Geometric and functional constraints on bivalve shell morphology

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Abstract
The range of shell morphologies available to bivalves is constrained by the geometric properties of coiled shells, and by two contrasting functional necessities: positioning the umbones at a distance from each other, to allow an adequate amount of shell gape, and limiting linear growth of the axial shell margin, in order to prevent the ligament from being rapidly stretched beyond its elasticity limits. These necessities are achieved, or circumvented, in one or more of the following ways: (1) evolving a range of inequivalve adaptations, (2) allowing a large amount of interumbonal growth, while simultaneously adopting a ligament that quickly breaks and is continuously replaced during ontogeny, (3) adopting an outward curving ligament which flexes along its entire width, thus effectively placing the actual pivoting axis of the valves dorsally to the axial shell margin, (4) substituting the ligament with diductor muscles, (5) stopping growth before shell coiling reaches half whorl, (6) decreasing the whorl expansion rate throughout ontogeny, (7) orienting the coiling axes of the umbones at an angle to each other and to the hinge axis.