Effects of aggregative and solitary individual behaviors on the dynamics of predator–prey game models

We present predator–prey models taking into account the individual behaviors of prey individuals and predators, which can use either grouped or solitary strategies. When prey individuals are grouped, they face less predation but have less access to the resource, which is shared with other individuals of the group. Groups of predators are more efficient to capture a prey than solitary ones. However, predators in groups must share captured prey with predators of their group. We study two models which differ in the way encounter rates are calculated. We present the effects of the different behavioral strategies on the overall dynamics of the predator–prey model. Next, we couple the fast theoretical game dynamics to a slow population dynamics model. We use aggregation methods to obtain the aggregated model. Such a model allow us to study the effects of the strategies selected by prey individuals and predators on the stability of the prey–predator system. Under some conditions, we show that, when aggregating, lonely preys can exclude cooperative predators. We also show how predators can coexist against aggregative preys, when changing strategy from solitary to cooperative.