Allometry Correction in Taximetrics

Abstract

Corruccini, R. S. (Dept. of Anthropology, Univ. of California, Berkeley, Calif. 94720) 1972. Allometry Correction in Taximetrics. Syst. Zool. 21:375-383.-The process of allometry often distorts numerical results, causing size-related effects in coefficients. The study of allometry has traditionally emphasized only aspects of detection and description, rather than correction, of allometric trends. A method of allometry correction is offered for the specific purpose of adjusting metrical data prior to quantitative taxonomic analysis. [Allometry; taximetrics; hominoids.] Systematists in increasing numbers are uncritically accepting the mathematical models underlying the various methods of numerical taxonomy (Johnson, 1970). In so doing, they overlook the fact that most statistical procedures were developed for certain purposes or types of data. When obviously inaccurate classifications result, or when different techniques produce seriously divergent results using the same data, it is often claimed that this constitutes a practical detraction from the value of numerical taxonomy. However, if the assumptions underlying the techniques (e.g., linear relationship of variables, homogeneity of covariance matrices, normality of distribution, large sample size) are not satisfied, reasonable results cannot be expected. The present paper discusses the analysis of metric characters by Q-mode correlation coefficients. Shortcomings of the technique will be shown to result from failure of the data to meet the conditions necessary to the method's definition, and successful determination, of similarity. In particular. allometric distortion in the data, and the need and practicality of correcting for it, will be discussed. THE EFFECT OF ALLOMETRY ON Q-MODE CORRELATION COEFFICIENTS The debate over selection of similarity coefficients and clustering methods in numerical taxonomy is a long and continuing one. However, when dimensions (measurements) alone are used as descriptive data for organisms, there is general concurrence that shape coefficients of affinity are superior to size (distance) coefficients: (Huxley, 1932; Rohlf and Sokal, 1965; Boyce, 1964, 1965, 1969; Penrose, 1947, 1954; Burnaby, 1966; Giles, 1956; Sokal and Sneath, 1963; Gould, 1967; Stahl, 1962; Oxnard, 1968, 1969a, 1969b; White and Gould, 1965; Minkoff, 1965; Kowalski, 1972; Blackith, 1965; Mosimann, 1970; Jolicoeur and Mosimann, 1960; Blackith and Reyment, 1971). Rohlf and Sokal (1965) and Boyce (1964, 1969) specifically recommend Q-mode correlation as the best co-