Effect of scaling genomic relationship matrix on estimation of variance components and accuracy of breeding values

In this study, Bayesian approach via Gibbs sampling was used to predict unknown parameters of five equivalent Genomic Best Linear Unbiased Predictions (G-BLUP), each with different scale of G matrix by using allele frequency of founder population (Gfoun), allele frequency of reference population (Gref), allele frequency equal to 0.5 (G05), a normalized matrix with average diagonal coefficients equal to 1 (Gnorm) and a weighted G matrix with A matrix (Gwei). A random mating population and a selected population were used to compare results of a trait with heritability of 0.25 on a genome constructed of three chromosomes with 105 QTLs and 3000 single nucleotide polymorphisms. The results showed that higher variance existed in the elements of G matrices compared with A matrix. Average diagonal and off-diagonal elements except Gnorm and Gwei were higher than corresponding elements in A. Gnorm-BLUP and G05-BLUP methods led to inflated genetic variance in contrast other three methods and this inflation was lower in selected population. Average accuracy over 5 G-BLUP in random population was 0.084 higher than selected population (0.762 vs. 0.652) and bias was 0.041 lower (0.026 vs. 0.04). Bias of prediction of true breeding value of selected population by using Gwei almost was zero but with Gref greater than 0.06. The greatest accuracy and the smallest bias can be obtained by using allele frequency of reference population that re-scaled with A matrix.