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The Races of Maize: II. Use of Multivariate Analysis of Variance to Measure Morphological Similarity¹

The racial means and the residual covariance matrix from the multivariate analysis of variance of an experiment based on a randomized block design involving 15 races of maize (Zea mays L.) from southeastern South America were used to calculate generalized distances between the races. Sixteen characters commonly used in taxonomic studies of the races of maize were employed. The effects of transformations designed to eliminate some of the heterogeneity among the withinrace, within-row covariance matrices were studied, and the effects of within-plot sampling were investigated. It was shown that the use of transformations had very little effect on the relative distances (and hence that highly significant heterogeneity — as measured by the multivariate extension of Bartlett's test — had little effect on the analysis of the non-transformed data). Similarly, essentially the same relative distances were obtained when only a single plant from each race was used per block (eight blocks were used). In all cases the distances obtained were relatively very similar (i.e., Spearman rank correlation coefficient between 0.91 and 0.99) to the distances obtained from the commonly employed Mahalanobis’ generalized distance technique.

Key Words: Zea mays • generalized distance • mahalanobis • taxometrics • classification • numerical taxonomy

² Assistant Professor of Experimental Statistics, North Carolina State University at Raleigh (Formerly NSF Postdoctoral Fellow, Instituto de Genetica, E.S.A.L.Q., Piracicaba, S. P., Brazil). A part of the computations were carried out at the Centro de Computacao Electronica, Escola Politecnica, Universidade de Sao Paulo, Sao Paulo, Brazil. This investigation was supported in part by Public Health Service Grant GM 11546.The cooperation of A. Blumenschein, E. Paterniani, M. R.Alleoni, and the Cadeira de Matematica e Estatistica, E.S.A.L.Q.,and the assistance of H. Kuniyuki are gratefully acknowledged.

Received for publication January 24, 1968.