Comparing ontogenetic trajectories using growth process data

Ontogenetic trajectories are commonly quantified by characterizing changes in the sizes and shapes of organisms over the course of development. This formulation of ontogenetic transformations can be misleading in that it ignores critical aspects of the biological processes responsible for constructing morphology. Hypothetical examples are used to illustrate some of the shortcomings of methods that rely exclusively on size and shape data for ontogenetic analyses. By characterizing growth as a vector field, and representing growth vectors as complex numbers, one can simultaneously analyze size, shape, and growth processes. The utility of such an approach is demonstrated in a study of shape and growth process variation in turtle shells.