Mechanical Limits to Size in Wave‐Swept Organisms
Authors: Denny Mark W. , Daniel Thomas L. , Koehl M. A. R. 
Published: April 2006

Plants and animals that inhabit the intertidal zone of wave—swept shores are generally small relative to terrestrial or subtidal organisms. Various biological mechanisms have been proposed to account for this observation (competition, size—specific predation, food—limitation, etc.). However, these biological mechanisms are constrained to operate within the mechanical limitations imposed by the physical environment, and these limitations have never been thoroughly explored. We investigated the possibility that the observed limits to size in wave—swept organisms are due solely or in part to mechanical, rather than biological, factors. The total force imposed on an organism by breaking waves and postbreaking flows is due to both the water's velocity and its acceleration. The force due to velocity (a combined effect of drag and lift) increases in strict proportion to the organism's structural strength as the organism increases in size, and therefore cannot act as a mechanical limit to size. In contrast, the force due to the water's acceleration increases faster than the organism's structural strength as the organism grows, and thus constitutes a potential mechanical limit to its size. We incorporated this fact into a model that predicts the probability that an organism will be destroyed (by breakage or dislodgement) as a function of five parameters that can be measured empirically: (1) the organism's size, (2) the organism's structural strength, (3) the maximum water acceleration in each wave, (4) the maximum water velocity at the time of maximum acceleration in each wave, and (5) the probability of encountering waves with given flow parameters. The model was tested using a variety of organisms. For each, parameters 1—4 were measured or calculated; the probability of destruction, and the size—specific increment in this probability, were then predicted. For the limpets Collisella pelta and Notoacmaea scutum, the urchin Strongylocentrotus purpuratus, the mussel Mytilus californianus (when solitary), and the hydrocoral Millepora complanata, both the probability of destruction and the size—specific increase in the risk of destruction were determined to be substantial. It is conjectured that the size of individuals of these species may be limited as a result of mechanical factors, though the case of M. complanata is complicated by the possibility that breakage may act as a dispersal mechanism. In other cases (the snails Thais canaliculata, T. emarginata, and Littorina scutulata; the barnacle Semibalanus cariosus), the size—specific increment in the risk of destruction is small and the size limits imposed on these organisms are conjectured to be due to biological factors. Our model also provides an approach to examining many potential effects of environmental stress caused by flowing water. For example, these methods may be applied to studies of: (1) life—history parameters (e.g., size at first reproduction, age at first reproduction, timing of reproductive cycles, length of possible reproductive lifetime), (2) the effects of gregarious settlement on the flow encountered, (3) the physical basis for patterns of disturbance, (4) the optimum (as opposed to the maximum) size of organisms, and (5) the energetic cost of maintaining a skeleton with an appropriate safety factor. A definitive answer regarding the possibility of mechanical limits to size depends both upon an accurate measurement of the probability of encountering a wave of specific flow parameters and upon factors that are external to the model considered (e.g., life—history parameters). Further, due to their ability to move with the flow, organisms that are sufficiently flexible can escape the size limits imposed on more rigid organisms. Thus, some macroalgae attain large sizes (2—3 m in maximum dimension). The precise role of these factors awaits further research.