1. Marine Biological Association of the United Kingdom, The Laboratory, Citadel Hill, Plymouth PL1 2PB, UK
2. Marine Biology and Ecology Research Centre, School of Biological Sciences,
3. School of Computing, Communications and Electronics, University of Plymouth, Drake Circus, Plymouth PL4 8AA, UK
4. Department of Biological Sciences, Institute of Environmental Sustainability, Swansea University, Singleton Park, Swansea SA2 8PP, UK
5. School for Environmental Research, Charles Darwin University, Darwin, Northern Territory 0909, Australia
6. Department of Biology and York Centre for Complex Systems Analysis, University of York, York YO10 5YW, UK
7. Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand
8. Gatty Marine Laboratory, School of Biology, University of St Andrews, Fife KY16 8LB, UK
9. School of Zoology, University of Tasmania, Private Bag 05, Hobart, Tasmania 7001, Australia
10. School of Biological Sciences, Royal Holloway, University of London, Egham TW20 0EX, UK
11. Joint Institute for Marine and Atmospheric Research, Pelagic Fisheries Research Programme, University of Hawaii at Manoa, Kewalo Research Facility/NOAA Fisheries, 1125-B Ala Mona Boulevard, Honolulu, Hawaii 96814, USA
12. Centre for Environment, Fisheries and Aquaculture Science, Lowestoft Laboratory, Pakefield Road, Lowestoft NR33 0HT, UK
13. Centre for Ecology and Conservation, University of Exeter in Cornwall, Tremough TR10 9EZ, UK
14. Present address: Research Institute for Climate Change and Sustainability, School of Earth and Environmental Sciences, University of Adelaide, Adelaide, South Australia 5005, Australia.

Correspondence to: David W. Sims^1,2 Correspondence and requests for materials should be addressed to D.W.S. (Email: dws@mba.ac.uk).

Many free-ranging predators have to make foraging decisions with little, if any, knowledge of present resource distribution and availability¹. The optimal search strategy they should use to maximize encounter rates with prey in heterogeneous natural environments remains a largely unresolved issue in ecology^{1, 2, 3}. Lévy walks⁴ are specialized random walks giving rise to fractal movement trajectories that may represent an optimal solution for searching complex landscapes⁵. However, the adaptive significance of this putative strategy in response to natural prey distributions remains untested^{6, 7}. Here we analyse over a million movement displacements recorded from animal-attached electronic tags to show that diverse marine predators—sharks, bony fishes, sea turtles and penguins—exhibit Lévy-walk-like behaviour close to a theoretical optimum². Prey density distributions also display Lévy-like fractal patterns, suggesting response movements by predators to prey distributions. Simulations show that predators have higher encounter rates when adopting Lévy-type foraging in natural-like prey fields compared with purely random landscapes. This is consistent with the hypothesis that observed search patterns are adapted to observed statistical patterns of the landscape. This may explain why Lévy-like behaviour seems to be widespread among diverse organisms³, from microbes⁸ to humans⁹, as a 'rule' that evolved in response to patchy resource distributions.

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