Multivariate Allometry

The subject of allometry is variation in morphometric variables or other features of organisms associated with variation in size. Such variation can be produced by several biological phenomena, and three different levels of allometry are therefore distinguished: static allometry reflects individual variation within a population and age class, ontogenetic allometry is due to growth processes, and evolutionary allomctry is thc rcsult of phylogcnctic variation among taxa. Most multivariate studies of allometry have used principal component analysis. I review the traditional technique, which can be interpreted as a least-squares fi t of a straight line to the scatter of data points in a multidimensional space spanned by the morphometric variables. I also summarize some recent developments extending principal component analysis to multiple groups. "Size correction" for comparisons between groups of organisms is an important application of allometry in morphometrics. I recommend use of Bumaby's technique for "size correction" and compare it with some similar approaches. The procedures described herein are applied to a data set on geographic variation in the waterstrider Gerris costae (Insecta: Heteroptera: Gcrridac). In this cxamplc, I use the bootstrap technique to compute standard errors and perform statistical tcsts. Finally, I contrast this approach to the study ofallometry with some alternatives, such as factor analytic and geometric approaches, and briefly analyze the different notions of allometry upon which these approaches are based.