Continuous cycling of grouped vs. solitary strategy frequencies in a predator-prey model

We present a model of predator and prey grouping strategies using game theory. As predators respond strategically to prey behavior and vice versa, the model is based on a co-evolution approach. Focusing on the "many eyes-many mouths" trade-off, this model considers the benefits and costs of being in a group for hunting predators and foraging prey: predators in a group have more hunting success than solitary predators but they have to share the prey captured; prey in a group face a lower risk of predation but greater competition for resources than lone prey. The analysis of the model shows that the intersections of four curves define distinct areas in the parameter space, corresponding to different strategies used by predators and prey at equilibrium. The model predictions are in accordance with empirical evidence that an open habitat encourages group living, and that low risks of predation favor lone prey. Under some conditions, continuous cycling of the relative frequencies of the different strategies may occur. In this situation, the proportions of grouped vs. solitary predators and prey oscillate over time.