Rules are presented for assigning coefficients to the genetic group portion(s) of the mixed model equations after transformation to solve directly for total genetic value (group plus animal solutions) simultaneously for sires and cows using an animal model. Inclusion of all known relationships seems to reduce the need for groups to account for genetic selection and genetic trend. Migration of animals into a population, however, results in a need for grouping to account for genetic merit of the migrants. Selection of parents on which records are not available also creates a need for grouping. Group solutions represent the average genetic merit of phantom (unidentified, or represented by only one descendant) animals selected to be parents that do not have records available. Groups can be crossclassified with time and the genetic path of selection. The total genetic value for every animal includes a function of genetic groups. The function of genetic groups is specific for each individual animal and depends on the number of generations to the base phantom ancestors and on the genetic groups to which those phantom ancestors are assigned. The group coefficients presented account for genetic selection that cannot be defined by known genetic relationships.

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 herdyear-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.

Data were lactations of 82,971 Canadian Holstein-Friesian cows by 4,778 sires recorded from 1975 to 1978 and included final disposal codes. Progeny were required to have first lactation records and were grouped according to whether they had the opportunity to complete one, two, or three lactations. Henderson's Method I technique was used to estimate sire, herd, and error variances within opportunity group for culling for low production, sickness, and all undesirable causes. Variances were low, and many were negative. Heritabilities ranged from 0 to .13. Best linear unbiased prediction techniques were used to estimate sire proofs for disposal reasons. Sire proofs were not distributed normally. Sire proofs were correlated between opportunity groups within disposal reason. All correlations were positive and ranged from .21 to .82. Correlations were greatest between contiguous opportunity groups and lowest between proofs on early opportunity groups and proofs on cows that were close to maturity, indicating that first opportunity group proofs for disposal are not accurate predictors of longevity. Routine evaluation of sires on disposal reasons is not recommended.

Estimated transmitting abilities for milk of 258,201 Holstein heifers from first lactations were regressed on sire's milk proof, maternal grandsire's milk proof, and either dam's estimated transmitting ability from milk in first lactation or dams's estimated transmitting ability from milk of all lactations. Effects of year of birth of dam, dam's estimated transmitting ability for milk from first lactation, for milk from all lactations, estimated transmitting ability for fat from first lactation or for fat from all lactations were determined by sorting data into deciles by each of these criteria and calculating partial regression coefficients within each decile. For data in deciles on dams's estimated transmitting ability for milk in first lactation, no further information was gained from all lactations. Partial regression coefficients from regression of heifer's estimated transmitting ability from first lactation on dam's estimated transmitting ability from first lactation, maternal grandsire's proof, and sire's proof were similar to approximate theoretical upper limits. The partial regression coefficient for dam's estimated transmitting ability from all lactations was much smaller than expected. Because regression on dam's estimated transmitting ability from first lactation resulted in weights more closely approximating theoretical upper limits than weights from regression on dam's estimated transmitting ability from all lactations, the use of the former is preferred to predict heifer's estimated transmitting ability from first lactation.

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