Bivalves are among the commonest shelly components of beach sands throughout the world. Many taxa are farmed and harvested for human consumption, and pearls are a valuable by-product of bivalve growth. The bivalves developed a spectacular variety of shell shapes and life strategies, during a history spanning the entire Phanerozoic, and all are based on a simple bilaterally symmetric exoskeleton. The first bivalves were marine shallow burrowers; epifaunal, deep
Most valves of any shelled organism can be modeled as a coil and, in fact, the ontogeny of living Nautilus was known to approximate to a logarithmic spiral in the 18th century. David Raup (University of Chicago), in an influential study, defined and computer-simulated the ontogeny of shells on the basis of a few parameters: (i) the shape of the generating curve or axial ratio of the ellipse; (ii) the rate of whorl expansion after one revolution (W); (iii) the position of the generating curve with respect to the axis (D); and (iv) the whorl translation rate (T). Shells are generated by translating a revolving generating curve along a fixed axis (Fig. 13.4). For example, when T = 0, shells lacking a vertical component such as bivalves and brachiopods, are simulated, whereas those with a large value of T are typical of high-spired gastropods. Only a small variety of possible shell shapes occur in nature. Raup's (1966) original simulations were executed on a mainframe system. Andrew Swan (1990) adapted the software for microcomputers and has simulated a wide variety of shell shapes. More recent work has applied more complex techniques to simulate ammonite hetero-morphs. Nevertheless only a relatively small percentage of the theoretically available morphospace has actually been exploited by fossil and living mollusks. Clearly some fields map out functionally and mechanically improbable morphologies - perhaps the aperture is too small for the living animal to feed from within the shell, or the shape would not allow the animal to move; other fields have yet to be tested in evolution. Raup's morphospace is, however, non-orthogonal and it has been argued that the mosaic of morphospace occupation is merely an artifact of presentation. Theoretical mor-phospace has been explored for a range of other groups including bryozoans, echinoids, graptolites, some fishes and some plants (Erwin 2007).
There have been many modifications of Raup's original algorithm and a number of web interfaces that can generate shell shapes; one of the simplest may be accessed via http://www. blackwellpublishing.com/paleobiology/.
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