Strategies to Improve Numerical Stability of Equations used for Genomic Prediction of Genetic Merit

The pedigree-based additive relationship matrix (PARM) has long been used for prediction of genetic merit by best linear unbiased prediction (BLUP), using only pedigree and phenotypic data. When genotype data are used, genomic BLUP (GBLUP) can be obtained by replacing the PARM by a genomic additive relationship matrix (GARM). Obtaining the inverse of this GARM, which is needed to obtain BLUP by solving Henderson's mixed model equations (MME), can be challenging. Furthermore, when the number n of individuals in the analysis exceeds the number p of genotyped loci, the GARM will be singular and will not have an inverse. Even when n < p, the GARM can be close to singular, and this can result in MME that are numerically unstable. Here, we will present strategies to improve the numerical stability of the MME for GBLUP.