Models for genetic evaluation of milk yield in multiple lactations

The objective of this work was to evaluate covariance components and breeding values for 305-day cumulative milk yield with data from the first three lactations of Gyr cows. A total of 14,659 lactations of 9,079 cows were evaluated, using the models of repeatability, multiple-trait (MT), and random regression with residual homoscedasticity (RRMHo) or heteroscedasticity (RRMHe). Milk yield was considered as a different trait in each lactation, in the MT model. Linear polynomials were used in random regression models to fit the mean trajectories and the additive genetic and permanent environment individual effects, according to calving order. Posteriori means for heritability were similar among different models and lactations, and varied from 0.24 to 0.29. The MT and RRMHe models had a better fit to the data, since heterogeneity was observed for genetic and residual variances between lactations. The genetic correlations of cumulative milk yield up to 305 days in the first three lactations were close to 1.0; therefore, the selection of reproducers can be made with data already from the first lactation. Random regression models with heterogenous genetic and residual variances allow for proper modeling of the covariances in cumulative milk yields in multiple lactations and for obtaining the genetic values to be used in the selection of reproducers, based on data already from the first lactation.