In order to estimatecovariance 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 Tabapuãcattle were used. The models included: as random effects, direct additive geneticeffect, maternal effect, and animal and maternal permanent environmental effets;contemporary groups were included as fixed effects; and as covariables, animalage at weighing and age of dam at calving (linear and quadratic effects) andon age at weighing,, the orthogonal Legendre polynomial (cubic regression) wasconsidered to model the mean curve of the population. Residuals effects weremodeled considering seven classes of variance. The models were compared by Akaikecriterion and Bayesian information criterion. The best model showed orders 4,3, 6, and 3 for maternal and direct additive genetic effect, and maternal andanimal permanent enviroment, respectively. Estimates of (co)variance and heritabilityobtained with the bi-trait and random regression models were similar. The heritabilityestimates for direct additive genetic effect obtained by the random regressionmodels increased from birth (0.15) to 660 days of age (0.45). The greatest estimatesof maternal heritability were obtained for weights measured right after birth.In general, the genetic correlation estimates were moderate to high, and theydecreased as the distance between weights increased. Selection for higher weightsat any age will promote weight gain from birth to 660 days of age.
