Simultaneous genetic evaluation of sires and cows for a large population of dairy cattle.

A strategy for simultaneous sire and cow evaluation of genetic merit was implemented. First lactation records of 1,074,971 Holstein cows in 20,065 herds were included. After inclusion of ancestors, there were 1,741,356 equations: 1,505,938 cow, 229,394 herd-year-season, 6000 sire, and 24 genetic group equations. All known genetic relationships among animals were considered. Genetic group coefficients were assigned based on animals that had one or more parents unidentified. Mixed model equations from an animal model were transformed to solve for total additive genetic merit. The coefficient matrix was sparse with .00039% nonzero elements. Equations were blocked by herds. A final block included sires, groups, and cows that had no daughters or records. Effects of herd-year-season were solved last within each herd. All herd blocks were solved before sire equations. A form of block iteration with successive overrelaxation was used to obtain solutions. A total of 30 rounds were completed. Number of iterations per round for herd blocks decreased from an average of 4.93 in round 1 to the minimum allowed, 3.00, in round 30. The correlation between Northeast Artificial Insemination Sire Comparisons and sire solutions from this study stabilized at .94. At round 30, 96.4, 95.2, 99.4, and 75.0% of solutions for cow, sire, herd-year-season, and group effects changed less than 4.54 kg from the previous round.