On the Use of Discriminant Functions in Taxonomy

The most effective use of discrimninant functions presumes an expedient selection of character for measurement. Such characters should possess (a) individually, a high coefficient of discrimination, K, relating interspecific and intraspecific variability, and (b) taken in pairs, a high intraspecific correlation, with the interspecific correlation of opposite sign. A considerable increase of discrimination can be attained graphically following V. I. Romanovsky. The consideration of scatter-diagrams and correlation-ellipses suggests a new criterion, the rank of discrimination, R, whose relation to K is R = VK/2. For any two out of three species of Chaetocnema, a pair of discriminant functions, each based on three characters, provides excellent discrimination: discrimination between the species used to construct the functions and the third species is less satisfactory. Corresponding coefficients in the three pairs of functions differ appreciably, but when correlation ellipses for the three pairs are plotted, the relative positions of the ellipses for the three species are the same. New pairs of functions, whose coefficients are arithmetic or (Figure 9) geometric means of the coefficients in the separate pairs permit a clean separation of all three species in one figure. The results obtained indicate the possibility of measuring taxonomic likeness, and of developing objective criteria for the construction of a natural system of