A Three-Phase Model for Predator-Prey Analysis
L. M. Finney, Jade P. Vinson, Derek Zaba · 1997
We model the hunt as a game of three explicit stages: the stalk, the attack, and the subdual. We implemented this model in Matlab to simulate a velociraptor hunting a thescelosaurus and an African lion hunting a gazelle. During the attack phase, also known as the macroscopic game, the speed constraints are binding but the curvature and acceleration constraints are not. The predator’s goal for this game is to minimize the time that it takes to intercept the prey. We introduce a two-predator strategy that is space-optimal for both the predator and prey and conjecture that it is also time-optimal. In the subdual phase, also known as the microscopic game, the time constraints are insignificant. In this game, the predator’s goal is to minimize its closest approach to the prey. The prey’s strategy is to use its smaller turning radius to outmaneuver the predator until time runs out. Based on our model and simulations, we conclude that the hunting strategies of an African lion and of a velociraptor differ. The lion has a slower maximum speed but has greater acceleration and is more maneuverable than a gazelle. Conversely, the velociraptor has greater speed but less maneuverability than a thescelosaurus. An ambush is the most effective strategy for a pair of lions, and chasing from behind is the most effective strategy for a pair of velociraptors. The three-phase model may apply to other situations, such as a guided missile chasing an aircraft.