Theoretical morphology of echinoid growth

Deutler's classic work (1926) provides the basis for an analysis of plate growth in echinoids. Deutler showed that the concentric growth rings found within each plate may be used to reconstruct the ontogeny of the entire plate pattern. New observations of growth-line configurations, particularly in Strongylocentrotus pallidus (Sars), have been used to derive a general model for echinoid growth. The plate mosaic is assumed to be the result of close packing of the growing plates. The shape of a given plate thus depends on its size and position relative to surrounding plates. The rate of meridional growth of a plate can be shown to change regularly with increasing distance from the echinoid's apical system. Migration of plates away from the apical system thus causes change in the rate of plate growth. The rate of plate migration is strongly influenced, in turn, by the rate of supply of new plates at the apical system. A mathematical model has been developed from these considerations which, when treated by digital computer (with x-y plotter output), produces ideal plate patterns (including growth rings). The constants in the model may be varied to produce a broad spectrum of echinoid plate patterns.