ABSTRACT
The entire shape of most camarodont sea urchins, during any post-larval stage in ontogeny, is correctly predicted using only a measurement of height and diameter. The prediction of shape is based on the engineering theory of thin-shells. This theory is normally used to predict the shape of a water-droplet sitting on a table or to specify the shape of an optimally-designed storage dome. That it successfully predicts the shape of these sea urchins suggests that the assumptions behind the theory can be interpreted to correspond to forces exerted on an urchin’s skeleton during growth. The theory specifies two underlying developmental parameters that determine an urchin’s shape : (1) the apical curvature, and (2) the ratio of the vertical gradient of tube-foot forces to the internal coelomic pressure. The model predicts the magnitude of these three measurable parameters for a given height and diameter of sea urchin. The predicted magnitudes of tube-foot forces, internal pressure and apical curvature are reasonable for sea urchins, thus supporting the theory. An urchin’s shape, despite all the complex details of individual growth, is thus determined by a force balance at each point in the skeleton. Despite the skeleton’s apparent rigidity, over developmental time spans an urchin’s skeleton is better conceptualized as similar to a stretchy balloon.
