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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.

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Two previously identified single-nucleotide polymorphism markers located within the micromolar calcium-activated neutral protease gene (CAPN1) were evaluated for their association with variation in meat tenderness using one commercial sample of Simmental x Angus crossbred calves and one multibreed, crossbred research herd. The commercial sample included 362 animals sired by 23 registered Simmental bulls bred to unregistered Angus cows and represented current industry animals in which to test the predictive merit of the markers. The second sample was a research herd including 564 steers from the Germplasm Evaluation Cycle VII population at the U.S. Meat Animal Research Center, produced with semen from popular sires of the seven Bos taurus beef breeds with the most registrations in the United States (Angus, Charolais, Gelbvieh, Hereford, Limousin, Red Angus, and Simmental) on Angus, Hereford, and MARC III cows. These animals form a relatively outbred population that constituted a stringent test of the predictive merit of the genetic markers, although small groups were half-sibs. Warner-Bratzler shear force measurements were used to determine tenderness phenotypes for all animals. The populations were genotyped for two markers that predict variation at amino acid positions 316 and 530 of the mu-calpain polypeptide, produced by the CAPN1 gene. Minor allele frequencies for markers 316 and 530 in the commercial sample were 0.17 and 0.37, respectively, and in the Cycle VII animals, were 0.20 and 0.28, respectively. Both markers showed association with shear force in the commercial sample (P = 0.04) and the Cycle VII population (P = 0.02), supporting the hypothesis that they represent potential markers to aid selection for improved meat tenderness in commercial populations of beef cattle in the United States.

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