Modeling scan and interscan durations in antipredator vigilance

Many prey species alternate between bouts of foraging and bouts of antipredator vigilance. Models of vigilance typically predict how much total time prey animals should allocate to vigilance but do not specify how that time should be scheduled throughout foraging. Here, we examine how the scheduling of vigilance pays off in terms of food intake and predator detection. Specifically, we study how changes in ecological factors affect the expected duration of scans to look out for predators and the duration of interscan intervals dedicated to foraging. Our framework includes factors like the risk of attack, how difficult it is to locate food and predators, and the distance to protective cover. Our individual-based model makes several predictions about scan and interscan durations, which are discussed in relation to the available empirical evidence in birds and mammals. This model of antipredator vigilance is a first step in incorporating constraints related to food gathering and the detection of predators. Adding such constraints adds a novel dimension to vigilance models and produces a variety of predictions that await empirical scrutiny.