Changes in antipredator vigilance over time caused by a war of attrition between predator and prey

Prey animals often move from patch to patch in search of food and must evaluate the likelihood that a predator is present in each patch to adjust their antipredator behavior. This is important because a prey animal might have inadvertently arrived at a patch on which a sit-and-wait predator is lurking, a common situation in many species of animals. In a simulation model, we explore how long the ambushing predator should wait before attacking the prey animal and how the prey animal can adjust its vigilance in response. We adopted a war-of-attrition framework where the predator selects randomly an attack time from a distribution to keep the prey guessing and where the prey also keep the predator guessing by selecting randomly a time at which to switch from high to low vigilance. We found that an evolutionarily stable solution can emerge in this game and has the following form under a broad range of ecological conditions: the predator attacks early and the prey adopts a high vigilance early and then switches later to a lower vigilance. The results indicate that antipredator vigilance may change as a function of time rather than being a constant value as assumed in most vigilance models. We conclude that the uncertainty that ambushing predators and their prey must plant in the minds of the other can have important consequences for the evolution of predator and prey tactics.