On Lison's Model of Bivalve Shell Form, and Its Biological Interpretation

In the half-century that has elapsed since the publication of W. D'Arcy Thompson's classic study On Growth and Form, there have been several attempts to explain rigorously the phenomenon of shell growth in the Mollusca (Huxley, 1932; Lison, 1949; Owen, 1953; Yonge, 1952; Stasek, 1963) and Brachiopoda (Rudwick, 1959; Krans, 1965). Apart from the comprehensive and undeservedly neglected paper of Lison (1949), all these authors have used essentially the same approach as that of Thompson (1942, p. 756), though refining this approach in detail. It is my belief that Thompson's work entails certain a priori assumptions which, although intuitively plausible, are not valid, and that the application of these assumptions results in a confusion, rather than a clarification, of understanding of shell growth.