Geometry of an ecological arms race

Biological Sciences: L. David Smith (Smith College)
Mathematics: Christophe Golé (Smith College)

This project examines the geometry of a predator-prey arms race between populations of introduced crabs and native snails along the New England coast. In particular, we are interested in understanding the role that phenotypic plasticity (environmentally induced change in a character during an organism’s lifetime) plays in this ecological interaction.

Experiments using diverse taxonomic groups have shown that both predator trophic (feeding) structures and prey morphological defenses can change in response to environmental cues during development. In our system, invasive crabs fed thick-shelled snails develop relatively larger, stronger claws after molting than do crabs fed thin-shelled snails. In turn, snails reared in the presence of crabs build, over the course of weeks, thicker, more resistant shells than in their absence. Thus, phenotypic plasticity provides a means by which an invader can respond relatively quickly to its new environment, and induced defenses may allow resident prey species to mitigate impacts of the invader. Predicting the consequences of a predator introduction, however, requires an understanding of how key environmental variables (e.g., predator density, shell defenses, water temperature) influence both the magnitude and rate of induced responses in antagonists over the invader’s range.

This project will use field and lab experiments to compare crab foraging performance and defensive effectiveness of shells with respect to the geometric parameters of growth, environmental cues, and functional trade-offs. Mathematical modeling for this project includes geometry, size scaling of predator-prey interactions (allometry), dynamical systems, game theory, programming in Mathematica, and statistics.