The objectives of this study were to estimate heritabilities as well as phenotypic, genetic and environmental relationship between milk yield (MY), age at first calving (AFC) and calving intervals (CI) on Gyr dairy breed, using a multivariate derivative-free restricted maximum likelihood (MTDFREML) with an animal model. The mathematic model included herd-year of calving, calving season, and age of cows (covariate) as fixed effects, and animal, permanent environmental and error as random effects for milk yield. The model for age at first calving included herd-year of birth and season of birth as fixed effects, animal and error as random effects. The mathematic model for calving interval included herd-year of calving, calving season, and the covariate age of cow as fixed effects, and animal, permanent environment and error as random effects. Through the bivariate analysis, estimates of heritability were, respectively: for MY1 and AFC = 0.25 and 0.18; MY1 and CI1 = 0.27 and 0.07; MY2 e CI2 = 0.20 and 0.05; MY3 and CI3 = 0.17 and 0.05. The phenotypic, genetic and environmental correlations were, respectively: MY1 and AFC = 0.02, -0.29 and 0.11; MY1 and CI1 = 0.23, 0.52 and 0.19; MY2 and CI2 = 0.26, 0.54 and 0.23; MY3 and CI3 = 0.25, 0.13 and 0.27.
milking zebu; economic traits; genetic parameters; genetic antagonism
