Clustering Cultivars into Groups without Rank‐Change Interactions

Crossover (i.e., rank‐change) interactions (COIs) are of particular interest in the interpretation of cultivar yield trial data. The shifted multiplicative model (SHMM) was used to search for subsets of cultivars in which cultivar COIs could be regarded as insignificant or small in a 1985 Kentucky wheat ( Triticum aestivum L.) trial with 41 cultivars and seven locations. The first step was to obtain a dendrogram by complete linkage (farthest neighbor) cluster analysis with the “distance” between a pair of cultivars defined as the residual sum of squares when SHMM with one multiplicative term (SHMM 1 ) is fitted subject to a constraint that the fitted model be free of COIs. Statistical tests were computed on subsets of cultivars suggested by branching of the dendrogram to identify subsets in which a constrained SHMM, would account for the variation. Five clusters of five cultivars each and four smaller clusters were found satisfactory. Six cultivars did not cluster with any other cultivar. Analysis of all 2 × 2 interactions indicated that the method effectively assigned cultivars involved in large COIs to different clusters. Only 6% of COIs within clusters were significant as compared to 29% among clusters. Clustering would allow breeders and growers to restrict selection of cultivars to the better ones in each cluster.