Estimation of nonadditive genetic variances for a total-merit model including maternal effects.
Henderson described a method to reduce the number of mixed-model equations when estimating additive and nonadditive genetic variances or predicting additive and nonadditive genetic merits. The extension to a maternal effects model is straight-forward. When maternal genetic effects are strictly additive, an algebraic identity was found that reduces by a factor of two the order of a matrix that must be inverted each round to account for the genetic covariances among direct and maternal genetic effects. An algorithm for derivative-free restricted maximum likelihood was developed based on Henderson's total-merit model that is the basis for a reduced number of equations. The same values for the logarithm of the likelihood can be calculated from components of the equations for the total-merit model and from components of the equations for the individual effects model. The computational properties of the equations for the total-merit model, however, do not lend themselves to sparse-matrix methods. Both memory and time requirements were much greater for the total-merit model than for the individual-effects model for a data set of 871 animals and a model with additive, dominance, and additive x additive direct and additive maternal genetic effects. Approximately 14 times more memory was required, although the number of equations decreased from 3,773 to 2,031. Computing time per round increased by a factor of 50.
Roman L. Hruska U.S. Meat Animal Research Center, USDA, Clay Center, NE 68933-0166.
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Van Vleck
D000465:Algorithms; D000818:Animals; D000829:Animals, Domestic / Q000235:genetics*; D005260:Female; D014644:Genetic Variation; D016013:Likelihood Functions; D008297:Male; D008957:Models, Genetic; D009035:Mothers