"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.

Official Congratulations to Drs. Sofia Piltz and Marta Sarzynska!

My doctoral students Sofia Piltz (co-supervised with Philip Maini), who started a postdoc in ecology at DTU in June 2014, and Marta Sarzynska, who will be working at Bain & Company starting next month, both have gotten the revised versions of their doctoral theses approved in final form. Thus, they are now both officially done! Sofia's thesis is called "Models for Adaptive Feeding and Population Dynamics in Plankton", and some of her thesis work (with a couple more papers on the way) was published in SIADS. Marta's thesis is about "Spatial Community Structure and Epidemics", and you can read about some of it in this paper (whose sequel is on the way).

"Prey Switching with a Linear Preference Trade-Off"

For the third day in a row, one of my papers has appeared in final published form. Here are the details.

Title: Prey Switching with a Linear Preference Trade-Off

Authors: Sofia H. Piltz, Mason A. Porter, and Philip K. Maini


Abstract: In ecology, prey switching refers to a predator’s adaptive change of habitat or diet in response to prey abundance. In this paper, we study piecewise-smooth models of predator-prey interactions with a linear trade-off in a predator’s prey preference. We consider optimally foraging predators and derive a model for a 1 predator-2 prey interaction with a tilted switching manifold between the two sides of discontinuous vector fields. We show that the 1 predator-2 prey system undergoes a novel adding-sliding-like (center to two-part periodic orbit; "C2PO") bifurcation in which the prey ratio transitions from constant to time-dependent. Farther away from the bifurcation point, the period of the oscillating prey ratio doubles, which suggests a possible cascade to chaos. We compare our model predictions with data on freshwater plankton, and we successfully capture the periodicity in the ratio between the predator’s preferred and alternative prey types. Our study suggests that it is useful to investigate prey ratio as a possible indicator of how population dynamics can be influenced by ecosystem diversity.


P.S. Check out the name we introduced for the new bifurcation that we discovered.