Implosion and maximum inhabitable depths throughout ontogeny in phragmocone-bearing cephalopods: the Punctuated Pfaff Model

The Pfaff model postulates that the final septum in the phragmocone of a cochleate cephalopod must always be adapted to resist the external pressure transmitted through the animal’s body onto its apertural surface at its maximum inhabitable depth. Stress-strain relationships developed for thin membranes predict that under that condition, septal thickness throughout ontogeny should increase in strict proportion to increased septal span, namely the minimum dimension over which the septum is unsupported. Equivalently, the septal thickness ratio STR, defined as the septal thickness divided by the septal span, should be a constant as long as there is a constant maximum pressure; migration to shallower or deeper habitats should cause a transition to a new ratio. The Punctuated Pfaff Model (PPM) analyses such transitions between multiple stages of stasis throughout ontogeny. All genera examined herein conform to the PPM, including Nautilus, Spirula, Gaudryceras, Argonauticeras, Eogaudryceras, Cleoniceras and Desmoceras. Multiple transitions to shallower or deeper depths are observed across ontogeny; some transitions are sharp, being completed between successive septa, while some are broad, requiring several septa for completion; many transitions are accompanied by septal approximation. The derived maximum inhabitable depths are consistent with the average precipitation depths estimated from stable oxygen analyses.
David L. Kennedy* [[e-mail]], The Fossil Club of Australia, 73 Fullagar Road, Wentworthville, New South Wales 2145, Australia.