title: Understanding rapid evolution in predator‐prey interactions using the theory of fast‐slow dynamical systems.
abstract: The accumulation of evidence that ecologically important traits often evolve at the same time and rate as ecological dynamics (e.g., changes in species' abundances or spatial distributions) has outpaced theory describing the interplay between ecological and evolutionary processes with comparable timescales. The disparity between experiment and theory is partially due to the high dimensionality of models that include both evolutionary and ecological dynamics. Here we show how the theory of fast-slow dynamical systems can be used to reduce model dimension, and we use that body of theory to study a general predator-prey system exhibiting fast evolution in either the predator or the prey. Our approach yields graphical methods with predictive power about when new and unique dynamics (e.g., completely out-of-phase oscillations and cryptic dynamics) can arise in ecological systems exhibiting fast evolution. In addition, we derive analytical expressions for determining when such behavior arises and how evolution affects qualitative properties of the ecological dynamics. Finally, while the theory requires a separation of timescales between the ecological and evolutionary processes, our approach yields insight into systems where the rates of those processes are comparable and thus is a step toward creating a general ecoevolutionary theory.
authors.affiliation: Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, USA. mhc37@cornell.edu
authors.forename: Michael  H
authors.initials: M
authors.lastname: Cortez
authors.forename: Stephen P
authors.initials: SP
authors.lastname: Ellner
mesh_terms: D000818:Animals; D005075:Biological Evolution; D008954:Models, Biological; D011156:Population Density; D011157:Population Dynamics; D011235:Predatory Behavior; D013997:Time Factors