Lévy flight foraging hypothesis

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]

Background

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]

References

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. doi:10.1016/j.plrev.2008.03.002.
2. Buchanan, Mark (4 June 2008). "Ecological modelling: The mathematical mirror to animal nature". Nature 453: 714–716. doi:10.1038/453714a.
3. Viswanathan, G. M.; Buldyrev, Sergey V.; Havlin, Shlomo; da Luz, M. G. E.; Raposo, E. P.; Stanley, H. Eugene (28 October 1999). "Optimizing the success of random searches". Nature 401 (6756): 911–914. doi:10.1038/44831.
4. Edwards, A. M.; Phillips, R. A.; Watkins, N. W.; Freeman, M. P.; Murphy, E. J.; Afanasyev, V.; Buldyrev, Sergey V.; da Luz, M. G. E.; Raposo, E. P.; Stanley, H. Eugene; Viswanathan, G. M. (25 October 2007). "Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer". Nature 449: 1044–1048. doi:10.1038/nature06199.
5. Sims, David W.; Southall, Emily J., Humphries, Nicolas E., Hays, Graeme C., Bradshaw, Corey J. A., Pitchford, Jonathan W., James, Alex, Ahmed, Mohammed Z., Brierley, Andrew S., Hindell, Mark A., Morritt, David, Musyl, Michael K., Righton, David, Shepard, Emily L. C., Wearmouth, Victoria J., Wilson, Rory P., Witt, Matthew J., Metcalfe, Julian D. "Scaling laws of marine predator search behaviour". Nature 451 (7182): 1098–1102. doi:10.1038/nature06518. Cite uses deprecated parameter |coauthors= (help)
6. Humphries, Nicolas E.; Queiroz, Nuno, Dyer, Jennifer R. M., Pade, Nicolas G., Musyl, Michael K., Schaefer, Kurt M., Fuller, Daniel W., Brunnschweiler, Juerg M., Doyle, Thomas K., Houghton, Jonathan D. R., Hays, Graeme C., Jones, Catherine S., Noble, Leslie R., Wearmouth, Victoria J., Southall, Emily J., Sims, David W. "Environmental context explains Lévy and Brownian movement patterns of marine predators". Nature 465 (7301): 1066–1069. doi:10.1038/nature09116. PMID 20531470. Cite uses deprecated parameter |coauthors= (help)
7. Raichlen, David A.; Wood, Brian M.; Gordon, Adam D.; Maballa, Audax Z.P.; Marlowe, Frank W.; Pontzer, H. (2014). "Evidence of Lévy walk foraging patterns in human hunter-gatherers". Proceedings of the National Academy of Sciences 111: 728–733. doi:10.1073/pnas.1318616111.
8. Sims, David W.; Reynolds, Andrew M.; Humphries, Nicholas E.; Southall, Emily J.; Wearmouth, Victoria J.; Metcalfe, Brett; Twitchett, Richard J. (14 July 2014). "Hierarchical random walks in trace fossils and the origin of optimal search behavior". Proceedings of the National Academy of Sciences. doi:10.1073/pnas.1405966111. Retrieved 16 July 2014.
9. Clauset, Aaron; Shalizi, Cosma R.; Newman, Mark E.J. (2009). "Power-law distributions in empirical data". SIAM Review 51: 661–703. doi:10.1137/070710111.
10. Sims, David W.; Humphries, Nicolas E.; Bradford, Russell W.; Bruce, Barry D. "Lévy flight and Brownian search patterns of a free-ranging predator reflect different prey field characteristics". Journal of Animal Ecology 81: 432–442. doi:10.1111/j.1365-2656.2011.01914.x.
11. Humphries, Nicolas E.; Weimerskirch, H.; Queiroz, N.; Southall, Emily J.; Sims, David W. (2012). "Foraging success of biological Lévy flights recorded in situ". Proceedings of the National Academy of Sciences 109: 7169–7174. doi:10.1073/pnas.1121201109.
12. Humphries, Nicolas E.; Weimerskirch, Henri; Sims, David W. (2013). "A new approach for objective identification of turns and steps in organism movement data relevant to random walk modelling". Methods in Ecology and Evolution 4: 480–490. doi:10.1111/2041-210X.12096.