Figure 1

(a) The prediction on the histogram of inter-individual distances. When the group contains more than two-levels of social organization with different sets of parameters for the attraction–repulsion model, the histogram should be multi-modal. The distance of the first peak and the second peak are referred to as p₁ and p₂, and the valley between p₁ and p₂ is v₁₂. p_1, and p₂ could be considered as the most frequent value of inter-individual distances within a unit and between units, respectively. v₁₂ represents the threshold that divides the intra- and inter-unit association. (b) The prediction on the inter-unit association. If units just coincide in the same field (null model), units just spread in the foraging area. However, in multilevel society, units preferentially associate and forage together. Thus, the inter-unit distance in a multilevel society should be smaller and have steeper distribution than that of null model. The graphs were created using Microsoft Power Point for Mac 16.16.25 (https://office.live.com/start/powerpoint.aspx).