G-Blup without inverting G

Abstract

Regular mixed model methodology requires inversion of the variance-covariance matrix of the random effects. In the regular animal model the inverse of the numerator relationship matrix (A) can be easily set up directly due to its sparse nature with many simple coefficients. In G-Blup a genomic relationship matrix (G) is used, which is a dense matrix wherein the coefficients are determined by many loci. Inversion of the G matrix is a time-consuming or even a limiting factor with increasing training populations. Assuming a genomic model including SNP effects and a residual polygenic component, a derivation of G-Blup without inverting the G matrix is presented here. DGVs can be computed from the residual polygenic components given the relationship matrices G and A and the variance components.