Characteristics of ultrastructural morphology and chemical composition of epicuticular waxes on glumes of Triticeae were combined for two series of numerical taxonomic analyses. The first, incorporating within-genus variability, utilized frequencies and information radius. The information radius matrix was subjected to Jardine–Sibson Bk clustering, then transformed to Euclidean distances for distance Wagner and principal-coordinate analyses. The second series employed a table of average character values for each genus which was subjected to four ordinations: (i) principal-component analysis of the correlation matrix, (ii) principal-component analysis of the variance-covariance matrix, (iii) principal-coordinate analysis, and (iv) nonmetric multidimensional scaling. The results are compared and general inferences are drawn. Occurrence of wax filaments on the glumes was highly correlated with presence of appreciable amounts of β-diketones in wax from the whole plant. While some genera, such as Triticum and Aegilops, appeared less closely related than expected from classification based on morphology, this procedure has suggested relationships between other genera, such as Roegneria and Hordeum and Secale and Elymus. The genera Leymus, Elymus, and Aneurolepidium were also closely related to each other and more distantly to Elytrigia, Triticum, and Agropyron. A relatively close relationship was also shown between the seven genera, Crithopsis, Eremopyron, Heteranthelium, Hordelymus, Psathyrostachys, Sitanion, and Taeniatherum, which have waxes which do not contain any β-diketones.
Asymptotic expansions for the distributions of statistics based on the sample correlation matrix in principal component analysis
