A predator–prey model with predators using hawk and dove tactics

In this work we present a predator–prey model that incorporates individual behavior of the predators. A classical Lotka–Volterra model with self-limiting prey describes the predator–prey interaction. Predator individuals can use two behavioral tactics to dispute a prey when they meet, the classical hawk and dove tactics. Each individual can use both tactics along its life. The predator behavioral change is described by means of a game dynamic model based upon the replicator equations, where the gain depends on prey density. We assume that the demographic process, predator–prey interactions, acts at a slow time scale in comparison with the evolution of the behavior of the predator population. The existence of two time scales allows studying the complete system from a reduced one, which describes the dynamics of the total predator and prey densities at the slow time scale. The aim of this work is to study the effects of individual predator behavior on the dynamics of the predator–prey system. The main conclusion that emerges from this study is the existence of a relationship between prey density and the strategy adopted by predators: aggressive behavior is connected to high prey and low predator densities, whereas a polymorphism dove–hawk is found at low prey and high predator densities.