Strong Anomalous Diffusion for Free-Ranging Birds

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 (), we reveal strong anomalous diffusion as nonlinear growth of displacement moments. The moment spectrum function <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>λ</a:mi><a:mi>t</a:mi></a:msub><a:mrow><a:mo>(</a:mo><a:mi>q</a:mi><a:mo>)</a:mo></a:mrow></a:mrow></a:math>, defined by <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:msup><b:mrow><b:mo>〈</b:mo><b:mo>|</b:mo><b:mi mathvariant="bold-italic">x</b:mi><b:mrow><b:mo>(</b:mo><b:mi>t</b:mi><b:mo>)</b:mo></b:mrow><b:mo>|</b:mo></b:mrow><b:mi>q</b:mi></b:msup><b:mrow><b:mo>〉</b:mo><b:mo>∼</b:mo></b:mrow><b:msup><b:mi>t</b:mi><b:mrow><b:msub><b:mi>λ</b:mi><b:mi>t</b:mi></b:msub><b:mrow><b:mo>(</b:mo><b:mi>q</b:mi><b:mo>)</b:mo></b:mrow></b:mrow></b:msup></b:mrow></b:math>, displays piecewise linearity in <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>q</d:mi></d:math>, 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:msub><e:mi>λ</e:mi><e:mi>t</e:mi></e:msub><e:mrow><e:mo>(</e:mo><e:mi>q</e:mi><e:mo>)</e:mo></e:mrow></e:mrow></e:math>. 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.