Predator group size distributions in predator-prey systems

The grouping behavior is common in nature, e.g., fish school, bird flocks and insects swarms. Indeed, numerous theoretical and empirical predator-prey models have demonstrated the impact of group-living animals on ecosystems. To examine the interactions between individuals in the same group or competition between groups, we introduced different models based on Monte Carlo simulation and mean-field theory and found that the predator group sizes follow the geometric distribution and logarithmic distribution, as in previous empirical and theoretical cases. Our models also provide an intuitive explanation for these distributions. A new distribution based on the Holling-III functional response is presented; this distribution is heavy tailed in some specific cases.