Multiplicative Mixed Model Approach to Analyze Genotype by Environment Interactions in Multi-Environment Trials.

The genotype by environment interaction (GxE) is an important component when analyzing multi-environment trials (MET) in plant breeding. Many methodologies were proposed in order to better understand this component. The Multiplicative Mixed Model (MMM) approach models the GxE component as a random effect and its main advantages are the ability to handle unbalance data and within trial correction (it can easily incorporate spatial analysis). In this work, we used the MMM to investigate the GxE in a Brazilian maize MET dataset. The MMM assuming a one-factor diagonal (co)variance structure had the best fit for this dataset. Some environments (Indianopolis and Rio Verde) had a high genetic correlation (0.99) which means they have similar effect over the genotypes in the dataset and, therefore, having both environments in a trial does not add addition information. The MMM also allows the comparison among genotypes in each environment and across environments that can be used to identify, respectively, the most adapted genotypes in each location and the most stable genotypes across locations. Despite the MMM great flexibility and ability to leverage in all data available, GxE is a very complex issue and it is paramount to have a good data structure to obtain meaningful results.