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A Shifted Multiplicative Model Fusion Method for Grouping Environments without Cultivar Rank Change

International Maize and Wheat Improvement Center (CIMMYT), Lisboa 27 Apdo. Postal 6-641, México D. F., México
Dep. of Agronomy and Dep. of Statistics, Univ. of Kentucky, Lexington, KY 40546-0091
International Maize and Wheat Improvement Center (CIMMYT), Lisboa 27 Apdo. Postal 6-641, México D. F., México

^* Corresponding author (jcrossa{at}alphac. cimmyt.mx).

Genotype x environment interactions of most concern to plant breeders involve cultivar rank change across environments, i.e., crossover interaction (COl). When COls are present, cluster strategies can be used to group environments without significant changes in cultivar ranks. Several methods for classifying environments without COI have recently been proposed. In this study, the shifted multiplicative model (SHMM) fusion method based on a building block principle is used for grouping environments which rank cultivars similarly. The SHMM fusion selects the best action by computing for each new cluster formed, a new set of distance measures with the other clusters and with the unclustered individuals. Experimental data were collected on 55 cultivars evaluated under five irrigation levels in each of two trials (I0 environments). Groups of environments obtained with SHMM fusion were compared with those obtained using cluster analysis based on Euclidean distances computed from unstandardized and standardized data. The SHMM fusion formed four final clusters of environments. The final clusters grouped environments with similar irrigation levels. Conventional cluster analysis based on Euclidean distances produced final clusters with much larger percentage of COls than SHMM fusion. Results show that SHMM fusion is a useful strategy for classifying environments without cultivar rank change.

Received for publication June 15, 1993.

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