Ecology of fear: Foraging games between predators and prey with pulsed resources

We model the foraging game between a prey and predator when the prey experi ences a temporally pulsed resource (e.g., seed-eating gerbils). Animals hav e the options of foraging or remaining inactive. Prey harvest resources and incur a mortality risk only while foraging. ESS levels of prey and predato r activity have three distinct phases over the time course of a resource pu lse. During the first phase, resources are sufficiently abundant to permit profitable foraging by all prey and predators. During the second phase, onl y a fraction of prey and predator are active. The fraction of active prey i s sufficient to allow profitable foraging by the predators. Resource abunda nces and activity level of predators decline synchronously, balancing the p rey's needs for food and safety. During the third phase, resources decline to where both prey and predator cease activity. These adaptive behaviors of prey and predator to resources and to each other promote the stability of the predator-prey dynamics.