Modelling Interactions in on-Farm Trials of Bread and Durum Wheats in the Yaqui Valley of Sonora Mexico.

On farm trials of bread and durum wheat in the Yaqui Valley region of southern Sonora, Mexico have been implemented for three years (2012, 2013, and 2015). Farmers established the trails comprising two sets of wheat, Bread and Durum wheats that were sown together under two water regimes, full irrigation and reduced irrigation; with experiments being replicated in incomplete block designs and imbalance as several bread wheat and durum wheat lines were not repeated during the three years. Several traits, including diseases, and grain yield were measured. It was of interest to assess the interaction between Bread and Durum wheats with environments comprising the combination of framer-irrigation-year. For modelling the interaction between the wheat lines and the environments, we used a linear mixed model with a parsimonious model, the Factor Analytic (FA) model that is similar to the multiple regression of lines in environments based on latent variables. In this case, we model the combined effects of the wheat lines and their interaction with the combination of farmer-irrigation-year. Results show the separation of the dynamic (unpredictable) component of the interaction (year) from the more static component due to farmer and irrigation levels. We show how to use the linear mixed model to incorporate relationship information between the wheat lines included in the multi-environment trials The FA offers a useful alternative to model interactions in agronomy-breeding experiments in order to dissect and account for complex interactions commonly existing in agriculture experiments.