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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. Avaliaram-se modelos estatísticos com diferentes pressuposições para definir o que melhor descreva a presença de interação genótipo × ambiente no ganho de peso pós-desmama ajustado (GPD345) de bovinos Hereford, mediante o estudo de normas de reação ao ambiente, obtidas por regressão aleatória, usando uma abordagem bayesiana. Quatro modelos hierárquicos de normas de reação (MHNR) foram empregados por meio do programa INTERGEN. O MHNR K utiliza as soluções de grupos contemporâneos estimadas previamente pelo modelo animal padrão (MA) e as considera como nível ambiental para predizer as normas de reação e o MHNR S, que estima simultaneamente esses dois conjuntos de incógnitas. Para ambos os modelos, foram consideradas duas versões, uma com variância residual homogênea (hm) e outra heterogênea (ht). Pelo critério de informação da deviance e fator de Bayes, o MHRN Shm apresentou melhor ajuste aos dados e, pela deviance baseada na ordenada preditiva condicional, o melhor ajuste foi do MHNR Kht, enquanto, pelos três critérios, o pior ajuste foi obtido pelo modelo animal padrão. As herdabilidades estimadas nos MHNR foram crescentes nos gradientes ambientais em GPD345 de -60; 0 e +60 kg. As correlações genéticas estimadas entre o nível e inclinação das normas de reação foram de alta magnitude, entre 0,97 e 0,99, caracterizando efeito de escala em interação genótipo × ambiente. Os modelos hierárquicos de normas de reação são eficientes para descrever as alterações nos componentes de variância decorrentes do ambiente e para descrever a presença de interação genótipo × ambiente na característica GPD345 em bovinos Hereford

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