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Strong anomalous diffusion for free-ranging birds

Natural and anomalous diffusion are widely observed and used to explore causes and consequences of movement across organisms, resulting in extensive use of the mean and mean-squared displacement (MSD). Using high-resolution data from over 70 million localizations of young and adult free-ranging Barn Owls (\textit{Tyto alba}), we demonstrate the necessity of a broad spectrum of displacement moments to characterize bird movement across scales. The mean and MSD -- interchangeable with moments $q=1$ and 2 -- are insufficient special cases. We reveal empirical strong anomalous diffusion as a nonlinear growth of displacement moments according to $\left<|x(t)|^q\right> \sim t^{\lambda(q)}$. The moment spectrum function $\lambda(q)$ displays piecewise linearity with a critical moment marking the crossover point between two scaling regimes, linked to a combination of age-specific behavioral modes. A critical timescale of five minutes marks an unexpected transition from a convex $\lambda_s(q)$ to a concave $\lambda_\ell(q)$, related to environmental and behavioral constraints. Using two stochastic models of varying ecological complexity, we demonstrate that strong anomalous diffusion may be widespread in animal movement, underscoring the importance of expanding analysis beyond the average and MSD.

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