The effect of predator avoidance and travel time delay on the stability of predator-prey metacommunities

The stability conditions for an isolated specialist predator-prey community are fairly well understood. The spatial coupling of several such systems through dispersal of individuals can generate new dynamic behavior that is not yet completely understood. Many factors are known to be stabilizing or neutral, e.g., random dispersal or time delays, while others may induce instabilities in some cases but not others, e.g., density-dependent movement. We study the combination of two stabilizing mechanisms in a two-patch Rosenzweig-MacArthur model with a novel density-dependent movement term. Specifically, we assume that prey move between patches according to their perceived predation risk, and we include travel time between patches as a time delay. We show that the combination of mechanisms may be destabilizing even though each mechanism by itself is stabilizing. Our results show that a detailed knowledge of mechanisms and their temporal scales is necessary to correctly predict the stability of a metacommunity.