Alternative partitioning of the genotype-by-environment interaction.

Alternative methods for partitioning the genotype-by-environment interaction, for an arbitrary number of genotypes or environments, were examined. Partitioning of the interaction is important in order to determine the nature of the interaction. Two methods of partitioning were examined; both separated the interaction into two types: (1) due to heterogeneous variances or (2) due to imperfect correlations. Method 1 was based on heterogeneity among environments in the scaling of differences among genotypes. Method 2 was based on heterogeneity among genotypes in the scaling of differences among environments. Any remaining interaction arises from deviations from the perfect positive correlation of genotypic rankings among environments (Method 1) or of environmental rankings among genotypes (Method 2). Method 1 is more appropriate for random genotypes that are to be tested in either fixed or random environments. With Method 1, the interactions that arise mainly from heterogeneity of genotypic scaling among environments are generally unimportant. However, if environments are fixed and interactions are mainly due to imperfect correlations of rankings, specialized lines may be indicated for each environment. Method 2 is more useful in evaluating fixed genotypes for sensitivity to random environments. A partitioning of the interaction into that due to the type of interaction within each genotype was shown to be useful in that situation.