Genetic parameters for test day milk yield of first lactation Holstein cows estimated by random regression using Legendre polynomials

Data comprising 263,390 test-day (TD) records of 32,448 first parity cows calving in 467 herds between 1991 and 2001 from the Brazilian Holstein Association were used to estimate genetic and permanent environmental variance components in a random regression animal model using Legendre polynomials (LP) of order three to five by REML. Residual variance was assumed to be constant in all or in some classes of lactation periods for each LP. Estimates of genetic and permanent environmental variances did not show any trend due to the increase in the LP order. Residual variance decreased as the order of LP increased when it was assumed constant, and it was highest at the beginning of lactation and relatively constant in mid lactation when assumed to vary between classes. The range for the estimates of heritability (0.27 - 0.42) was similar for all models and was higher in mid lactation. There were only slight differences between the models in both genetic and permanent environmental correlations. Genetic correlations decreased for near unity between adjacent days to values as low as 0.24 between early and late lactation. A five parameter LP to model both genetic and permanent environmental effects and assuming a homogeneous residual variance would be a parsimonious option to fit TD yields of Holstein cows in Brazil