Seminar in PSA 102

ABSTRACT

Title: Cats Protecting Birds Revisited

 By:    Meng Fan, Department of Mathematics and Statistics, Arizona State University

In this paper, we revisit the dynamical interaction among prey (bird), mesopredator (rat), and superpredator (cat) discussed by Courchamp in 1999. First, we develop a prey-mesopredator-superpredator (i.e., bird-rat-cat,briefly, BRC) model, where the predator's functional responses are derived based on the classical Holling's time budget arguments. Our BRC model overcomes several model construction problems in Courchamp's model and admits richer, reasonable and realistic dynamics. We explore the possible control strategies to save or restore the bird by control or eliminate the rat or the cat when the bird is endangered. In particular, we establish the existence of two types of mesopredator release phenomena: severe mesopredator release, where once superpredators are suppressed, a burst of mesopredators follows which leads their shared prey to extinction; and mild mesopredator release, where the mesopredator release could exert more negative impact on the endemic prey but does not lead the endemic prey to extinction. A sharp sufficient criterion is established for the occurrence of the severe mesopredator release. We also show that, in a prey-mesopredator-superpredator trophic food web, eradication of introduced superpredators such as feral domestic cats in BRC models, is not always the best solution to protect endemic insular prey. The presence of a superpredator may have a beneficial effect in such systems.