Inferring the parameters of Taylor's law in ecology

TL;DR

This paper develops statistical methods to accurately estimate the parameters of Taylor's power law in ecology, addressing biases in large-sample inference and providing confidence intervals for diverse ecological data.

Contribution

It introduces asymptotic guarantees and bias corrections for parameter estimation of Taylor's law in nonstationary spatiotemporal ecological data.

Findings

Bias correction improves confidence interval accuracy

Large-sample asymptotics provide statistical guarantees

Methods validated on simulated and real data

Abstract

Taylor's power law (TL) or fluctuation scaling has been verified empirically for the abundances of many species, human and non-human, and in many other fields including physics, meteorology, computer science, and finance. TL asserts that the variance is directly proportional to a power of the mean, exactly for population moments and, whether or not population moments exist, approximately for sample moments. In many papers, linear regression of log variance as a function of log mean is used to estimate TL's parameters. We provide some statistical guarantees with large-sample asymptotics for this kind of inference under general conditions, and we derive confidence intervals for the parameters. In many ecological applications, the means and variances are estimated over time or across space from arrays of abundance data collected at different locations and time points. When the ratio between the time-series length and the number of spatial points converges to a constant as both become large, the usual normalized statistics are asymptotically biased. We provide a bias correction to get correct confidence intervals. TL, widely studied in multiple sciences, is a source of challenging new statistical problems in a nonstationary spatiotemporal framework. We illustrate our results with both simulated and real data sets.