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Properties of Mendelian Residuals when regressing Breeding Values using a Genomic Covariance Matrix
Properties of Mendelian residuals when predicting breeding values (BV) with a positive definite genomic covariance matrix are presented. It is well known that in an infinitesimal model with an additive relationship matrix built from pedigree data, the variance of the Mendelian residuals (MR) from the regression of BV on those from the ancestors, explains half the additive variance without inbreeding (F), and a little less than that if F of the parents is not zero. We show that: 1) the residual variance of BV regression using a genomic covariance matrix is always less or equal, than Mendelian variance obtained from predictions calculated without using genomic information; 2) MR are independent if BV of ancestors, parents and collateral related non-descendants animals (i.e. full and half-sibs, uncles, cousins) are included in the regression equation.
Keywords: Genomic covariance matrix; Mendelian and regression residuals; Residual independence
