Kinematics of accretionary shell growth, with examples from brachiopods and molluscs

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Abstract
A moving reference frame is introduced for the analysis of accretionary shell growth. Simple principles of motion and stepwise growth define the model. At each growth step, the aperture migrates from its present position to a new position, according to locally defined rules. The aperture becomes the focus of the analysis, mathematically and conceptually, in conformity with biological reality. Kinematic principles provide the analytical framework for describing the aperture's trajectory (kinematics is the study of motion). The aperture “translates,” “rotates,” and “dilates.” The model offers exceptional flexibility in the analysis of accretionary growth forms and is particularly well-suited to analysis of conical and loosely coiled shell geometries. Computer simulations illustrate the principles of a moving reference model. The inverse problem of finding the aperture motions from actual shell data is rigorously specified, for both planispiralled and helicospiralled shell forms.