Lévy flight foraging hypothesis

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The Lévy flight foraging hypothesis is a hypothesis in the field of biology that may be stated as follows:

Since Lévy flights and walks can optimize search efficiencies, therefore natural selection should have led to adaptations for Lévy flight foraging.[1]


The movement of animals closely resembles in many ways the random walks of dust particles in a fluid.[2] This similarity led to interest in trying to understand how animals move via the analogy to Brownian motion. This conventional wisdom held until the early 1990s. However, starting in the late 1980s, evidence began to accumulate that did not fit the theoretical predictions.[2]

In 1999, a theoretical investigation of the properties of Lévy flights showed that an inverse square distribution of flight times or distances could optimize the search efficiency under certain circumstances.[3] Specifically, a search based on a Lévy walk, consisting of a constant velocity search following a Lévy flight path, is optimal for searching sparsely and randomly distributed revisitable targets in the absence of memory. The team of researchers, consisting of Gandhimohan M. Viswanathan, Sergey V. Buldyrev, Marcos Gomes E. da Luz, Shlomo Havlin, Ernesto P. Raposo and H. Eugene Stanley, published these results in 1999 in the journal Nature.

There has been some controversy about the reality of Lévy flight foraging. Early studies were limited to a small range of movement, and thus the type of motion could not be unequivocally determined; and in 2007 flaws were found in a study of wandering albatrosses which was the first empirical example of such a strategy.[4] There are however many new studies backing the Lévy flight foraging hypothesis.[5][6][7][8]

Recent studies use newer statistical methods[9] and larger data sets showing longer movement paths.[10] Studies published in 2012 and 2013 re-analysed wandering albatross foraging paths and concluded strong support for truncated Lévy flights and Brownian walks consistent with predictions of the Lévy flight foraging hypothesis.[11][12]


  1. ^ Viswanathan, G.M.; Raposo, E.P.; da Luz, M.G.E. (September 2008). "Lévy flights and superdiffusion in the context of biological encounters and random searches". Physics of Life Reviews. 5 (3): 133–150. Bibcode:2008PhLRv...5..133V. doi:10.1016/j.plrev.2008.03.002.
  2. ^ a b Buchanan, Mark (5 June 2008). "Ecological modelling: The mathematical mirror to animal nature". Nature. Springer Nature. 453 (7196): 714–716. doi:10.1038/453714a. ISSN 0028-0836. PMID 18528368.
  3. ^ Viswanathan, G. M.; Buldyrev, Sergey V.; Havlin, Shlomo; da Luz, M. G. E.; Raposo, E. P.; et al. (1999). "Optimizing the success of random searches". Nature. Springer Nature. 401 (6756): 911–914. Bibcode:1999Natur.401..911V. doi:10.1038/44831. ISSN 0028-0836.
  4. ^ Edwards, Andrew M.; Phillips, Richard A.; Watkins, Nicholas W.; Freeman, Mervyn P.; Murphy, Eugene J.; et al. (25 October 2007). "Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer" (PDF). Nature. Springer Nature. 449 (7165): 1044–1048. Bibcode:2007Natur.449.1044E. doi:10.1038/nature06199. ISSN 0028-0836. PMID 17960243.
  5. ^ Sims, David W.; Southall, Emily J.; Humphries, Nicolas E.; Hays, Graeme C.; Bradshaw, Corey J. A.; et al. (2008). "Scaling laws of marine predator search behaviour". Nature. Springer Nature. 451 (7182): 1098–1102. Bibcode:2008Natur.451.1098S. doi:10.1038/nature06518. ISSN 0028-0836.
  6. ^ Humphries, Nicolas E.; Queiroz, Nuno; Dyer, Jennifer R. M.; Pade, Nicolas G.; Musyl, Michael K.; et al. (2010). "Environmental context explains Lévy and Brownian movement patterns of marine predators". Nature. Springer Nature. 465 (7301): 1066–1069. Bibcode:2010Natur.465.1066H. doi:10.1038/nature09116. ISSN 0028-0836. PMID 20531470.
  7. ^ Raichlen, D. A.; Wood, B. M.; Gordon, A. D.; Mabulla, A. Z. P.; Marlowe, F. W.; et al. (23 December 2013). "Evidence of Levy walk foraging patterns in human hunter-gatherers". Proceedings of the National Academy of Sciences. Proceedings of the National Academy of Sciences. 111 (2): 728–733. Bibcode:2014PNAS..111..728R. doi:10.1073/pnas.1318616111. ISSN 0027-8424. PMC 3896191.
  8. ^ Sims, D. W.; Reynolds, A. M.; Humphries, N. E.; Southall, E. J.; Wearmouth, V. J.; et al. (14 July 2014). "Hierarchical random walks in trace fossils and the origin of optimal search behavior". Proceedings of the National Academy of Sciences. Proceedings of the National Academy of Sciences. 111 (30): 11073–11078. Bibcode:2014PNAS..11111073S. doi:10.1073/pnas.1405966111. ISSN 0027-8424. PMC 4121825. PMID 25024221.
  9. ^ Clauset, Aaron; Shalizi, Cosma Rohilla; Newman, M. E. J. (4 November 2009). "Power-Law Distributions in Empirical Data". SIAM Review. Society for Industrial & Applied Mathematics (SIAM). 51 (4): 661–703. arXiv:0706.1062. doi:10.1137/070710111. ISSN 0036-1445.
  10. ^ Sims, David W.; Humphries, Nicolas E.; Bradford, Russell W.; Bruce, Barry D. (17 October 2011). "Lévy flight and Brownian search patterns of a free-ranging predator reflect different prey field characteristics". Journal of Animal Ecology. Wiley. 81 (2): 432–442. doi:10.1111/j.1365-2656.2011.01914.x. ISSN 0021-8790.
  11. ^ Humphries, N. E.; Weimerskirch, H.; Queiroz, N.; Southall, E. J.; Sims, D. W. (23 April 2012). "Foraging success of biological Levy flights recorded in situ". Proceedings of the National Academy of Sciences. Proceedings of the National Academy of Sciences. 109 (19): 7169–7174. Bibcode:2012PNAS..109.7169H. doi:10.1073/pnas.1121201109. ISSN 0027-8424. PMC 3358854. PMID 22529349.
  12. ^ Humphries, Nicolas E.; Weimerskirch, Henri; Sims, David W. (2013). Freckleton, Robert (ed.). "A new approach for objective identification of turns and steps in organism movement data relevant to random walk modelling". Methods in Ecology and Evolution. Wiley: 480–490. doi:10.1111/2041-210x.12096. ISSN 2041-210X.

Further reading[edit]

  • Viswanathan, Gandhimohan. M.; Luz, Marcos G. E. da; Raposo, Ernesto P.; Stanley, H. Eugene (2011). The Physics of Foraging: An Introduction to Random Searches and Biological Encounters. Cambridge University Press. ISBN 9781139497558.
  • Kagan, Eugene; Ben-Gal, Irad (2015). Search and foraging : individual motion and swarm dynamics. CRC Press. ISBN 9781482242102.
  • Reynolds, Andy (September 2015). "Liberating Lévy walk research from the shackles of optimal foraging". Physics of Life Reviews. 14: 59–83. doi:10.1016/j.plrev.2015.03.002.