Animal Science Department


Date of this Version

January 1985


Published in J Dairy Sci1985, 68:760-767. Copyright © 1985 The American Dairy Science Association. Used by permission.


A potential difficulty with mixed model equations for multiple trait evaluation of sires is solving the equations as the number of equations increases proportionally to the number of traits. Time required to obtain inverse solutions increases by the number cubed. Thus, iterative procedures often are used. Three iterative procedures, successive over-relaxation, block iteration with relaxation, and the method of conjugate gradients, were compared for four sets of multiple trait equations for sire evaluation. Equations were solved after absorption of equations for random herd-year-season effects. Equations for two and four traits each with test and complete data sets made up the four sets of equations. The two-trait system featured high heritabilities and large negative correlations among effects whereas the four-trait system had low heritabilities and smaller negative correlations. Rate of convergence for block iteration was faster than for successive over-relaxation, especially for the four-trait system and especially for more exacting convergence criteria. The method of conjugate gradients was efficient only for test data sets (30 and 60 equations) and was not competitive with the other methods for complete data sets (1426 and 2852 equations). Test data sets accurately predicted optimum relaxation factors for successive over-relaxation for complete data sets. Optimum relaxation factor for the two-trait system was 1.5 to 1.7 and for the four-trait system was 1.3 to 1.5. Gauss-Seidel iteration took 33 to 400% more rounds than successive over-relaxation with the optimum relaxation factor depending on stopping criteria and data set.