"Inferring Parameters of Prey Switching in a 1 Predator–2 Prey Plankton System with a Linear Preference Tradeoff"

Another of my papers came out in final published form today.

Title: Inferring Parameters of Prey Switching in a 1 Predator–2 Prey Plankton System with a Linear Preference Tradeoff

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

Abstract: We construct two ordinary-differential-equation models of a predator feeding adaptively on two prey types, and we evaluate the models’ ability to fit data on freshwater plankton. We model the predator’s switch from one prey to the other in two different ways: (i) smooth switching using a hyperbolic tangent function; and (ii) by incorporating a parameter that changes abruptly across the switching boundary as a system variable that is coupled to the population dynamics. We conduct linear stability analyses, use approximate Bayesian computation (ABC) combined with a population Monte Carlo (PMC) method to fit model parameters, and compare model results quantitatively to data for ciliate predators and their two algal prey groups collected from Lake Constance on the German–Swiss–Austrian border. We show that the two models fit the data well when the smooth transition is steep, supporting the simplifying assumption of a discontinuous prey-switching behavior for this scenario. We thus conclude that prey switching is a possible mechanistic explanation for the observed ciliate–algae dynamics in Lake Constance in spring, but that these data cannot distinguish between the details of prey switching that are encoded in these different models.


Note: This paper is actually the third in a series of papers that arose from Sofia's doctoral thesis. In all three, we studied prey switching in plankton as a dynamical system. However, although we were concerned in all three papers with the same ecological situation, we modeled it in three different mathematical ways: using piecewise-smooth dynamical systems (in paper 1), using fast–slow dynamical systems (in paper 2), and using smooth dynamical systems (in this paper). It is really important to model the same phenomenon in different ways and to compare the qualitative features of the different models against each other as well as to empirical data. I am really pleased with this effort, which Sofia did a superb job of leading.

"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.