Contributions to the Analysis of Genotype × Environment Interactions: Experimental Results of the Application and Comparison of Clustering Techniques for the Stratification of Field Test Sites

The results from multienvironment field performance trials of cultivars are usually analysed as two‐way classification data with rows=genotypes/cultivars and columns=environments (locations and/or years). To reduce the impact of genotype × environment interaction effects, one commonly stratifies genotypes/cultivars or environments by cluster analysis techniques into homogeneous groups so that interactions within groups are minimized. By such a stratification, for example of test sites, with regard to similarity of genotype × environment interactions and the selection of only one representative test site from each group, the overall number of necessary test sites for yield trials can be reduced. In the literature, many clustering techniques have been proposed. Systematic comparisons between different cluster methods, however, are rather rare. A single cluster method is characterized by `measure of distance', `stopping criterion', `algorithm' and `level of significance'. In this paper, 11 clustering techniques were applied to extensive yield data sets of several agricultural crops (faba bean, fodder beet, oat, winter oilseed rape and sugar beet) from the official registration trials of the German `Bundessortenamt'. The results were compared with each other using two proposed parameters: measure of resemblance (for two classifications) and cluster size (for one classification). Neither the level of significance nor the algorithm has a substantial impact on the resulting clusters. The final results of clustering are therefore mainly determined by the stopping criterion with its associated measure of distance. If one uses tests for crossover interactions as stopping criteria, the resulting clusters are larger than the resulting clusters for the F‐test of conventional interactions in an analysis of variance. The cluster size decreases with increasing sensitivity of the tests that are used as stopping criteria. Finally, recommendations for the choice and handling of clustering techniques for practical applications are given.