Hierarchical Bayesian models for genotype × environment estimates in post-weaning gain of Hereford bovine via reaction norms

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It was evaluated statistical models with different assumptions to define the one that best describes the presence of genotype × environment interaction on adjusted post-weaning weight gain (PWG345) of Hereford cattle, through the study of reactions norms to the environment, obtained by random regression using a Bayesian approach. Four reaction norms hierarchical models (RNHM) were used through the INTERGEN program. The RNHM K uses the solutions of contemporary groups previously estimated by the standard animal model (AM) and considers them as environmental level for predicting the reaction norms and the RNHM S, which jointly estimate 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, RNHMs hm showed the best fit to the data, and by the deviance based on conditional predictive ordinate, the best fit was the RNHM Kht, whereas, by all the three criteria used, the worst fit was obtained by using the standard animal model. Heritabilities estimated on RNHM were increasing in the environmental gradients for PWG345, at -60 kg, 0 and +60 kg. The genetic correlation estimated between the level and slope of reaction norms was high, from 0.97 to 0.99, characterizing a scale effect on genotype × environment interaction. The reaction norms hierarchical models are efficient to describe the changes in variance components due to the environment and to describe the presence of genotype × environment interaction on PWG345 trait of Hereford cattle.