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Lévy flight patterns are predicted to be an emergent property of a bumblebees’ foraging strategy

  • Andy M. ReynoldsEmail author
Original Paper

Abstract

Bumblebees forage uninterrupted for long periods of time because they are not distracted by sex or territorial defense and have few predators. This has led to a long running debate about whether bumblebees forage optimally. This debate has been enriched by the possibility that bumblebees foraging within clover patches have flight patterns that can be approximated by Lévy flights. Such flight patterns optimise the success of random searches. Bumblebees foraging within a flower patch tend to approach the nearest flower but then often depart without landing or probing it if it has been visited previously; unvisited flowers are not rejected in this manner. Here, this foraging behaviour has been replicated in numerical simulations. Lévy flight patterns are found to be an inconsequential emergent property of a bumblebees’ foraging behaviour. Lévy flights are predicted to emerge when bees reject at least 99% of previously visited flowers. A foraging bumblebee can certainly empty a clover flower head of nectar in one visit, but lower rates of rejection are observed for many other flowers. These findings suggest that Lévy flight patterns in foraging bumblebees are rare and specific to a few flower species and that if they exist, then they are not part of an innate, evolved optimal searching strategy.

Keywords

Bumblebees Emergence Foraging behaviours Heavy tails Lévy flights 

Notes

Acknowledgements

Rothamsted Research receives grant-aided support from the Biotechnology and Biological Sciences Research Council. I thank Juliet Osborne and Andrew Martin for many constructive comments about the behaviour of foraging bumblebees.

References

  1. Boyer D, Ramos-Fernandez G, Miramontes O, Mateos JL, Cocho G, Larralde H, Ramos H, Rojas F (2006) Scale-free foraging by primates emerges from their interaction with a complex environment. Proc R Soc B 273:1743–1750CrossRefPubMedGoogle Scholar
  2. Cresswell JE, Osborne JL (2004) The effect of patch size and separation on bumblebee foraging in oilseed rape: implications for gene flow. J Appl Ecol 41:539–546CrossRefGoogle Scholar
  3. Edwards AM, Phillips RA, Watkins NW, Freeman MP, Murphy EJ, Afanasyev V, Buldyrev SV, da Luz MGE, Raposo EP, Stanley HE, Viswanathan GM (2007) Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer. Nature 449:1044–1048CrossRefPubMedGoogle Scholar
  4. Giufra M, Nunez JA (1992) Honeybees mark with scent and reject recently visited flowers. Oecologia 89:113–117CrossRefGoogle Scholar
  5. Goulson D, Stout JC, Langley J, Hughes WOH (2000) Identity and function of scent marks deposited by foraging bumblebees. J Chem Ecol 26:2897–2911CrossRefGoogle Scholar
  6. Guy GA, Bohan DA, Powers SJ, Reynolds AM (2008) Avoidance of conspecific odour by carabid beetles: a mechanism for the emergence of scale-free searching patterns. Anim Behav 76:585–591CrossRefGoogle Scholar
  7. Heinrich B (1979) Resource heterogeneity and patterns of movement of foraging bumblebees. Oecologia 40:235–245CrossRefGoogle Scholar
  8. Heinrich B (1983) Do bumblebees forage optimally, and does it matter? Am Zool 23:273–281Google Scholar
  9. Ings TC, Chittka L (2008) Speed accuracy tradeoffs and false alarms in bee responses to cryptic predators. Curr Biol 18:1520–1524CrossRefPubMedGoogle Scholar
  10. Levin SA (1992) The problem of pattern and scale in ecology. Ecology 73:1943–1967CrossRefGoogle Scholar
  11. Pyke GH (1978) Optimal foraging: Movement patterns of bumblebees between inflorescences. Theor Popul Biol 13:72–98CrossRefPubMedGoogle Scholar
  12. Reynolds AM (2007) Avoidance of conspecific odour trails results in scale-free movement patterns and the execution of an optimal searching strategy. Europhys Lett 79, article 30006Google Scholar
  13. Reynolds AM (2008) Deterministic walks with inverse-square power-law scaling are an emergent property of predators that use chemotaxis to locate randomly distributed prey. Phys Rev E 78, article 011906Google Scholar
  14. Reynolds AM, Bartumeus F (2009) Optimizing the success of random destructive searches: Lévy walks can outperform ballistic motions. J Theor Biol (in press)Google Scholar
  15. Reynolds AM, Smith AD, Menzel R, Greggers U, Reynolds DR, Riley JR (2007a) Displaced honeybees perform optimal scale-free search flights. Ecology 88:1955–1961CrossRefPubMedGoogle Scholar
  16. Reynolds AM, Smith AD, Reynolds DR, Carreck NL, Osborne JL (2007b) Honeybees perform optimal scale-free searching flights when attempting to locate a food source. J Exp Biol 210:3763–3770CrossRefPubMedGoogle Scholar
  17. Saleh N, Chittka L (2006) The importance of experience in the interpretation of conspecific chemical signals. Behav Ecol Sociobiol 61:215–220CrossRefGoogle Scholar
  18. Santos MC, Boyer D, Miramontes O, Viswanathan GM, Raposo EP, Mateos JL, da Luz MGE (2007) The origin of power-law distributions in deterministic walks: The influence of landscape geometry. Phys Rev E 75:061114CrossRefGoogle Scholar
  19. Stout JC, Goulson D (2001) The use of conspecific and interspecific scent marks by foraging bumblebees and honeybees. Anim Behav 62:183–189CrossRefGoogle Scholar
  20. Stout JC, Goulson D, Allen JA (1998) Repellent scent-marking of flowers by a guild of foraging bumblebees (Bombus supp.). Behav Ecol Sociobiol 43:317–326CrossRefGoogle Scholar
  21. Viswanathan GM, Buldyrev SV, Havlin S, da Luz MGE, Raposo EP, Stanley HE (1999) Optimizing the success of random searches. Nature 401:911–914CrossRefPubMedGoogle Scholar
  22. Waddington KD (1980) Flight patterns of foraging bees relative to density of artificial flowers and distribution of nectar. Oecologia 44:199–204CrossRefGoogle Scholar
  23. Waddington KD (1981) Factors influencing pollen flow in bumblebee-pollinated Delphinium virescens. Oikos 37:153–159CrossRefGoogle Scholar
  24. White EP, Enquist BJ, Green JL (2008) On estimating the exponent of power-law frequency distributions. Ecology 89:905–912CrossRefPubMedGoogle Scholar
  25. Williams CS (1998) The identity of the previous visitor influences flower rejection by nectar-collecting bees. Anim Behav 56:673–681CrossRefPubMedGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Rothamsted ResearchHarpendenUK

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