Stacking Increments: A New Model and Morphospace for the Analysis of Bivalve Shell Growth

A model employing stacking increments is introduced for the analysis of bivalve shell growth and form. The model is based on the components of shell growth that are potentially independent: the rate of mantle cell proliferation, the rate of precipitation of shell material, and the rate of translation of the pallial line, where the mantle is attached to the shell. This model is defined in terms of the following parameters: (1) the ratio of accretion of shell material at the shell margin to growth of the mantle by cell division, (2) the ratio of shell accretion at the pallial line to mantle growth, and (3) the ratio of the amount of pallial muscle translation, away from the umbo toward the shell margin, to mantle growth. In this model, the shape of a radial section through the shell is simulated by stacking of internal microgrowth increments. The mode of stacking of the increments is determined by the balance among the parameters defining growth. A theoretical morphospace defined on the basis of this model is largely consistent with the range of forms of naturally occurring bivalve shells. Analysis of the distribution of actual shell forms in relation to this morphospace suggests that the absolute rate of shell precipitation and the gradient in precipitation rate away from the shell margin along a radial cross-section are physiologically as well as geometrically constrained.

Keywords:

• Bivalve Shell
• Growth And Form
• Theoretical Morphology
• Stacking Increments
• Computer Simulation
• Bivalvia