Genetic evaluation of growth in nellore cattle by multiple-trait and random regression models

The objective of this study was to identify issues in genetic evaluation of beef cattle for growth by a random regression model (RRM). Genetic evaluation data included 2,946,847 records of up to nine sequential weights of 812,393 Nellore cattle measured at ages ranging from birth to 733 d. Models considered were a five-trait multiple-trait model (MTM) and a cubic RRM. The MTM included the effects of contemporary group, age of dam class, additive direct, additive maternal, and maternal permanent environment. Both additive effects were assumed correlated. The RRM included the same effects as MTM, with the addition of permanent and random error effects. The purpose of the random error effect, which was in addition to a residual effect with constant variance, was to model heterogeneous residual variances. All effects in RRM were modeled as cubic Legendre polynomials. Expected progeny differences (EPD) were obtained iteratively using a preconditioned conjugate gradient algorithm. Numerically accurate solutions with RRM were not obtained until the random regressions were orthogonalized. Computing requirements of RRM were reduced by more than 50%, without affecting the accuracy by removing regressions corresponding to very low eigen-values and by replacing the random error effects with weights. Afterward, the correlations between EPD from RRM and from MTM for EPD on selected weights were between 0.84 and 0.89. For sires with at least 50 progeny, these correlations increased to 0.92 to 0.97. Low correlations were caused by differences in parameters. The RRM applied to growth i s prone to numerical problems. Estimates of EPD with RRM may be more accurate than those with MTM only if accurate parameters are applied.