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Scaling laws of marine predator search behaviour

Abstract

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 ecology1,2,3. 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 untested6,7. 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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Figure 1: Lévy-like scaling law among diverse marine vertebrates.
Figure 2: Macroscopic properties of a prey field.

References

  1. 1

    Stephens, D. W. & Krebs, J. R. Foraging Theory (Princeton Univ. Press, Princeton, 1986)

    Google Scholar 

  2. 2

    Viswanathan, G. M. et al. Optimizing the success of random searches. Nature 401, 911–914 (1999)

    CAS  Article  ADS  Google Scholar 

  3. 3

    Bartumeus, F., da Luz, M. G. E., Viswanathan, G. M. & Catalan, J. Animal search strategies: a quantitative random-walk analysis. Ecology 86, 3078–3087 (2005)

    Article  Google Scholar 

  4. 4

    Shlesinger, M. F., Zaslavsky, G. M. & Klafter, J. Strange kinetics. Nature 363, 31–37 (1993)

    CAS  Article  ADS  Google Scholar 

  5. 5

    Viswanathan, G. M. et al. Lévy flights in random searches. Physica A 282, 1–12 (2000)

    Article  ADS  Google Scholar 

  6. 6

    Russell, R. W., Hunt, G. L., Coyle, K. O. & Cooney, R. T. Foraging in a fractal environment: spatial patterns in a marine predator-prey system. Landscape Ecol. 7, 195–209 (1992)

    Article  Google Scholar 

  7. 7

    Sims, D. W., Witt, M. J., Richardson, A. J., Southall, E. J. & Metcalfe, J. D. Encounter success of free-ranging marine predator movements across a dynamic prey landscape. Proc. R. Soc. Lond. B 273, 1195–1201 (2006)

    Article  Google Scholar 

  8. 8

    Schuster, F. L. & Levandowsky, M. Chemosensory responses of Acanthamoeba castellani: Visual analysis of random movement and responses to chemical signals. J. Eukaryot. Microbiol. 43, 150–158 (1996)

    CAS  Article  Google Scholar 

  9. 9

    Brockmann, D., Hufnagel, L. & Geisel, T. The scaling laws of human travel. Nature 439, 462–465 (2006)

    CAS  Article  ADS  Google Scholar 

  10. 10

    Sims, D. W. & Quayle, V. A. Selective foraging behaviour of basking sharks on zooplankton in a small-scale front. Nature 393, 460–464 (1998)

    CAS  Article  ADS  Google Scholar 

  11. 11

    Bradshaw, C. J. A., Hindell, M. A., Sumner, M. D. & Michael, K. J. Loyalty pays: potential life history consequences of fidelity to marine foraging regions by southern elephant seals. Anim. Behav. 68, 1349–1360 (2004)

    Article  Google Scholar 

  12. 12

    Houghton, J. D. R., Doyle, T. K., Wilson, M. W., Davenport, J. & Hays, G. C. Jellyfish aggregations and leatherback turtle foraging patterns in a temperate coastal environment. Ecology 87, 1967–1972 (2006)

    Article  Google Scholar 

  13. 13

    Mackus, D. L. & Boyd, C. M. Spectral analysis of zooplankton spatial heterogeneity. Science 204, 62–64 (1979)

    Article  ADS  Google Scholar 

  14. 14

    Makris, N. C. et al. Fish population and behaviour revealed by instantaneous continental shelf-scale imaging. Science 311, 660–663 (2006)

    CAS  Article  ADS  Google Scholar 

  15. 15

    Steele, J. H. The ocean ‘landscape’. Landscape Ecol. 3, 185–192 (1989)

    Article  Google Scholar 

  16. 16

    Bartumeus, F., Catalan, J., Fulco, U. L., Lyra, M. L. & Viswanathan, G. M. Optimizing the encounter rate in biological interactions: Lévy versus Brownian strategies. Phys. Rev. Lett. 88, 097901 (2002)

    CAS  Article  ADS  Google Scholar 

  17. 17

    Sims, D. W., Righton, D. & Pitchford, J. W. Minimizing errors in identifying Lévy flight behaviour of organisms. J. Anim. Ecol. 76, 222–229 (2007)

    Article  Google Scholar 

  18. 18

    Benhamou, S. How many animals really do the Lévy walk? Ecology 88, 1962–1969 (2007)

    Article  Google Scholar 

  19. 19

    Edwards, A. M. et al. Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees or deer. Nature 449, 1044–1048 (2007)

    CAS  Article  ADS  Google Scholar 

  20. 20

    Boyer, D. et al. Scale-free foraging by primates emerges from their interaction with a complex environment. Proc. R. Soc. Lond. B 273, 1743–1750 (2006)

