"A Predator–2 Prey Fast–Slow Dynamical System for Rapid Predator Evolution"

One of my papers has now been posted in final form. (A second one appeared online today, but it joins a long list of papers that are still awaiting their coordinates. I will blog about those papers when they have those coordinates.)

Anyway, let's talk about the paper that does have its coordinates. It's about plankton modeling, and here are the details.

Title: A Predator–2 Prey Fast–Slow Dynamical System for Rapid Predator Evolution

Authors: So a H. Piltz, Frits Veerman, Philip K. Maini, and Mason A. Porter

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 su ciently 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 di erence 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.