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

TL;DR

This paper models rapid predator evolution in a three-population system using a novel fast-slow dynamical framework, revealing periodic orbits and oscillation patterns consistent with experimental observations.

Contribution

It introduces a new 1 fast--3 slow dynamical system to analyze predator diet evolution and demonstrates the existence of periodic orbits under various time scale separations.

Findings

Existence of a two-parameter family of periodic orbits.

Persistence of oscillation patterns when ecological and evolutionary timescales are similar.

Qualitative agreement with experimental oscillation patterns.

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.