Geodesy

Quantum mechanics

Scale (ratio)

Materials science

Displacement (psychology)

Anomalous diffusion

Tracking (education)

Mean squared displacement

Astrophysics

Pedagogy

Range (aeronautics)

Computer science

Magnitude (astronomy)

Statistical physics

Geology

Physics

Nonlinear system

Diffusion

Psychology

Molecular dynamics

Psychotherapist

Ranging

Composite material

Innovation diffusion

Knowledge management

Physical Review Research

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 nonstationarity (``Moses effect''). We show that such a decomposition of real-life data allows us to infer nontrivial behavioral predictions and to resolve open questions in the fields of single-particle tracking in living cells and movement ecology.

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