Best Linear Unbiased Prediction of Nonadditive Genetic Merits in Noninbred Populations

Additive genetic, dominance, additive by dominance epistatic, et cetera merits are un-correlated in unselected, noninbred populations with linkage equilibrium. The variance-co-variance matrix of each of these components is the product of a variance and a martix that can be computed from the numerator relationship matrix A. These properties enable mixed model equations for best linear unbiased prediction (BLUP) to be derived easily. Unfortunately, the number of equations can become very large if each genetic component is included in the equations. This paper presents a method for BLUP that requires no more equations than the number of animals to be evaluated plus the number of levels of other factors in the model. An algorithm for restricted maximum likelihood estimation of the genetic components using this reduced set of equations is described. Also an approximate minimum variance quadratic unbiased estimator (MIVQUE) is described.