Foraging, vigilance and risk of predation in birds—a dynamic game study of ESS

Abstract

A dynamic multi-period game theory model is developed to study evolutionary stable scanning strategies of birds foraging in flocks. Scanning, while foraging, is carried out to detect attacking predators. In our model there is a chance that birds are killed by predators during foraging days. After each loss of a flock mate the remaining birds face the following foraging day in a smaller flock. The model has non-unique solutions. The evolutionary stable scanning rates may be constant over the foraging season, or they may show a monotonic decreasing trend with time. The former ESS solution does not depend on the future survival probabilities, and is independent of the future flock dynamics. Hence, the scanning rates depend on the current flock size only. The latter ESS solution is interpreted as follows. A loss of a flock mate decreases the future survival of each remaining bird. Hence, the birds increase their scanning rates to take care of their flock mates and to face the future predator attacks in a bigger flock. The choice between the ESS solutions depends on the behavior of the birds at the end of the foraging season. The scanning rates depend on the behavior of the predators.