The analysis of ontogenetic trajectories: when a change in size or shape is not heterochrony

Heterochrony has become a central organizing concept relating development and evolution. Unfortunately, the standard definition of heterochrony--evolutionary change in the rate or timing of developmental processes--is so broad as to apply to any case of phenotypic evolution. Conversely, the standard classes of heterochrony only accurately describe a small subset of the possible ways that ontogeny can change. I demonstrate here that the nomenclature of heterochrony is meaningful only when there is a uniform change in the rate or timing of some ontogenetic process, with no change in the internal structure of that process. Given two ontogenetic trajectories, we can test for this restricted definition of heterochrony by asking if a uniform stretching or translation of one trajectory along the time axis superimposes it on the other trajectory. If so, then the trajectories are related by a uniform change in the rate or timing of development. If not, then there has been change within the ontogenetic process under study. I apply this technique to published data on fossil Echinoids and to the comparison of human and chimpanzee growth curves. For the Echinoids, some characters do show heterochrony (hypermorphosis), while others, which had previously been seen as examples of heterochrony, fail the test--implying that their evolution involved changes in the process of development, not just the rate at which it proceeded. Analysis of human and chimpanzee growth curves indicates a combination of neoteny and sequential hypermorphosis, two processes previously seen as alternate explanations for the differences between these species.