5Departamento de Engenharia Florestal, Universidade Federal de Viçosa,

ABSTRACT. The Brazilian Association of Simmental and Simbrasil Cattle Farmers provided 29,510 records from 10,659 Simmental beef cattle; these were used to estimate (co)variance components and genetic parameters for weights in the growth trajectory, based on multi-trait (MTM) and random regression models (RRM). The (co)variance components and genetic parameters were estimated by restricted maximum likelihood. In the MTM analysis, the likelihood ratio test was used to determine the significance of random effects included in the model and to define the most appropriate model. All random effects were significant and included in the final model. In the RRM analysis, different adjustments 2466 ©FUNPEC-RP www.funpecrp.com.brGenetics and Molecular Research 12 (3): 2465-2480 (2013) R.R. Mota et al. of polynomial orders were compared for 5 different criteria to choose the best fit model. An RRM of third order for the direct additive genetic