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,. However, these measures, corresponding to specific displacement moments, do not capture the full complexity of movement behavior. Using high-resolution data from more than 70 million localizations of young and adult free-ranging barn owls (Tyto alba), we reveal strong anomalous diffusion as nonlinear growth of displacement moments. The moment spectrum function λt(q), defined by 〈|x(t)|q〉∼tλt(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 5 minutes marks an unexpected transition from a convex to a concave λt(q). Using two stochastic models, a bounded Lévy walk and a multimode 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 Lévy-walklike patterns can arise from the underlying behavioral structure. Finally, we discuss the ecological significance of our results, arguing that strong anomalous diffusion may be widespread in animal movement.