Stability is a central keyword for plant breeders analysing genotype by environment data, a simple corresponding statistical term is "dispersion around a central value". So a natural way to approach genotype environment interactions is to model variances as well as expectations in relation to genotypes and/or environments. After reviewing classical models, we try to present a general scheme for describing heteroscedasticity with a reduced number of parameters using the framework of mixed models. This allows us to propose new parsimonious models. Two genuine data sets exemplify the concepts: the first concerns the virus-resistance of ten sugar beet cultivars to a virus grown at six different locations; the second involves three factors: variety, soil and year in a potato experiment.