Records of milk and fat yields were used to study the effects of sire x herd and sire x herd-year interactions on genetic values of Brown Swiss breed sires. The (co)variance components were estimated by the restricted maximum likelihood method, by using three models with multitrait. In these models, the genetic group, season of calving and herd-year class were considered as fixed effects, while the animal effects, the permanent environment, the interaction of either sire x herd or sire x herd-year were considered as random ones, when the interaction was considered in the model, and the error as well. The likelihood ratio test was used to verify the effectiveness in including the interaction effects into models. The estimates of components of the genetic addictive and residual (co)variances did not change when the models were adjusted for the interaction effects. Therefore, the heritability coefficients approximated to each others. The heritability estimate were of 0.40 for both characteristics, and the genetic correlation among the characteristics of 0.94, except when the model considered the effect of the interaction sire x herd. The heritability of fat yield was of 0.39, and the genetic correlation among the characteristics of 0.95. The proportion of the total variance explained by the sire x herd and the sire x herd -year interactions was low, but almost null for milk yield, and about 1% for fat yield. The natural logarithm of likelihood function increased, when the interaction effects were included in the models. Pearson and Spearman correlations among the genetic values obtained by these models were superior than 0.99 for both milk and fat yields, and above 0.897 among the studied characteristics.
dairy cattle; genotype by environment interaction; variance components
