Self-organized criticality of aggregated animals attributed to Tweedie convergence

Abstract

Ecologists have had an ongoing interest in a variance to mean power law that governs the clustering of individuals of animal and plant species. This same power law has been reported from disparate biological, physical and mathematical systems, and also characterizes a family of statistical distributions known as the Tweedie exponential dispersion models. Its widespread appearance can be explained by fundamental statistical convergence effects on random data that cause this, and related, power laws to emerge and provide mechanistic insight into its origin, as well as the origin of 1/$f$ noise, multifractality and other phenomena attributable to self-organized criticality. A meta-analysis of ecological field data was conducted here to examine how such statistical convergence might affect the power law. These findings provided conjectural insight into a form of self-organized criticality, driven and modulated by the statistical convergence of random data, which could underlie the power law’s emergence.