Predators risk injury too: the evolution of derring-do in a predator-prey foraging game

Derring-do is how aggressive a predator is in stalking and capturing prey. We model predator-prey interactions in which prey adjust vigilance behavior to mitigate risk of predation and predators their derring-do to manage risk of injury from capturing prey. High derring-do increases a predator's likelihood of capturing prey, but at higher risk of injury to itself. For fixed predator derring-do, prey increase vigilance in response to predator abundance, predator lethality, and predator encounter probability with prey and decrease vigilance with their own feeding rate; there is a humped-shaped relationship between prey vigilance and effectiveness of vigilance. For fixed prey vigilance, predators increase derring-do with the abundance of prey and predator lethality and decrease it with benefit of vigilance to prey and level of prey vigilance. When both prey and predator are behaviorally flexible, a predator-prey foraging game ensues whose solution represents an evolutionarily stable strategy (ESS). At the ESS, prey provide themselves with a public good as their vigilance causes predators to decrease derring-do. Conversely, predators have negative indirect effects on themselves as their derring-do causes prey to be more vigilant. These behavioral feedbacks create negative intra-specific interaction coefficients. Increasing the population size of prey (or predators) now has a direct negative effect on the prey (or predators). Both effects help stabilize predator-prey dynamics. Besides highlighting a common way by which predators may experience a food-safety tradeoff via dangerous prey, the model suggests why natural selection favors even small defensive measures by prey and hulky predators.