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MIVQUE and REML Estimation of Additive and Nonadditive Genetic Variances¹

Cornell University, Ithaca, NY 14853

Abstract

Three methods are described for estimation of additive and nonadditive genetic components of variance under an animal model with no inbreeding, no selection, no linkage and normally distributed variables. The methods are minimum variance quadratic unbiased estimation (MIVQUE) and restricted maximum likelihood estimation (REML) by iterated MIVQUE and by an expectation-maximization (EM) algorithm. In all of these methods, a set of mixed model equations to predict producing ability is solved; and then quadratics in this solution and a quadratic in best linear unbiased predictions (BLUP) of the error vector are equated to their expectations. The matrices of these quadratics are computed from relationship matrices and from prior estimates of variances used in the mixed model equations. These methods utilize all relationships among the animals.

¹ This research was supported in part by the Dept of Anim. Sci., Univ. of Illinois.

² Dept. of Anim. Sci.

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