Theoretical morphology of bivalve shell sculptures

A theoretical morphologic model defining patterns of shell sculptures in Bivalvia is introduced. It is based on the displacement of sculptural elements along the growing shell margin and introduction of new sculptural elements. The kinematics of the sculptural elements are defined in terms of the following parameters: maximum speed of displacement of sculptural elements, position along the growing shell margin where a migrating element attains maximum speed, and position of the divergence axis of the riblets. Computer models successfully mimicked most of the diverse patterns of bivalve shell sculptures. Morphometric analysis revealed that the displacement speed of a sculptural element is not constant but depends on the relative position of the element on the shell margin. It was revealed that the primary component of variation in bivalve shell sculptures could be explained by variation in the displacement speed of sculptural elements around the divergence axis of riblets.