A geometric model for the evolution of development

The idea that early developmental characters are more constrained in their evolution than late developmental characters is one of the most widely accepted generalizations about the relationship between development and evolution. It is apparent, however, that evolutionary changes do occur in early ontogeny and that understanding the nature of these changes is essential if we are to understand a variety of evolutionary phenomena, such as the origin of higher taxa. In particular, we would like to know if certain ecological conditions are more likely than others to produce changes in early development. In this paper, I present a geometric model which predicts that changes in early ontogeny should most often be fixed in environments in which the adaptive landscape is changing drastically over time. In the model, a developmental program defines a set of subsets in a space of possible mutant phenotypes, a fitness function is then imposed on this space. It is demonstrated that early developmental characters, which correspond to high dimensional subsets, are only able to evolve when the fitness function is of low curvature. If the fitness function is thought of as an adaptive landscape, low curvature corresponds to great distance from any adaptive peak. The model is then used to investigate which ecological circumstances are most conducive to evolution of the basic ways in which organisms are put together. It is shown that this model predicts the pattern of nearshore innovation which has been observed in marine paleocommunities. The results are also used to discuss the concept of "developmental constraint". In particular, it is shown that mechanistic interactions in development can constrain the rate of evolution independently of its direction and that, in fact, this constraint on the rate of evolution may be greatest when constraints on direction are least.