A model of the burglar alarm hypothesis of prey alarm calls.

When approached by a predator many prey species will emit an "alarm call" as a form of anti-predator behavior. One hypothesis for the function of alarm calls is the "burglar alarm" hypothesis whereby upon attack, a prey renders itself dangerous to a predator by generating an alarm call that attracts a predator at higher trophic levels in the food chain; that is, attracts a predator to the prey's own predator. This paper concerns a model incorporating a mechanism to test the burglar alarm hypothesis. We prove in one space dimension global existence, of positive bounded classical solutions, and establish existence of non-constant equilibrium solutions and assess their stability. We provide some representative numerical simulations to emphasize the nature of pattern formation for this model and demonstrate the benefit achieved by a signal inducing prey species under the burglar alarm hypothesis.