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Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer

Nature volume 449, pages 1044–1048 (2007)Cite this article

Abstract

The study of animal foraging behaviour is of practical ecological importance1, and exemplifies the wider scientific problem of optimizing search strategies2. Lévy flights are random walks, the step lengths of which come from probability distributions with heavy power-law tails3,4, such that clusters of short steps are connected by rare long steps. Lévy flights display fractal properties, have no typical scale, and occur in physical3,4,5 and chemical6 systems. An attempt to demonstrate their existence in a natural biological system presented evidence that wandering albatrosses perform Lévy flights when searching for prey on the ocean surface7. This well known finding2,4,8,9 was followed by similar inferences about the search strategies of deer10 and bumblebees10. These pioneering studies have triggered much theoretical work in physics (for example, refs 11, 12), as well as empirical ecological analyses regarding reindeer13, microzooplankton14, grey seals15, spider monkeys16 and fishing boats17. Here we analyse a new, high-resolution data set of wandering albatross flights, and find no evidence for Lévy flight behaviour. Instead we find that flight times are gamma distributed, with an exponential decay for the longest flights. We re-analyse the original albatross data7 using additional information, and conclude that the extremely long flights, essential for demonstrating Lévy flight behaviour, were spurious. Furthermore, we propose a widely applicable method to test for power-law distributions using likelihood18 and Akaike weights19,20. We apply this to the four original deer and bumblebee data sets10, finding that none exhibits evidence of Lévy flights, and that the original graphical approach10 is insufficient. Such a graphical approach has been adopted to conclude Lévy flight movement for other organisms13,14,15,16,17, and to propose Lévy flight analysis as a potential real-time ecosystem monitoring tool17. Our results question the strength of the empirical evidence for biological Lévy flights.

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Figure 1: Rank/frequency plot 23 of 2004 wandering albatross data, showing no evidence for Lévy flight behaviour.
Figure 2: Data for the six wandering albatross trips in 1992 that have known departure and return times.
Figure 3: When corrected, the 1992 wandering albatross flight durations no longer follow a power law.
Figure 4: Foraging times of deer previously concluded to demonstrate Lévy flight behaviour10.

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Acknowledgements

We thank P. Rothery, W. Blanchard and L. Thomas for statistical advice, and R. Myers, I. Jonsen, G. Breed, S.-J. Dunn, F. de Moura, J. Cressoni and M. Lyra for discussions. We acknowledge the work by all fieldworkers involved, in particular thanking B. Phalan and I. Forster for deploying devices at Bird Island. We thank M. Francis, A. Fukuda and H. Higuchi for providing instruments used in 2004, and J. Croxall for supporting albatross research at Bird Island. This work was funded by the UK Natural Environment Research Council and the Brazilian research agency CNPq. The work at the British Antarctic Survey represents a collaboration between the Discovery 2010 and Natural Complexity Programmes, and we appreciate P. Trathan’s efforts in facilitating it.

Author Contributions A.M.E. performed the analyses, computations and derivations presented in this paper, and led its preparation with input from all authors. The paper presents a synthesis of the work of two different teams of researchers who independently and concurrently conceived of re-examining the Lévy flight hypothesis with newer albatross data. One team (A) comprised N.W.W., M.P.F. and E.J.M. and was subsequently joined by A.M.E. The other team (B) comprised V.A., S.V.B., M.G.E.dL., E.P.R., H.E.S. and G.M.V.; R.A.P. provided albatross expertise to both teams. Team B were the first to show the implication of the long first and last dry sequences on the power-law distribution of albatross flight durations.

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  1. Andrew M. Edwards

    Present address: Present address: Pacific Biological Station, Fisheries and Oceans Canada, 3190 Hammond Bay Road, Nanaimo, British Columbia V9T 6N7, Canada.,

Authors and Affiliations

  1. British Antarctic Survey, High Cross, Madingley Road, Cambridge CB3 0ET, UK ,

    Andrew M. Edwards, Richard A. Phillips, Nicholas W. Watkins, Mervyn P. Freeman, Eugene J. Murphy & Vsevolod Afanasyev

  2. Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA,

    Sergey V. Buldyrev & H. Eugene Stanley

  3. Department of Physics, Yeshiva University, 500 West 185th Street, Room 1112, Belfer Hall, New York, New York 10033, USA,

    Sergey V. Buldyrev

  4. Departamento de Física, Universidade Federal do Paraná, C. P. 19044, 81531-990, Curitiba-PR, Brazil,

    M. G. E. da Luz

  5. Departamento de Física, Laboratório de Física Teórica e Computacional, Universidade Federal de Pernambuco, 50670-901, Recife-PE, Brazil,

    E. P. Raposo

  6. Instituto de Física, Universidade Federal de Alagoas, 57072-970, Maceió-AL, Brazil ,

    Gandhimohan M. Viswanathan

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The file contains extensive Supplementary Methods, Supplementary Tables 1-2 and Supplementary Figures 1-6 with Legends. (PDF 4331 kb)

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Edwards, A., Phillips, R., Watkins, N. et al. Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer. Nature 449, 1044–1048 (2007). https://doi.org/10.1038/nature06199

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