A DYNAMICAL THEORY OF HETEROCHRONY: TIME-SEQUENCING CHANGES IN ECOLOGY, DEVELOPMENT AND EVOLUTION

Abstract

This work provides a foundation for a quantitative dynamical theory of heterochronic processes in the evolution of colonial invertebrate animals including Bryozoans, Siphonophores and Ants. These processes are environmentally induced changes in the time-sequencing of growth and development which can produce alterations in the morphotypes or castes within an individual colony. Motivation comes from Křivan’s theory of environmentally induced constraints on population densities for ecological interactions, but the present theory is second order with allometric production variables xi and population densities for morphotypes, Ni. We are able to unite ecological theory and the allometric form of the Wilson Ergonomic Theory via projective differential geometry and Wagner spaces which provide a natural description of environmentally induced time-sequencing changes altering the allometric curve of a species. Such changes define a model of heterochronic processes important in paleontology.