A process-independent explanation for the general form of Taylor's Law

TL;DR

This paper proposes a universal, process-independent explanation for Taylor's Law, showing it arises from basic constraints on population counts and censuses, and is thus a widespread statistical pattern rather than solely ecological.

Contribution

It introduces a feasible set approach that explains the general form of Taylor's Law as a consequence of simple constraints, independent of specific ecological processes.

Findings

Most configurations produce power-law mean-variance relationships with exponents between 1 and 2.

The approach explains the ubiquity of Taylor's Law across systems.

It suggests that the specific exponent varies due to ecological factors, not the underlying pattern.

Abstract

Taylors Law (TL) describes the scaling relationship between the mean and variance of populations as a power-law. TL is widely observed in ecological systems across space and time with exponents varying largely between 1 and 2. Many ecological explanations have been proposed for TL but it is also commonly observed outside ecology. We propose that TL arises from the constraining influence of two primary variables: the number of individuals and the number of censuses or sites. We show that most possible configurations of individuals among censuses or sites produce the power-law form of TL with exponents between 1 and 2. This feasible set approach suggests that TL is a statistical pattern driven by two constraints, providing an a priori explanation for this ubiquitous pattern. However, the exact form of any specific mean-variance relationship cannot be predicted in this way, i.e., this approach does a poor job of predicting variation in the exponent, suggesting that TL may still contain ecological information.