The Mathematics of Size and Shape

Abstract

SUMMARY Allometry is the study of differences in shape associated with size. The bivariate case has been studied intensively for nearly fifty years, with attention devoted almost exclusively to the so-called simple allometry equation which implies a linear relationship between logarithms of the two size measurements. Multivariate generalizations of the bivariate concepts present difficulties that have not been fully resolved. These concern questions about appropriate generalizations from 2 to p dimensions. This paper reviews some of the more important work on allometry and related problems. Comments on the various approaches are made and some suggestions are given for future research. Alternative approaches to studies of size and shape are briefly mentioned, and it is suggested that at least one of these is likely to be more useful biologically in a certain type of study than the conventional approach through allometry.