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A Sequential Clustering Strategy for Classifying Gene Bank Accessions

Programa de Estadística, ISEI, Colegio de Postgraduados, Montecillo, Méxicoand Biometrics and Statistics Unit, CIMMYT, Lisboa 27, Apdo Postal 6-641, 06600 México D.F., México
Biometrics and Statistics Unit, CIMMYT, México

Jaime Díaz and Suketoshi Taba

Maize Genetic Resources Unit, CIMMYT, México

José Villaseñor and Steve A. Eberhart

Programa de Estadística, ISEI, Colegio de Postgraduados
National Seed Storage Lab., USDA-ARS, Fort Collins, CO 80523

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

Statistical classification methods such as Normix, applied to groups previously formed (a priori groups) using hierarchical methods, can improve the a priori groups and give estimation of probabilities for membership. In this study, we used data from the evaluation of 29 maize (Zea mays L.) races to (i) apply Normix to the a priori groups formed by the Ward method (Normix after Ward), (ii) use the upper tail approach and a likelihood ratio test to estimate the optimal number of groups, and (iii) use three geometrical and statistical criteri (Mahalanobis distances, multivariate statistics, and trace and determinant of the within- and among-group variability matrices) to compare the groups obtained from Ward per se and the Normix after Ward method. Results indicated that the reclassification of accessions by Normix substantially improved the a priori groups obtained by Ward in four ways: (i) the average Mahalanobis distance between groups was larger among Normix than among Ward groups; (ii) the ratio variability between groups to variability within groups is increased after Normix compared with that obtained after Ward; (iii) the generalized variance within groups is decreased in Normix compared with Ward; and (iv) the correlation coefficients between variables are increased after Normix compared with those correlation values obtained by Ward. Results suggested that the groups formed by the Normix after Ward procedure allows (i) good estimation of the optimal group number, (ii) formation of more compact and separated groups than the a priori groups formed by Ward per se, and (iii) estimation of the probability of accession membership to the groups.

Received for publication September 30, 1996.

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