First lactation milk and fat yields of 5086 purebred and crossbred Gir cows were used to estimate genetic components of (co)variance using multivariate and bivariate animal models solved by a REML derivative-free algorithm. Both models were used to predict breeding values (EBV) for milk (MY) and fat (FY) yields of purebred and crossbred Gir cows. In the multivariate model it was assumed yields from each genetic group as different traits to account for heterogeneous phenotypic variance for milk yield. This model was compared to a bivariate model assuming homogeneous genetic expression between genetic groups (purebred and crossbred cows). Additive genetic and residual variances were heterogeneous for genetic groups. Genetic variances for milk (115,536.4 kg²) and fat (214.8 kg²) of purebred Gir cows were approximately three folds larger than estimates for milk (39,080.4 kg²) and fat (60.8 kg²) of crossbred cows. Genetic correlations ranged from 0.73 to 0.99 between milk and fat yields and were larger for milk yields (0.86) than for fat yields (0.76) between different genetic groups. Heritability (h²) for milk and fat yields were larger in purebred (0.23 and 0.20 respectively) than in crossbred cows (0.08 and 0.07 respectively). Genetic correlation between milk and fat yields were 0.95 and 0.99 for purebred and crossbred Gir cows respectively. Genetic variances for milk (99,104.92 kg², h² = 0.20) and fat (181.21 kg², h² = 0.18) estimated from the bivariate model were respectively 85.9% and 84.4% of the corresponding estimates for purebred Gir cows from the mutivariate model. Genetic covariance and correlation between milk and fat yields estimated from the bivariate model were respectively 4,071.14 kg² and 0.96. Rank correlation estimates were larger than 0.96 between EBV for MY of Gir cows and EBV for MY and FY of crossbred cows and EBV for MY and FY from the bivariate model. Changes in ranking of sires and cows suggest higher selection accuracy and greater potential of genetic progress by application of a multiple trait animal model for genetic evaluations.
heterogeneity of variance; genetic parameter; selection; genetic evaluation
