It was evaluatedstatistical models with different assumptions to define the one that best describesthe presence of genotype × environment interaction on adjusted post-weaningweight gain (PWG345) of Hereford cattle, through the study of reactions normsto the environment, obtained by random regression using a Bayesian approach.Four reaction norms hierarchical models (RNHM) were used through the INTERGENprogram. The RNHMK uses the solutions of contemporary groups previouslyestimated by the standard animal model (AM) and considers them as environmentallevel for predicting the reaction norms and the RNHMS, which jointlyestimate these two sets of unknowns. For both models, two versions were considered,one with a homogeneous (hm) and another with a heterogeneous (ht) residual variance.Based on the deviance information criterion and Bayes factor, RNHMshmshowed the best fit to the data, and by the deviance based on conditional predictiveordinate, the best fit was the RNHMKht, whereas, by all the threecriteria used, the worst fit was obtained by using the standard animal model.Heritabilities estimated on RNHM were increasing in the environmental gradientsfor PWG345, at -60 kg, 0 and +60 kg. The genetic correlation estimated betweenthe level and slope of reaction norms was high, from 0.97 to 0.99, characterizinga scale effect on genotype × environment interaction. The reaction normshierarchical models are efficient to describe the changes in variance componentsdue to the environment and to describe the presence of genotype × environmentinteraction on PWG345 trait of Hereford cattle.
