Joint Genomic Prediction and Estimation of Variance Components of Additive and Dominance Effects using SNP Markers

Mixed model methods for joint genomic prediction and estimation of variance components for additive and dominance effects using SNP markers were developed based on the quantitative genetics model that partitions a genotypic value into breeding value and dominance deviation. Genomic additive and dominance relationship matrices were defined as SNP additive and dominance correlation matrices such that diagonal elements are ‘1’ and off-diagonal elements are in the range of -1 and 1 in each correlation matrix. Two sets of formulations were developed. Set 1 is referred to as the CE set of GBLUP and GREML, where CE stands for the conditional expectation of breeding values and dominance deviations given phenotypic observations with fixed effects estimated by the best linear unbiased estimator (BLUE). The CE set of GBLUP and GREML applies to both cases of ‘q<m’ and ‘q>m’ and applies to cases with singular matrices of genomic additive and dominance correlations, where q = number of individuals and m = number of SNP markers. Set 2 is referred to as the MME set of GBLUP and GREML, where MME stands for mixed model equations. GREML formulations based on MME may be computationally more efficient for the case of ‘q>m’ and less efficient for the case of ‘q<m’ than GREML formulations based on CE. Accuracy formulations were derived for GBLUP of breeding value, dominance deviation and genetic value as summation of breeding value and dominance deviation. Realized accuracy of the GBLUP and GREML formulations were evaluated using simulation data.