Understanding The Effects Of Rapid Adaptation On Predator-Prey Interactions Using The Theory Of Fast-Slow Dynamical Systems
Interspecific interactions depend not only on the population densities of the interacting species, but on their phenotypes as well. Variation in ecologically important species traits can be heritable or plastic in nature and both yield phenotypic change that occurs at rates comparable to or faster than those of ecological dynamics. This thesis explores how the effects of heritable and plastic phenotypic variation on community dynamics can be captured under one unifying theory using the theory of fast-slow dynamical systems. The analysis presented here focuses on the limit where phenotypic change occurs faster than changes in species' abundances in predator-prey systems. This approach reduces model dimension and yields analytical results and graphical methods with predictive power about when new and unique dynamics will arise in ecological systems with rapid phenotypic change. In addition, while explicitly assuming a separation of time scales, the analysis of the fast adaptation limit yields insight into the consequences of adaptive change when the rates of the adaptive and ecological processes are comparable. The results presented here show that evolution and phenotypic plasticity have different effects on the community dynamics of predator-prey systems. Rapid evolution has the potential to stabilize or destabilize population oscillations while phenotypic plasticity only stabilizes population oscillations. Evo- lution can also yield population oscillations where the predator and prey are completely out-of-phase or one species oscillates while the other remains essentially constant. These two behaviors are not possible in phenotypically plastic or phenotypically fixed predator-prey systems. This thesis also presents an analysis of the dynamics that arise in the vicinity of a transversal intersection of the critical manifold in multiple time scale biological systems. Such intersections are generic in fast-slow eco-evolutionary models and the results presented here show that complex dynamics arise near the transversal intersections of the critical manifold. These dynamics arise in regions of parameter space where periodic orbits exist and in phase space where the fast-slow structure of the system is no longer present.
phenotypic plasticity; rapid evolution; fast-slow systems
Ellner, Stephen Paul
Hairston Jr, Nelson George; Guckenheimer, John Mark
Ph.D. of Applied Mathematics
Doctor of Philosophy
dissertation or thesis