Environmental context explains Lévy and Brownian movement patterns of marine predators



An optimal search theory, the so-called Lévy-flight foraging hypothesis1, predicts that predators should adopt search strategies known as Lévy flights where prey is sparse and distributed unpredictably, but that Brownian movement is sufficiently efficient for locating abundant prey2,3,4. Empirical studies have generated controversy because the accuracy of statistical methods that have been used to identify Lévy behaviour has recently been questioned5,6. Consequently, whether foragers exhibit Lévy flights in the wild remains unclear. Crucially, moreover, it has not been tested whether observed movement patterns across natural landscapes having different expected resource distributions conform to the theory’s central predictions. Here we use maximum-likelihood methods to test for Lévy patterns in relation to environmental gradients in the largest animal movement data set assembled for this purpose. Strong support was found for Lévy search patterns across 14 species of open-ocean predatory fish (sharks, tuna, billfish and ocean sunfish), with some individuals switching between Lévy and Brownian movement as they traversed different habitat types. We tested the spatial occurrence of these two principal patterns and found Lévy behaviour to be associated with less productive waters (sparser prey) and Brownian movements to be associated with productive shelf or convergence-front habitats (abundant prey). These results are consistent with the Lévy-flight foraging hypothesis1,7, supporting the contention8,9 that organism search strategies naturally evolved in such a way that they exploit optimal Lévy patterns.

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Figure 1: Examples of good fits to power-law and truncated power-law distributions.
Figure 2: Behavioural switching between Lévy and Brownian motion in relation to habitat type.
Figure 3: Spatial occurrence of Lévy and Brownian behaviour types.


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This research was facilitated through the European Tracking of Predators in the Atlantic programme in the European Census of Marine Life. Funding was provided by the UK Natural Environment Research Council (NERC) Oceans 2025 Strategic Research Programme (Theme 6 Science for Sustainable Marine Resources), the Save Our Seas Foundation, the Leverhulme Trust, the UK Department for Environment Food and Rural Affairs, Fundação para a Ciência e a Tecnologia grant SFRH/BD/21354/2005, the UK Royal Society, the Fisheries Society of the British Isles, the Údarás na Gaeltachta, the Taighde Mara Teo, the Marine Institute (Ireland), the Irish Research Council for Science Engineering and Technology, the Shark Foundation Switzerland, a University of Aberdeen Scholarship and PADI Project Aware. The tuna research of K.M.S. and D.W.F. was made possible through financial contributions by the Japan Fisheries Agency, the US Tuna Foundation and the Tagging of Pacific Pelagics programme in the Census of Marine Life. M.K.M. was funded by Cooperative Agreements NA37RJ0199 and NA67RJ0154 between the National Oceanic and Atmospheric Administration (US Department of Commerce) and the Pelagic Fisheries Research Program (University of Hawaii). The authors or their agencies do not necessarily approve, recommend or endorse any proprietary hardware or software mentioned in this publication. The views expressed herein are those of the authors and do not necessarily reflect the views of their agencies. For field assistance, D.W.S. thanks P. Harris and D. Uren; T.K.D. thanks V. Roantree, M. Norman, M. Lilley and P. F. O’Súilleabháin; J.M.B. thanks G. Adkison, J.-P. Botha, H. Baensch and A. Cumming. D.W.S. and N.E.H. thank A. Clauset and J. Pitchford for help with maximum-likelihood estimation and log-likelihoods, and E. P. White for manuscript comments. This research complied with all animal welfare laws of the countries or sovereign territories in which it was conducted. C.S.J. was supported by a Royal Society of Edinburgh Sabbatical Fellowship, G.C.H. by a Ray Lankester Investigatorship from the Marine Biological Association of the UK (MBA) and D.W.S. by a UK NERC-funded MBA Senior Research Fellowship.

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D.W.S. designed the study. N.E.H. and D.W.S. completed data analysis with contributions from N.Q. and J.R.M.D. N.E.H. designed and developed the software for MLE and split moving-window analyses. D.W.S. and N.E.H. wrote the paper and all authors contributed to subsequent drafts. Field data were collected by D.W.S., E.J.S., N.Q., N.G.P., M.K.M., K.M.S., D.W.F., J.M.B., T.K.D., J.D.R.H., G.C.H. and V.J.W.

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Correspondence to David W. Sims.

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The authors declare no competing financial interests.

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Humphries, N., Queiroz, N., Dyer, J. et al. Environmental context explains Lévy and Brownian movement patterns of marine predators. Nature 465, 1066–1069 (2010). https://doi.org/10.1038/nature09116

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