Bayesian posterior estimates of variances of maternal lineage effects were obtained with a procedure that used Gibbs sampling. Data were records of yield during first parity from 245,510 Holstein cows that calved in Canada between 1990 and 1994. Maternal lineages were defined by tracing the maternal ancestry of cows to common female ancestors. Traits were standardized yields of milk, fat, and protein and percentages of fat and protein. Estimates of maternal lineage variance were <0.5% of the total variance for all traits. Effects of this size hardly affected the cow rankings for estimated breeding value. Another analysis defined maternal lineages by establishing groups of dams and their daughters in an attempt to maximize the variance of environmental effects associated with maternal lineages, but only 1.1% of the variance in milk yield was associated with effects of the dam and daughter groups. Analyses of simulated data indicated that positive estimates of maternal lineage effects were not a result of restriction of estimates to positive values and that estimates of maternal lineage variance were biased slightly downward because of incomplete pedigree information. The partitioning of maternal lineage and additive genetic variance was correct when pedigree information was complete, according to results from simulation.
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