Inferring parameters of prey switching in a plankton 1 predator--2 prey system with a linear preference tradeoff

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: (1) smooth switching using a hyperbolic tangent function; and (2) 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 predictions 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.