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J Theor Biol. 2014 Oct 7;358:179-93. doi: 10.1016/j.jtbi.2014.05.032. Epub 2014 Jun 2.

Optimal foraging strategies: Lévy walks balance searching and patch exploitation under a very broad range of conditions.

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Marine Biological Association of the United Kingdom, The Laboratory, Citadel Hill, Plymouth PL1 2PB, UK. Electronic address:
Marine Biological Association of the United Kingdom, The Laboratory, Citadel Hill, Plymouth PL1 2PB, UK; Ocean and Earth Science, National Oceanography Centre Southampton, University of Southampton, Waterfront Campus, Southampton SO14 3ZH, UK; Centre for Biological Sciences, Building 85, University of Southampton, Highfield Campus, Southampton SO17 1BJ, UK.


While evidence for optimal random search patterns, known as Lévy walks, in empirical movement data is mounting for a growing list of taxa spanning motile cells to humans, there is still much debate concerning the theoretical generality of Lévy walk optimisation. Here, using a new and robust simulation environment, we investigate in the most detailed study to date (24×10(6) simulations) the foraging and search efficiencies of 2-D Lévy walks with a range of exponents, target resource distributions and several competing models. We find strong and comprehensive support for the predictions of the Lévy flight foraging hypothesis and in particular for the optimality of inverse square distributions of move step-lengths across a much broader range of resource densities and distributions than previously realised. Further support for the evolutionary advantage of Lévy walk movement patterns is provided by an investigation into the 'feast and famine' effect, with Lévy foragers in heterogeneous environments experiencing fewer long 'famines' than other types of searchers. Therefore overall, optimal Lévy foraging results in more predictable resources in unpredictable environments.


Composite Brownian; Movement; Power-law; Predator; Simulation

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