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CROP BREEDING, GENETICS & CYTOLOGY

A Multivariate Method for Classifying Cultivars and Studying Group x Environment x Trait Interaction

^a Facultad de Agronomia, Universidad de la República Oriental del Uruguay, Avd. Garzon 780 CP 12900. Montevideo, Uruguay
^b Biometrics and Statistics Unit, CIMMYT, Apdo. Postal 6-641, 06600, México DF, México
^c Maize Genetic Resources Unit, CIMMYT, México
^d National Seed Storage Laboratory, USDA, ARS, Fort Collins, CO 80523

^* Corresponding author (j.crossa{at}cgiar.org)

Classification methods are used in genetic resource conservation and plant breeding. The two-stage Ward-Modified Location Model (Ward-MLM) clustering strategy defines initial groups by the Ward method and the MLM is then used to improve those groups. The three-way clustering strategy considers the same trait measured in different environments as different variables (environment–trait combination), so that the resulting clusters of cultivars have a small group x environment interaction (GEI) for all the traits included in the study. An important component of the GEI is the imperfect genotypic correlation or crossover interaction (COI). This study used the three-way Ward-MLM clustering strategy in three different data sets with the objectives of (i) evaluating the ability of the Ward-MLM methodology for clustering cultivars into groups with low COI, (ii) obtaining a graphical representation of the variables in a low dimensional scatter plot produced by the multidimensional scaling method (MDS) in which the GEI of continuous and categorical traits and environments can be visualized, and (iii) studying how the relationship between a pair of traits changes across environments. The three-way Ward-MLM strategy produced groups of cultivars with low levels of COI. The increment of the correlation coefficient values between groups with respect to the total correlation coefficients indicated that the groups formed by the three-way Ward-MLM strategy comprised subsets of individuals that had similar trait responses across environments.

Abbreviations: GM, Gaussian Mixture • LM, Location model • MLM, Modified location model • EM, Expectation maximization • p.d.f., probability density function • UPGMA, unweighted pair grouping with the arithmetic means • COI, crossover interaction • GEI, group x environment interaction. V_T, total variance-covariance matrix • V_B, between-groups variance-covariance matrix • V_W, pooled within-group variance-covariance matrix • R_T, total correlation matrix • R_B, between-groups correlation matrix • R_W, pooled within-group correlation matrix • DA, days to anthesis • P, plant height • DS, days to senescence • EL, ear length • A, anthesis-silking interval • E, number of rows per ear • F, days to silking • DM, days to maturity • AS, agronomic scale • Y, grain yield • SP, Septoria leaf blotch • LR, leaf rust • PM, powdery mildew • SE, proportion of selected plants • MDS, multidimensional scaling

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