First lactationmilk and fat yields of 5086 purebred and crossbred Gir cows were used to estimategenetic components of (co)variance using multivariate and bivariate animal modelssolved by a REML derivative-free algorithm. Both models were used to predictbreeding values (EBV) for milk (MY) and fat (FY) yields of purebred and crossbredGir cows. In the multivariate model it was assumed yields from each geneticgroup as different traits to account for heterogeneous phenotypic variance formilk yield. This model was compared to a bivariate model assuming homogeneousgenetic expression between genetic groups (purebred and crossbred cows). Additivegenetic and residual variances were heterogeneous for genetic groups. Geneticvariances for milk (115,536.4 kg2) and fat (214.8 kg2)of purebred Gir cows were approximately three folds larger than estimates formilk (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 andwere larger for milk yields (0.86) than for fat yields (0.76) between differentgenetic groups. Heritability (h2) for milk and fat yields were largerin purebred (0.23 and 0.20 respectively) than in crossbred cows (0.08 and 0.07respectively). Genetic correlation between milk and fat yields were 0.95 and0.99 for purebred and crossbred Gir cows respectively. Genetic variances formilk (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 mutivariatemodel. Genetic covariance and correlation between milk and fat yields estimatedfrom 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 cowsand EBV for MY and FY of crossbred cows and EBV for MY and FY from the bivariatemodel. Changes in ranking of sires and cows suggest higher selection accuracyand greater potential of genetic progress by application of a multiple traitanimal model for genetic evaluations.
