Modeling how hunting strategies and pack size shape each other.

Social foraging exhibits unexpected features, such as the existence of a group size threshold above which hunting success is not improved, mainly because, above this threshold, additional individuals are free-riders that withhold effort. These observations have been supported by computational models of group hunting, which reveal a mechanism that causes hunting success to peak at small group sizes. In the model, hunters follow two simple rules: approach the prey until a safe distance is reached, and when closer to the prey than a critical avoidance distance, move away from other hunters. The mechanism is that the spatial configuration that the hunters adopt during the hunt is disrupted by the excessive number of participants. Direct observations of wolves (Canis lupus) in Yellowstone Park have shown that the group size threshold when hunting bison (Bison bison), their most formidable prey, is nearly three times greater than when hunting elk (Cervus elaphus). However, the relationship between prey type and the threshold pack size is complex and non-linear, driven by a feedback loop: hunting strategies are adjusted based on prey size and behaviour, which in turn affects the formation and effectiveness of the pack. This study explores how prey size influences the optimal pack size and vice versa. Our analysis confirms the non-linearity of this relationship. As the size and danger of the prey change, the optimal pack size does not follow a simple linear pattern. Instead, it reflects a more complex interaction, where both prey characteristics and wolf hunting strategies determine the most effective group size. This complexity arises from the need to balance the pressure exerted on the prey with the spatial arrangement of the pack. The feedback loop between hunting success and pack size illustrates how adaptations in hunting strategies lead to changes in pack organization, which then impact hunting success. This dynamic interaction underlines the need for models that account for these complex interactions to better understand and predict the behavior of wolf packs in different prey scenarios.