    Article  Google Scholar 

  21. 21

    Bartumeus, F., Peters, F., Pueyo, S., Marrasé, C. & Catalan, J. Helical Lévy walks: adjusting search statistics to resource availability in microzooplankton. Proc. Natl Acad. Sci. USA 100, 12771–12775 (2003)

    CAS  Article  ADS  Google Scholar 

  22. 22

    Bartumeus, F. Lévy processes in animal movement: an evolutionary hypothesis. Fractals 15, 151–162 (2007)

    Article  Google Scholar 

  23. 23

    Ropert-Coudert, Y. & Wilson, R. P. Trends and perspectives in animal-attached remote sensing. Front. Ecol. Environ. 3, 437–444 (2005)

    Article  Google Scholar 

  24. 24

    Myers, A. E. & Hays, G. C. Do leatherback turtles Dermochelys coriacea forage during the breeding season? A combination of data-logging devices provide new insights. Mar. Ecol. Prog. Ser. 322, 259–267 (2006)

    Article  ADS  Google Scholar 

  25. 25

    Bradshaw, C. J. A. & Sims, D. W. Solutions to problems associated with identifying Lévy walk patterns in animal movement data. J. Anim. Ecol. (submitted)

  26. 26

    Viswanathan, G. M. et al. Lévy flight search patterns of wandering albatrosses. Nature 381, 413–415 (1996)

    CAS  Article  ADS  Google Scholar 

  27. 27

    Brierley, A. S. et al. Use of moored acoustic instruments to measure short-term variability in abundance of Antarctic krill. Limnol. Oceanogr. Methods 4, 18–29 (2006)

    Article  Google Scholar 

  28. 28

    Field, I. C., Bradshaw, C. J. A., Burton, H. R., Sumner, M. D. & Hindell, M. A. Resource partitioning through oceanic segregation of foraging juvenile southern elephant seals (Mirounga leonina). Oecologia 142, 127–135 (2005)

    Article  ADS  Google Scholar 

  29. 29

    Perry, G. & Pianka, E. R. Animal foraging: past, present and future. Trends Ecol. Evol. 12, 360–364 (1997)

    CAS  Article  Google Scholar 

  30. 30

    McMahon, C. R. & Hays, G. C. Thermal niche, large-scale movements and implications of climate change for a critically endangered marine vertebrate. Glob. Change Biol. 12, 1330–1338 (2006)

    Article  ADS  Google Scholar 

  31. 31

    Chatfield, C. The Analysis of Time Series 6th edn (Chapman & Hall, London, 1996)

    MATH  Google Scholar 

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Acknowledgements

This research was facilitated through the European Tracking of Predators in the Atlantic (EUTOPIA) programme in the European Census of Marine Life (EuroCoML). Funding was provided by the UK Natural Environment Research Council (NERC) grant-in-aid to the Marine Biological Association of the UK (MBA), the NERC ‘Oceans 2025’ Strategic Research Programme (Theme 6 Science for Sustainable Marine Resources), UK Defra, The Royal Society and the Fisheries Society of the British Isles. D.W.S. thanks G. Budd, P. Harris, N. Hutchinson and D. Uren for field assistance. G.C.H. thanks Ocean Spirits Incorporated, J. Houghton and A. Myers for logistical help in the field. A.S.B. thanks E. Murphy, M. Brandon, R. Saunders, D. Bone and P. Enderlein for their contributions to mooring sampling at South Georgia. NERC Plymouth Marine Laboratory provided L4 zooplankton data. This research complied with all animal welfare laws of the countries or sovereign territories in which it was conducted. D.W.S. was supported by a NERC-funded MBA Research Fellowship.

Author Contributions D.W.S. conceived and planned the study, led the data analysis and wrote the manuscript. All co-authors contributed to subsequent drafts. Field data of animal movements and/or prey distributions were collected by D.W.S., E.J.S., J.D.M., G.C.H., C.J.A.B., A.S.B., M.A.H., D.M., M.K.M., D.R., V.J.W. and R.P.W. The simulation model was conceived by N.E.H. and D.W.S. with N.E.H. writing the programming code. J.W.P. and A.J. were responsible for analysis of projections of 3D Lévy movements, M.Z.A. and E.L.C.S. coded the power spectrum analysis, C.J.A.B. completed the relative likelihood modelling, and G.C.H. and M.J.W. provided additional data analysis.

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Correspondence to David W. Sims.

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The file contains Supplementary Figures S1- S3 with Legends and additional references. (PDF 1323 kb)

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Sims, D., Southall, E., Humphries, N. et al. Scaling laws of marine predator search behaviour. Nature 451, 1098–1102 (2008). https://doi.org/10.1038/nature06518

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