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arXiv · 2411.04684

Strong anomalous diffusion for free-ranging birds

Ohad Vilk·Motti Charter·Sivan Toledo·Eli Barkai·Ran Nathan
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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.

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Ohad Vilk, Motti Charter, Sivan Toledo, Eli Barkai, Ran Nathan. 2024-11-07. Strong anomalous diffusion for free-ranging birds. https://arxiv.org/abs/2411.04684

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