A model for planktic foraminiferal shell growth

In this paper we analyze the laws of growth that control planktic foraminiferal shell morphology. We assume that isometry is the key toward the understanding of their ontogeny. Hence, our null hypothesis is that these organisms construct isometric shells. To test this hypothesis, geometric models of their shells have been generated with a personal computer. It is demonstrated that early chambers in log-spirally coiled structures cannot follow a strict isometric arrangement. In the real world, the centers of juvenile chambers deviate from the logarithmic growth curve. Juvenile stages are generally more planispiral and contain more chambers per whorl than adult stages. These traits are shown to be essential in order to keep volumes of consecutive chambers in geometric progression. We are convinced that the neanic stage marks the constructional bridge from a juvenile set of growth parameters to an adult one. The adult stage can be strictly isometric, that is, the effective shape is constant and the increase in volume after a chamber addition is proportional to the preexisting volume of the shell. The shell volume is related to the biomass, the ratio of outer shell surface area to shell volume is related to the respiration rate and the ratio of the total shell surface area to shell volume is related to the total calcification effort. The influence of the parameters of the model on these relationships is investigated. Only the initial radius and the rate of radius increase affect the relationships between shell volume and surface area. The other shape parameters merely provide a fine tune-up of these relationships. Size itself plays a major role during foraminiferal development.