The “Destabilizing” Effect of Cannibalism in a Spatially Explicit Three-Species Age Structured Predator-Prey Model

Cannibalism, the act of killing and consumption of conspecifics, is generally considered to be a stabilising process in ODE models of predator-prey systems. On the other hand, Sun et al. were the first to show that cannibalism can cause Turing instability, in the classical Rosenzweig-McArthur two-species PDE model, which is an impossibility without cannibalism. Magnússon’s classic work is the first to show that cannibalism in a structured three-species predator-prey ODE model can actually be destabilising. In the current manuscript we consider the PDE form of the three-species model proposed in Magnússon’s classic work. We prove that, in the absence of cannibalism, Turing instability is an impossibility in this model, for any range of parameters . However, the inclusion of cannibalism can cause Turing instability. Thus, to the best of our knowledge, we report the first cannibalism induced Turing instability result, in spatially explicit three-species age structured predator-prey systems. We also show that, in the classical ODE model proposed by Magnússon, cannibalism can act as a life boat mechanism, for the prey .