Herding tendency as an aggregating factor in a binary mixture of social entities

The role of herding tendency in the group formation of social entities is hereby explored. The herding tendency is quantified by a parameter α∈[0,1]α∈[0,1]. The system consists of a mixture of two types of entities: (i) those with α>0α>0 and (ii) those with α=0α=0. The latter consist a fraction p   of the entire population. The dynamics of agent interactions leads to the formation of clusters of different sizes. The size distribution D(s)D(s) of these clusters are found to obey a power-law only in the limit that α→1α→1 and p→0p→0. Group-size data of several real-world animal systems are fitted with curves generated by the model. This study contributes further to the understanding of group-forming behavior commonly cited in ecological studies.