New insights on genotypes by environments interaction using geographical coordinates

Abstract

Multi-environmental trials are among the most commonly conducted experiments in the field of agricultural science. Due to the applicability of the AMMI method (Additive Main Effects and Multiplicative Interaction) and the way it has been studied and applied, this work explored new alternatives for the study of genotype x environment interaction (GEI) through this model. The first work was conducted with the objective of proposing a model of prediction of general and specific combining abilities, and their interactions with environments, associated with the use of credible regions in biplots obtained by the AMMI-Bayesian model. In general, for the analysis of simulated data, the predictions obtained had a high correlation with the real values. For the general and specific combining capabilities effects (GCA and SCA, respectively), the predictions maintained the signal pattern and ranking. In addition, the model was efficient in providing credible intervals that covered the simulated values. For real data analysis, GCA and SCA estimates for all evaluated genotypes did not differ from zero. The biplots for the GCA x Environments and SCA x Environments interactions allowed us to determine which genotypes have stable GCA and SCA effects in a more accurate way. Ellipses in the biplots demonstrated the uncertainty around the interaction estimates. The model is a promising tool to help the breeder's decision making in selecting and recommending genotypes. The second work was conducted with the objective of studying GEI through the use of environmental variables in the AMMI model under functional approach with different data volumes and unbalance levels. To this end, it was aimed to evaluate the behavior of the principal component analysis of functional

data (FPCA) in data imbalance scenarios and integrate it with the EM-AMMI (Expectation- Maximization Additive Main Effects and Multiplicative Interaction) method to perform the

genotypic prediction from a functional perspective. Through functional data analysis, it is possible to capture information that goes beyond discrete data representing genotypes and environments, which allows to capture the pattern of interaction and behavior of genotypes across environments. Integrating the smooth SVD (Singular Value Decomposition) or SSVD method with the EM-AMMI method to perform data imputation and deal with imbalance can change the perspective of GEI study. The identification of interaction effect patterns through the EM-AMMI Functional method represents a new way of understanding interaction, and opens up several possibilities for application in plant breeding.