was simulated for 325,266 animals; the last 100,078 animals in generations 9 to 12 of the population were genotyped, with 1,670 SNP markers. For the BLUP method, several SNP genotypes were analyzed with a multitrait model by assuming a heritability of 0.99 and no genetic correlation among them. This method was limited by the time required for each BLUP to converge (approximately 6 min per BLUP run of 15 SNP). The GLS method had 2 implementations. The first implementation, using imputation on the fly and multiplication of sparse matrices, was very efficient and required just 49 s and 1.3 GB of random access memory. The second implementation, using a dense full A₂₂^-1 matrix, was very inefficient and required more than 1 d of wall clock time and more than 118.2 GB of random access memory. When no selection was considered in the simulations, all methods predicted equally well. When selection was introduced, higher correlations between the estimated allele frequency and known base generation allele frequency were observed for BLUP (0.96 ± 0.01) and GLS (0.97 ± 0.01) compared with the current standard method (0.87 ± 0.01). The GLS method decreased in accuracy when introducing incomplete pedigree, with 25% of sires in the first 5 generations randomly replaced as unknown to erroneously identify founder animals (0.93 ± 0.01) and a further decrease for 8 generations (0.91 ± 0.01). There was no change in accuracy when introducing 5% genotyping errors (0.97 ± 0.01), 5% missing genotypes (0.97 ± 0.01), or both 5% genotyping errors and missing genotypes (0.97 ± 0.01). The GLS method provided the most accurate estimates of base generation allele frequency and was only slightly slower compared with the current method. The efficient implementation of the GLS method, therefore, is very well suited for practical application and is recommended for implementation.