Evaluation of methods for computing approximate accuracies of predicted breeding values in maternal random regression models for growth traits in beef cattle

The objective of this study was to determine the suitability of 2 methods for computing approximate accuracies of predicted breeding values, in which accuracy was defined as the squared correlation between the predicted and true breeding value, when modeling growth traits in beef cattle using random regression (RR) models. The first method (Strabel et al., S-M-B) was designed for use with multitrait models; thus, its use with RR models requires the clustering of measurements into different traits. The second method (Tier and Meyer, T-M) was more general, because it accounted for random coefficients other than zeros and ones and thus it could be used directly when fitting RR models. To investigate the performance of both methods, their results were compared with the true accuracies using a balanced simulated data set. The largest difference between approximate and true average accuracies for direct effects was observed at 205 d when SMB was used (4.6% males and 8.8% females). With regard to maternal effects, the largest differences in average accuracies were observed at 205 d in males when S-M-B was used (31.8%) and at the same age in females but when using T-M (33.3%). In general, bias increased for direct effect accuracies in males at the tails of the accuracy range, but for females and for maternal effect accuracies in both sexes, bias increased as accuracy increased. When a population was simulated to create large numbers of progeny for base females that did not have individual records, much greater errors were observed in the regression of approximate values on the true ones. When both approximate methods were compared using a real beef cattle data set, a good agreement was observed, particularly for direct effect accuracies in sires [i.e., at 205 d, the regressions were 0.98 (direct) and 0.95 (maternal) with r(2) over 0.99]. The largest discrepancies for sires between the methods were observed at 205 d for direct (2.7%) and maternal (16.3%) effect accuracies. For dams, the largest differences between methods were also observed at 205 d, 9.3% (direct), and 15.2% (maternal). The differences between methods for nonparent cattle were greater than for dams for maternal effect accuracies but intermediate between sires and dams for direct effect accuracies. In spite of the less biased results provided by T-M, its use could be problematic when employed in evaluations of large populations due to its greater memory and computation requirements (e. g., 170 and 478% more than S-M-B for a population of 11 million).