RESUMO
Polynomial regression models of the first, second, and third order were used to fit milk production deviations of daughters in Mexico on Canadian and US predicted transmitting ability values for 305-d mature-equivalent milk production (kg). For the pairs Canada-Mexico and Mexico-United States, 40 and 73 bulls with a minimum reliability of 0.75 were analyzed, respectively. Genetic correlations between pairs of countries were also estimated. The parameters were evaluated for all data, and for sires grouped according to the mean of the average phenotypic milk production (high and low) of their daughters' herd mates. Quadratic and cubic effects were not significant in any analysis. From linear regression models, slopes of Mexican daughter deviations on US and Canadian predicted transmitting abilities were 1.01 and 0.93, respectively. Slopes were greater but intercepts were smaller for the high versus low level of production of the sires' herd mates in Mexico. A greater difference between the genetic correlations was found for the high versus low environmental level than for the low level (0.79 vs. 0.70) for Mexico-US data compared with Canada-Mexico data (0.81 vs. 0.78). Genetic correlations between Mexico and the United States (0.74), and between Mexico and Canada (0.77), were smaller than the genetic correlation between the same Canadian and US sires (0.92), suggesting the presence of a moderate degree of genotype-environment interaction for milk production between Canada and the United States, and Mexico.
