Pattern formation and individual-based models: The importance of understanding individual-based movement

This paper demonstrates that while pattern formation can stabilize individual-based models of predator-prey systems, the same individual-based models also allow for stabilization by alternate mechanisms, particularly localized consumption or diffusion limitation. The movement rules of the simulation are the critical feature which determines which of these mechanisms stabilizes any particular predator-prey individual-based model. In particular, systems from well-connected subpopulations, in each of which a predator can attack any prey, generally exhibit stabilization by pattern formation. In contrast, when restricted movement within a (sub-)population limits the ability of predators to consume prey, localized consumption or diffusion limitation can stabilize the system. Thus while the conclusions from differential equations on the role of pattern formation for stability may apply to discrete and noisy systems, it will take a detailed understanding of movement and scales of interaction to examine the role of pattern formation in real systems. Additionally, it will be important to link an understanding of both foraging and inter-patch movement, since by analogy to the models, both would be critical for understanding how real systems are stabilized by being discrete and spatial.