Strong anomalous diffusion for free-ranging birds

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.