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

Abstract

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 a variable, such as size or latitude, which is thought to have some biological relevance to the problem at hand, and 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. [Animal species are used to illustrate the discussion.].