Adaptation from restricted geometries: the shell inclination of terrestrial gastropods

The adaptations that occur for support and protection can be studied with regard to the optimal structure that balances these objectives with any imposed constraints. The shell inclination of terrestrial gastropods is an appropriate model to address this problem. In this study, we examined how gastropods improve shell angles to well-balanced ones from geometrically constrained shapes. Our geometric analysis and physical analysis showed that constantly coiled shells are constrained from adopting a well-balanced angle; the shell angle of such basic shells tends to increase as the spire index (shell height/width) increases, although the optimum angle for stability is 90° for flat shells and 0° for tall shells. Furthermore, we estimated the influences of the geometric rule and the functional demands on actual shells by measuring the shell angles of both resting and active snails. We found that terrestrial gastropods have shell angles that are suited for balance. The growth lines of the shells indicated that this adaptation depends on the deflection of the last whorl: the apertures of flat shells are deflected downward, whereas those of tall shells are deflected upward. Our observations of active snails demonstrated that the animals hold their shells at better balanced angles than inactive snails.