What should students in plant breeding know about the statistical aspects of genotype × Environment interactions?

A good statistical analysis of genotype × environment interactions (G × E) is a key requirement for progress in any breeding program. Data for G × E analyses traditionally come from multi-environment trials. In recent years, increasingly data are generated from managed stress trials, phenotyping platforms, and high throughput phenotyping techniques in the field. Simultaneously, and complementary to the phenotyping, more elaborate genotyping and envirotyping occur. All of these developments further increase the importance of a sound statistical framework for analyzing G × E. This paper presents considerations on such a framework from the point of view of the choices that need to be made with respect to the content of short academic courses on statistical methods for G × E. Based on our experiences in teaching statistical methods to plant breeders, for specialized G × E courses between three and 5 d are reserved. The audience in such courses includes MSc students, PhD students, postdocs, and researchers at breeding companies. For such specialized courses, we propose a collection of topics to be covered. Our outlook on G × E analyses is two-fold. On the one hand, we see the G × E problem as the building of predictive models for genotype-specific reaction norms. On the other hand, the G × E problem consists in the identification of suitable variance-covariance models to describe heterogeneity of genetic variance and correlations across environments. Our preferred class of statistical models is the class of mixed linear-bilinear models. These statistical models allow us to answer breeding questions on adaptation, adaptability, stability, and the identification and subdivision of the target population of environments. By a citation analysis of the literature on G × E, we show that our preference for mixed linear-bilinear models for analyzing G × E is supported by recent trends in the types of methods for G × E analysis that are most frequently cited.