Measurement scale in maximum entropy models of species abundance

TL;DR

This paper explains the consistent species abundance distribution across communities using a maximum entropy framework that incorporates a log-linear measurement scale, leading to a gamma distribution that fits observed data well.

Contribution

It introduces a novel application of maximum entropy theory with a log-linear measurement scale to model species abundance distributions, unifying ecological patterns under a common symmetry.

Findings

Species abundance follows a gamma distribution predicted by the model.

The measurement scale transitions from logarithmic to linear with increasing population size.

Variation in samples is explained by the grading point of the measurement scale.

Abstract

The consistency of the species abundance distribution across diverse communities has attracted widespread attention. In this paper, I argue that the consistency of pattern arises because diverse ecological mechanisms share a common symmetry with regard to measurement scale. By symmetry, I mean that different ecological processes preserve the same measure of information and lose all other information in the aggregation of various perturbations. I frame these explanations of symmetry, measurement, and aggregation in terms of a recently developed extension to the theory of maximum entropy. I show that the natural measurement scale for the species abundance distribution is log-linear: the information in observations at small population sizes scales logarithmically and, as population size increases, the scaling of information grades from logarithmic to linear. Such log-linear scaling leads naturally to a gamma distribution for species abundance, which matches well with the observed patterns. Much of the variation between samples can be explained by the magnitude at which the measurement scale grades from logarithmic to linear. This measurement approach can be applied to the similar problem of allelic diversity in population genetics and to a wide variety of other patterns in biology.