Analyzing the genotype-by-environment interactions under a randomization-derived mixed model

This article describes procedures for studying parameters connected with the genotype-by-environment interactions appearing in a mixed model derived from the randomization principle. It considers estimation of these parameters and of their meaningful functions. A test for the overall no-interaction hypothesis is described, and relevant tests for some implied hypotheses concerning individual parametric functions are considered. Useful data transformations are proposed that allow the graphic presentation of interesting features of the genotype-by-environment interactions. The theoretical considerations are illustrated by an analysis of the results of a series of trials with pea varieties.