Regiões de credibilidade para escores genotípicos e ambientais em modelo AMMI com efeitos aleatórios para genótipos

Abstract

The additive main effects and multiplicative interaction (AMMI) model has often been applied in plant breeding to study the interaction between genotypes and environments (G E). One of the main problems related to this method of analysis is that conventional biplot representation do not support any uncertainty measurements concerning to the plotted bilinear terms. Thus, we conducted this study with the aim to incorporate the biplot inference by building credibility regions for both the genotypic and environmental scores from the AMMI model using prior informative for the genotype effect. This approach differs from Bayesian methods presented so far that assume the same restrictions present in the model for fixed effects (identifiability restrictions). As example of this method we used a set of data relating to the essay of 55 hybrids maize in 9 different environments, which the study variable is the productivity of husked maize, in tha􀀀1. The samples for the inference process were obtained using the Gibbs sampler. The analysis results showed a great flexibility of the Bayesian inference method to incorporating the parameters of model. The biplot graphical representations associated to the credibility regions built allowed the identification of genotypes and environments that do not have significant contributions to the (G E) interaction, the homogeneous genotypes and environments subgroups related to the interaction effect, and also adaptability of genotypes to specific environments, which are of great interest to agriculture reseachers. The ranking of BLUPs for the effect genotype, using the regions of highest posterior density (HPD), combined with information obtained through the regions of credibility for the genotypic and environmental scores allowed the identification of the best genotypes in relation to the characteristic analyzed.