In order to estimate covariance functions by using random regression models on Legendre polynomials, 35,732 weight records from birth to 660 days of age of 8,458 animals of Tabapuã cattle were used. The models included: as random effects, direct additive genetic effect, maternal effect, and animal and maternal permanent environmental effets; contemporary groups were included as fixed effects; and as covariables, animal age at weighing and age of dam at calving (linear and quadratic effects) and on age at weighing,, the orthogonal Legendre polynomial (cubic regression) was considered to model the mean curve of the population. Residuals effects were modeled considering seven classes of variance. The models were compared by Akaike criterion and Bayesian information criterion. The best model showed orders 4, 3, 6, and 3 for maternal and direct additive genetic effect, and maternal and animal permanent enviroment, respectively. Estimates of (co)variance and heritability obtained with the bi-trait and random regression models were similar. The heritability estimates for direct additive genetic effect obtained by the random regression models increased from birth (0.15) to 660 days of age (0.45). The greatest estimates of maternal heritability were obtained for weights measured right after birth. In general, the genetic correlation estimates were moderate to high, and they decreased as the distance between weights increased. Selection for higher weights at any age will promote weight gain from birth to 660 days of age.
beef cattle; genetic correlations; heritability; longitudinal data; weights
