It was evaluated data set of 19,303 weight records of Santa Inês sheep in order to evaluate distinct polynomial functions with different order for better adjustements of fixed and random regressions of growth trajectory and to estimate (co)variances components and genetic parameters of this trajectory. Fixed effects used in analysis were contemporary group, sex and birth type. Ordinary and Legendre polynomials, ranging from two to four orders, were evaluated for fixed regression of average growth trajectory. Legendre and quadratic b-spline functions, ranging from three to four orders, were evaluated for random regressions. Legendre polynomials of order fourth were suitable to fit random regression, while ordinary polynomials of third order were the best for fixed trajectory. Direct heritabilities on days 1, 50, 150, 250 and 411 were 0.24, 0.12, 0.44, 0.84, and 0.96, respectively, while maternal heritabilities for the same ages were 0.24, 0.19, 0.09, 0.02, and 0.01, respectively. Genetic correlations among weights in subsequent ages were high, tending to unity, and there were negative correlations between weights at early ages and weights at late ages. It is possible to modify the growth trajectory by selection with the observed genetic variability. Genetic control of weights at initial ages is not the same in late ages. So, selection of animals for slaughter in early age must be different from that of replacement animals.
β-spline functions; genetic correlation; heritability; Legendre polynomials; ordinary polynomials
