Análise bayesiana das interações genótipo×ambiente e marcador×ambiente utilizando o modelo AMMI-GBLUP-D em ensaios multiamientais

Abstract

The study of genotype-by-environment (G×E) interaction is fundamental to the advancement of genetic-breeding programs, enabling the recommendation of superior genotypes that are either stable or specifically adapted to particular environments. The additive main-effects and multiplicative interaction (AMMI) model has become a benchmark for analyzing this interaction and, in its Bayesian formulation, has enhanced inferential rigor by treating genotypic effects as random variables and displaying bivariate credibility regions through biplots. Nevertheless, even in its Bayesian versions, AMMI accounts only for additive genotypic effects, ignoring variability arising from dominance effects and marker-by-environment interactions (M×E). To fill these gaps, this thesis proposes two methodological innovations. First, it formally introduces the new AMMI-GBLUP-D model, which combines the bilinear decomposition of AMMI with genomic relationship matrices that capture both additive and dominance effects, thereby explaining a larger proportion of genetic variability. Second, it develops an original procedure that uses Markov chains generated by AMMI- GBLUP-D to obtain chains for the parameters associated with the M×E interaction, assigning bivariate credibility regions analogous to those for G×E. The methodology was evaluated through simulation studies and by analyzing a real data set from multi-environment trials comprising 200 maize hybrids tested in 14 environments under an incomplete-block design. All analyses were performed in R, and the corresponding AMMI-GBLUP-D code was integrated into the ammiBayes package. The results indicate that including dominance effects in the AMMI-GBLUP-D model increased predictive accuracy relative to the AMMI-GBLUP model, that consider only aditive effect, thereby enabling more efficient identification and selection of superior genotypes in multi- environment trials. Moreover, the new procedure for predicting M×E interactions allowed graphical representation of this interaction in biplots with bivariate credibility regions and facilitated the identification of markers directly or indirectly associated with M×E interaction. This approach enhances the extrapolation of genetic values to genotypes not yet phenotyped and informs marker-assisted selection strategies. Consequently, the innovations presented herein broaden the statistical toolkit available for genetic breeding by providing a robust framework to jointly model additive effects, dominance effects, and genomic interactions in multi-environment analyses.