A predator-2 prey fast-slow dynamical system for rapid predator evolution

Abstract

We consider adaptive change of diet of a predator population that switches its feeding between two prey populations. We develop a novel 1 fast--3 slow dynamical system to describe the dynamics of the three populations amidst continuous but rapid evolution of the predator's diet choice. The two extremes at which the predator's diet is composed solely of one prey correspond to two branches of the three-branch critical manifold of the fast--slow system. By calculating the points at which there is a fast transition between these two feeding choices (i.e., branches of the critical manifold), we prove that the system has a two-parameter family of periodic orbits for sufficiently large separation of the time scales between the evolutionary and ecological dynamics. Using numerical simulations, we show that these periodic orbits exist, and that their phase difference and oscillation patterns persist, when ecological and evolutionary interactions occur on comparable time scales. Our model also exhibits periodic orbits that agree qualitatively with oscillation patterns observed in experimental studies of the coupling between rapid evolution and ecological interactions.

References in corpus (2)

• Rapid contemporary evolution and clonal food web dynamics
• Nonsmooth analogues of slow-fast dynamics -- pinching at a folded node

Cited by in corpus (5)

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• A Criterion for the Existence of Relaxation Oscillations with Applications to Predator-Prey Systems and an Epidemic Model
• Relaxation Oscillations and the Entry-Exit Function in Multi-Dimensional Slow-Fast Systems
• Spruce budworm and oil price: a biophysical analogy
• Inferring parameters of prey switching in a plankton 1 predator--2 prey system with a linear preference tradeoff