# Newcomb-Benford number law and ecological processes

## TL;DR

This paper explores how the Newcomb-Benford number law can reveal patterns in ecological systems, helping detect changes and stability.

## Contribution

The paper introduces novel applications of Benford's law to ecological data for detecting state transitions and divergence.

## Key findings

- Benford's law shows statistical correspondence with ecological systems in dynamic equilibrium.
- Case studies demonstrate its use in detecting impending state transitions in marginally stable systems.
- Kullback-Leibler entropy measures reveal temporal and spatial divergence in ecological data.

## Abstract

The Newcomb-Benford number law has found applications in the natural and social sciences for decades, with limited ecological attention. The aim of this communication is to highlight a statistical correspondence between the first significant digit frequencies of the Benford probability distribution and ecological systems in a balanced state of dynamic equilibrium. Analytical methods, including multidimensional Euclidean distance, Cohen-W effect size, Kossovsky sum of squared deviations (SSD), and Pearson residuals are presented to facilitate the identification of this canonical representation across multiple levels of ecological organization and scale. Case studies reveal novel applications of the Benford distribution for detecting impending state transitions in marginally stable systems, as well as temporal and spatial divergence of ecological information through the measurement of Kullback-Leibler relative entropy. Widespread documentation of the leading digit phenomenon is expected as ecologists revisit empirical datasets and formalize sampling protocols for its detection. The conversion of randomly collected sets of arithmetic data into logarithmic probabilities of first significant digits presents unique opportunities to advance our understanding of ecological processes related with stability, complexity, and maturity.