Power-law versus exponential distributions of animal group sizes

TL;DR

This paper demonstrates that animal group sizes follow a power-law distribution with an exponent of 1, truncated at a cutoff size related to individual group engagement, supported by a simple aggregation model and empirical data.

Contribution

It introduces a simple binary splitting and coalescing model that predicts the power-law distribution of animal group sizes, clarifying previous misconceptions.

Findings

Animal group sizes follow a power-law decay with exponent 1.

The distribution is truncated at a size related to individual group engagement.

Empirical data from fishes and mammals support the model.

Abstract

There has been some confusion concerning the animal group-size: an exponential distribution was deduced by maximizing the entropy; lognormal distributions were practically used; a power-law decay with exponent {3/2} was proposed in physical analogy to aerosol condensation. Here I show that the animal group-size distribution follows a power-law decay with exponent 1, and is truncated at a cut-off size which is the expected size of the groups an arbitrary individual engages in. An elementary model of animal aggregation based on binary splitting and coalescing on contingent encounter is presented. The model predicted size distribution holds for various data from pelagic fishes and mammalian herbivores in the wild.