Strong anomalous diffusion for free-ranging birds

TL;DR

This study reveals strong anomalous diffusion in free-ranging Barn Owls, characterized by nonlinear displacement moments and a crossover timescale, highlighting complex movement behaviors linked to ecological factors and modeled by stochastic processes.

Contribution

It introduces the concept of strong anomalous diffusion in animal movement, demonstrating nonlinear displacement moments and a critical timescale, supported by stochastic models that relate behavior to movement patterns.

Findings

Displacement moments grow nonlinearly, indicating strong anomalous diffusion.

A critical moment marks a crossover between different scaling regimes.

A five-minute timescale signifies a transition in movement behavior.

Abstract

Diffusion and anomalous diffusion are widely observed and used to study movement across organisms, resulting in extensive use of the mean and mean-squared displacement (MSD). However, these measures - corresponding to specific displacement moments - do not capture the full complexity of movement behavior. Using high-resolution data from over 70 million localizations of young and adult free-ranging Barn Owls (\textit{Tyto alba}), we reveal strong anomalous diffusion as nonlinear growth of displacement moments. The moment spectrum function $\lambda_t(q)$ -- defined by $\left<|\bm{x}(t)|^q\right> \sim t^{\lambda_t(q)}$ -- displays piecewise linearity in $q$, with a critical moment marking the crossover between scaling regimes. This highlights the need of a broad spectrum of displacement moments to characterize movement, which we link to age-specific ecological drivers. Furthermore, a characteristic timescale of five minutes marks an unexpected transition from a convex to a concave $\lambda_t(q)$. Using two stochastic models - a bounded L\'evy walk and a multi-mode behavioral model - we account for the observed phenomena, showing good agreement with data, relating age-specific behavioral states to environmentally confined movement, and demonstrating how L\'evy walk-like patterns can arise from underlying behavioral structure. Finally, we discuss the ecological significance of our results, arguing that strong anomalous diffusion may be widespread in animal movement.