On the Widespread Occurrence of the Inverse Square Distribution in Social Sciences and Taxonomy

TL;DR

This paper demonstrates that the inverse square distribution observed in social and ecological hierarchies is primarily due to the tree-like classification method, rather than self-organization.

Contribution

It reveals that the inverse square distribution arises from the classification process itself, not necessarily from the systems' self-organized nature.

Findings

Tree-like classifications exhibit inverse square distribution regardless of system randomness.

Both real and random systems show similar statistical behavior in sub-branch sizes.

The observed distribution is a consequence of classification structure, not system dynamics.

Abstract

The widespread occurrence of an inverse square relation in the hierarchical distribution of sub-communities within communities (or sub-species within species) has been recently invoked as a signature of hierarchical self-organization within social and ecological systems. Here we show that, whether such systems are self-organized or not, this behavior is the consequence of the tree-like classification method. Different tree-like classifications (both of real and truly random systems) display a similar statistical behaviour when considering the sizes of their sub-branches.