Prey switching with a linear preference trade-off

TL;DR

This paper models predator-prey interactions with prey switching behavior, revealing a novel bifurcation and oscillatory dynamics, and demonstrates how prey ratio can indicate ecosystem diversity effects.

Contribution

It introduces a piecewise-smooth model with a linear preference trade-off, uncovering new bifurcation phenomena and linking prey ratio oscillations to ecosystem diversity.

Findings

Identified a new adding-sliding-like bifurcation in predator-prey models.

Observed period doubling in prey ratio oscillations, indicating potential chaos.

Validated model predictions with freshwater plankton data.

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. Further away from the bifurcation point, the period of the oscillating prey ratio period doubles, suggesting a possible cascade to chaos. We compare our model predictions with data and demonstrate that we successfully capture the periodicity in the ratio between the predator's preferred and alternative prey types in data on freshwater plankton. 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.