Unravelling the origins of anomalous diffusion: from molecules to migrating storks

TL;DR

This paper presents a method to analyze the origins of anomalous diffusion across diverse systems, revealing underlying effects like correlations, fat-tailed distributions, and non-stationarity, with implications for biology and ecology.

Contribution

It introduces a novel decomposition technique to identify the fundamental causes of anomalous transport in empirical data from microscopic to macroscopic scales.

Findings

Decomposition into Joseph, Noah, and Moses effects elucidates diffusion origins.

Method applied to systems spanning 12 orders of magnitude in length.

Provides behavioral predictions and resolves open questions in biology and ecology.

Abstract

Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of the mean-squared displacement on the measurement time, is ubiquitous in nature. It has been observed in processes ranging from microscopic movement of molecules to macroscopic, large-scale paths of migrating birds. Using data from multiple empirical systems, spanning 12 orders of magnitude in length and 8 orders of magnitude in time, we employ a method to detect the individual underlying origins of anomalous diffusion and transport in the data. This method decomposes anomalous transport into three primary effects: long-range correlations ("Joseph effect"), fat-tailed probability density of increments ("Noah effect"), and non-stationarity ("Moses effect"). We show that such a decomposition of real-life data allows to infer nontrivial behavioral predictions, and to resolve open questions in the fields of single particle tracking in living cells and movement ecology.