Limits to optimization: fluid dynamics, adhesive strength and the evolution of shape in limpet shells

Abstract

Limpets are commonly found on wave-swept rocky shores, where they may be subjected to water velocities in excess of 20 m s(−1). These extreme flows can impose large forces (lift and drag), challenging the animal's ability to adhere to the substratum. It is commonly thought that the conical shape of limpet shells has evolved in part to reduce these hydrodynamic forces while providing a large aperture for adhesion. This study documents how lift and drag actually vary with the shape of limpet-like models and uses these data to explore the potential of hydrodynamic forces to serve as a selective factor in the evolution of limpet shell morphology. At a low ratio of shell height to shell radius, lift is the dominant force, while at high ratios of height to radius drag is dominant. The risk of dislodgment is minimized when the ratio of height to radius is 1.06 and the apex is in the center of the shell. Real limpets are seldom optimally shaped, however, with a typical height-to-radius ratio of 0.68 and an apex well anterior of the shell's center. The disparity between the actual and the hydrodynamically optimal shape of shells may be due to the high tenacity of limpets' adhesive system. Most limpets adhere to the substratum so strongly that they are unlikely to be dislodged by lift or drag regardless of the shape of their shell. The evolution of a tenacious adhesion system (perhaps in response to predation) has thus preempted selection for a hydrodynamically optimal shell, allowing the shell to respond to alternative selective factors.