Coevolution-driven predator-prey cycles: predicting the characteristics of eco-coevolutionary cycles using fast-slow dynamical systems theory

Abstract

Eco-coevolutionary theory predicts that predator-prey coevolution occurring on the time scale of ecological dynamics (e.g., changes in population abundances) can drive novel kinds of predator-prey cycles, e.g., cryptic cycles where one species cycles while the other remains effectively constant and clockwise cycles where peaks in predator density precede peaks in prey density. However, because this body of theory has focused on particular models and studied the different cycle types in isolation, it is unclear what biological characteristics (e.g., costs for offense or defense) determine when a particular cycle type will arise. In this study, I explore the kinds of predator-prey cycles that arise in a general eco-coevolutionary model where there is disruptive selection and the coevolutionary dynamics are fast relative to the ecological dynamics of the system. With a graphical tool created using the theory of fast-slow dynamical systems, I predict what kinds of cycles can arise in the model and how cycle type depends on the costs for prey defense and predator offense. Fast-slow dynamical systems theory requires a separation of time scales between the ecological and evolutionary processes; however, numerical simulations show that this tool can help predict how coevolution drives populations cycles in systems where the speeds of ecological and evolutionary dynamics are comparable. Thus, this work is a step forward in building a general eco-coevolutionary theory.