The Study of Biological Versus Statistical Variation in Multivariate Morphometrics: The Descriptive Use of Multiple Regression Analysis

Abstract

Albrecht, G. H. (Department of Anatomy, School of Medicine, University of Southern California, Los Angeles, California 90033) 1979. The study of biological versus statistical variation in multivariate morphometrics: The descriptive use of multiple regression analysis. Syst. Zool. 28:338-344.-Multivariate statistical techniques (such as canonical variate and principal component analyses) are often used to ordinate or summarize morphometric data to facilitate biological interpretation of the morphological relationships under study. While the major axes of statistical variation which are derived in such analyses may have direct biological significance, there is no a priori reason that the biological and statistical determinants of morphological variation necessarily be concordant. Multiple regression provides a simple means of identifying and describing the maximum degree of relationship between (1) a variable, such as size or latitude, which is thought to have some biological relevance to the problem at hand, and (2) the set of uncorrelated variables, such as canonical or principal component variates, which represent the major axes of statistical variation and which may be thought of as a convenient, analytically efficient system of reference axes describing the multivariate data space. Of particular significance is the ability to examine the full multidimensional space and detect biological information having an angular relationship to the major axes of statistical variation. [Multiple regression analysis; multivariate analysis; morphometrics; statistical and biological variation.] Multivariate statistical techniques are often used to ordinate morphometric data so that biological parameters underlying morphological relationships among individuals or groups may be more readily discovered. Commonly used techniques include canonical variate, discriminant function, principal component, and principal coordinate analyses (see Blackith and Reyment, 1971, for definitions and examples). All have in common a primary purpose of summarizing multivariate data in a relatively few dimensions that retain the majority of information formerly dispersed among the larger array of original variables. An additional advantage shared by all is the lack of statistical correlation among the transformed variates as compared to the complex of statistical dependencies usually found among the original variables. Such a reduction in both dimensionality and correlation results in a greater probability that the investigator will be able to make biologicallv relevant statements about the morphometric relationships under study. Populations (or individuals) are often found to be ordered on the first few transformed variates of a multivariate analysis according to morphological gradients suggestive of differences in size, shape, time, function, behavior, or ecology. For example, Oxnard (1967; nine measurements of the scapula of 27 genera of primates) interpreted the first canonical variate as reflecting the extent to which the shoulder is subjected to compressive or tensile forces, the second canonical variate as reflecting relative degrees of arboreality or terrestriality, and the third canonical variate as reflecting the uniqueness of the human condition. Johnston and Selander (1971; 16 measurements of the skeleton of 33 populations of North American house sparrows) interpreted the first and second principal component variates, after regressiot analyses involving 15 environmental variables, as reflecting classic examples