Use of orthogonal functions in random regression models in describing genetic variance in Nellore cattle

A total of 204,912 records of birth weights up to 550 days of age, of 24,890 Nellore cattle, offspring of 375 sires and 16,917 dams from five herds in the state of Mato Grosso, Brazil, were used in order to describe the variability of the weight development by random regression models. The model evaluated as the most suitable used the covariance function of fourth order to describe the variability of the effects of additive genetic, animal permanent environmental and maternal effects of third order to describe the maternal genetic effect, with four classes of residual variance. Heritability estimates ranged from 0.18 to 0.46 from the beginning of trajectory to 210 days of age, from 0.45 to 0.48 post-weaning to 365 days of age and from 0.47 to 0.57 at later ages. The values of additive genetic correlations for different ages showed higher estimates between the closest ages, while birth weight was not very related to the weights at older ages. The body weight performance of the animals has additive genetic variation to respond to selection.