Genotype-by-environment interaction of wheat using Bayesian factor analytic models and environmental covariates

Wheat ( Triticum aestivum L . ) plays a significant role in the global agricultural economy. Breeding programs need to identify environments where genotype discrimination allows effective selection, as this is crucial for developing more productive wheat genotypes through genetic breeding. Factor analytic models can be applied to the analysis of the multi-environment trial. This approach is based on multivariate models that utilize factor analysis (FA) structures and consider environments (E), genotypes (G), and G × E effects. This study evaluated eight wheat genotypes in fifteen environments in southern Brazil to understand the G × E interactions of wheat genotypes. The primary objectives were identifying stable and responsive genotypes across a set of environments (mega-environments) and determining the main environmental covariates, such as temperature, solar radiation, precipitation, relative humidity, wind speed, and altitude, that can explain G × E interactions. The Bayesian factor analytic model was applied to the grain yield as the response variable. The model with four factors, FA(4), provided the best fit, allowing the creation of four mega-environments. Using latent regressions, we identified genotypes that are suitable for each mega-environment, as they demonstrate responsiveness and wide adaptability to those specific groups of environments. The correlations between the environmental loadings and the environmental covariates revealed that precipitation, maximum temperature, and wind speed negatively affected yield in these environments. On the other hand, the altitude covariate positively affected the grain yield in these environments. The occurrence of four mega-environments in this study suggests that the same information about genotypes can be obtained from fewer environments, indicating the possibility of reducing costs in breeding programs.