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The present study had the following objectives: to compare random regression models (RRM) considering the time-dependent (days in milk, DIM) and/or temperature × humidity-dependent (THI) covariate for genetic evaluation; to identify the effect of genotype by environment interaction (G×E) due to heat stress on milk yield; and to quantify the loss of milk yield due to heat stress across lactation of cows under tropical conditions. A total of 937,771 test-day records from 3603 first lactations of Brazilian Holstein cows obtained between 2007 and 2013 were analyzed. An important reduction in milk yield due to heat stress was observed for THI values above 66 (-0.23 kg/day/THI). Three phases of milk yield loss were identified during lactation, the most damaging one at the end of lactation (-0.27 kg/day/THI). Using the most complex RRM, the additive genetic variance could be altered simultaneously as a function of both DIM and THI values. This model could be recommended for the genetic evaluation taking into account the effect of G×E. The response to selection in the comfort zone (THI ≤ 66) is expected to be higher than that obtained in the heat stress zone (THI > 66) of the animals. The genetic correlations between milk yield in the comfort and heat stress zones were less than unity at opposite extremes of the environmental gradient. Thus, the best animals for milk yield in the comfort zone are not necessarily the best in the zone of heat stress and, therefore, G×E due to heat stress should not be neglected in the genetic evaluation.

The multi-trait reaction norm (MTRN) model was extended to beef cattle reared under tropical conditions with the following objectives: to compare multi-trait (MT) and MTRN models regarding the genetic parameters obtained; and to characterize G × E, the pattern of phenotypic expression, and the environmental sensitivity of animals for postweaning weight gain (PWG), scrotal circumference (SC), and annual average productivity of the cow (PRODAM). There was divergence in the estimates between the MT and MTRN models when the posterior probability intervals of additive genetic variances and heritability coefficients of PWG and PRODAM were analyzed. The MTRN model indicated an increase in heritability for PWG and PRODAM with improvement of the environmental conditions. For SC, heritability was practically the same, irrespective of the environmental conditions. The genetic correlations between the traits studied were low but varied over environments by the MTRN model. Considering genetic correlations obtained by the MTRN model for the same trait, lower estimates were obtained between extreme favorable and unfavorable environments. This finding suggest re-ranking of breeding values in different environments mainly for PWG and PRODAM. Thus, G × E is more important for PWG and PRODAM than for SC and should be included in the genetic evaluation of these traits. The traits PWG and PRODAM can be considered plastic traits, whereas SC is poorly plastic. The genetic trends in individual animal slopes indicate that the population is moving towards greater plasticity. This could be a matter of concern for breeders since greater plasticity seems to limit heritability and, consequently, the responses to selection.

The objectives of this study were to characterize and define homogenous production environments of composite beef cattle in Brazil in terms of climatic and geographic variables by using multivariate exploratory techniques; to evaluate the presence of genotype by environment interaction (GxE) for post-weaning weight gain (PWG), yearling scrotal circumference (SC), and yearling muscling (MUS). Hierarchical and nonhierarchical cluster analysis was used to group farms located in regions with similar environmental variables into clusters. Six clusters of farms were formed. The effect of sire-cluster interaction was tested by single-trait analysis. Genetic parameters were estimated by multi-trait analysis considering the same trait to be different in each cluster. The effect of sire-cluster interaction was significant (P <0.01) for PWG and MUS. Estimates of genetic correlations among clusters ranged from 0.31 to 0.93 for PWG, 0.64 to 0.89 for SC, and 0.18 to 0.80 for MUS. These results indicate the need for a genetic analysis on a regional basis or inclusion of the GxE effect in the statistical model to permit appropriate evaluation of the animals.

The objectives of the present study were: (1) to evaluate the importance of genotype × production environment interaction for the genetic evaluation of birth weight (BW) and weaning weight (WW) in a population of composite beef cattle in Brazil, and (2) to investigate the importance of sire × contemporary group interaction (S × CG) to model G × E and improve the accuracy of prediction in routine genetic evaluations of this population. Analyses were performed with one, two (favorable and unfavorable) or three (favorable, intermediate, unfavorable) different definitions of production environments. Thus, BW and WW records of animals in a favorable environment were assigned to either trait 1, in an intermediate environment to trait 2 or in an unfavorable environment to trait 3. The (co)variance components were estimated using Gibbs sampling in single-, bi- or three-trait animal models according to the definition of number of production environments. In general, the estimates of genetic parameters for BW and WW were similar between environments. The additive genetic correlations between production environments were close to unity for BW; however, when examining the highest posterior density intervals, the correlation between favorable and unfavorable environments reached a value of only 0.70, a fact that may lead to changes in the ranking of sires across environments. The posterior mean genetic correlation between direct effects was 0.63 in favorable and unfavorable environments for WW. When S × CG was included in two- or three-trait analyses, all direct genetic correlations were close to unity, suggesting that there was no evidence of a genotype × production environment interaction. Furthermore, the model including S × CG contributed to prevent overestimation of the accuracy of breeding values of sires, provided a lower error of prediction for both direct and maternal breeding values, lower squared bias, residual variance and deviance information criterion than the model omitting S × CG. Thus, the model that included S × CG can therefore be considered the best model on the basis of these criteria. The genotype × production environment interaction should not be neglected in the genetic evaluation of BW and WW in the present population of beef cattle. The inclusion of S × CG in the model is a feasible and plausible alternative to model the effects of G × E in the genetic evaluations.

The objectives of the present study were to compare alternative models for the genetic evaluation and assess the importance of genotype by environment interaction (G×E) in the estimation of genetic parameters and genetic evaluation of birth weight (BW), weight at 60 days of age (W60) and weight at 180 days of age (W180) of Santa Ines sheep. Data comprise 7622 BW, 4673 W60 and 2830 W180 records from animals born in 44 Brazilian herds. Four models were used for the analyses: animal model (AM) with homogeneous residual variance (1), or heterogeneous residual variance (2), hierarchical reaction norms model (HRNM) with homogeneous (1) or heterogeneous residual variance (2). The models that best fit the BW, W60 and W180 data were AM2, HRNM1 and HRNM2 respectively. Thus, models for genetic evaluation that consider heterogeneity of variances are recommended to evaluate growth traits of sheep. The correlation between intercept and slope of the HRNM was higher than 0.70 for all traits studied, indicating that animals with higher average breeding values responded better to improvement in environmental conditions, a fact characterizing the scale effect of G×E. Therefore, G×E is an important factor to be considered in the estimation of genetic parameters and genetic evaluation of growth traits of sheep., (© 2013 Blackwell Verlag GmbH.)