ESTIMATION OF NONADDITIVE GENETIC VARIANCES FOR A TOTAL-MERIT MODEL INCLUDING MATERNAL EFFECTS

Henderson described a method to reduce the number of mixed-model equat ions when estimating additive and nonadditive genetic variances or pre dicting additive and nonadditive genetic merits. The extension to a ma ternal effects model is straight-forward. When maternal genetic effect s 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 ro und to account for the genetic covariances among direct and maternal g enetic effects. An algorithm for derivative-free restricted maximum li kelihood was developed based on Henderson's total-merit model that is the basis for a reduced number of equations. The same values for the l ogarithm of the likelihood can be calculated from components of the eq uations 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 mode l 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 o f equations decreased from 3,773 to 2,031. Computing time per round in creased by a factor of 50.