Hunter–Gatherers Optimize Their Foraging Patterns Using Lévy Flights

  • Clifford T. Brown
  • Larry S. Liebovitch
  • Rachel Glendon


We present evidence that human hunter-gatherers employ foraging movement patterns that are described by the statistics of Lévy flights rather than by conventional Gaussian statistics. Human movement across the landscape is not usually considered an anthropological problem as such. For example, Green (1987, p. 273) observed that the way foragers move between resource patches has been the subject of little quantitative work. Nevertheless, movement patterns influence not only foraging itself but also cultural diffusion, demic diffusion, gene flow, and perhaps migration into virgin territory. So the discovery of Lévy flights in foraging patterns carries implications for various theories in anthropology, including optimal foraging theory as applied to hunter-gatherers and by extension for archeological models of human subsistence settlement systems in prehistory. Moreover, it may help us understand the processes of diffusion and migration. Here, however, we focus our discussion on the implications for optimal foraging theory in cultural ecology and archeology.


Step Length Migration Distance Spider Monkey Average Travel Time Resource Patch 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Abrams, Peter A. (1984). Foraging Time Optimization and Interactions in Food Webs. American Naturalist 124(1):80-96.CrossRefGoogle Scholar
  2. Ammerman, A. J. and Cavalli-Sforza, L. L. (1979). The Wave of Advance Model for the Spread of Agriculture in Europe. In Renfrew, C. and Cooke, K. L. (eds.), Transformations: Mathematical Approaches to Culture Change. Academic Press, New York, pp. 275-293Google Scholar
  3. Anthony, D. W. (1990). Migration in Archaeology: The Baby and the Bathwater. American Anthropologist 92(4):895-914.CrossRefGoogle Scholar
  4. Atkinson, R. P. D., Rhodes, C. J. D., Macdonald, W., and Anderson, R. M. (2002). Scale-free dynamics in the movement patterns of Jackals. Oikos 98:134-140.CrossRefGoogle Scholar
  5. Bartumeus, F., Peters, F., Pueyo, S., Marrasé, C., and Catalan, J. (2003). Helical Lévy Walks: Adjusting Searching Statistics to Resource Availability in Microzooplankton. Proceedings of the National Academy of Sciences 100(22):12771-12775.CrossRefGoogle Scholar
  6. Bartumeus, F., da Luz, M. G. E., Viswanathan, G. M., and Catalan, J. (2005). Animal Search Strategies: A Quantitative Random Walk Analysis. Ecology 86(11):3078-3087.CrossRefGoogle Scholar
  7. Belovsky, G. E. (1987). Hunter-Gatherer Foraging: A Linear Programming Approach. Journal of Anthropological Archaeology 6(1):29-76.CrossRefGoogle Scholar
  8. Belovsky, G. E. (1988). A Optimal Foraging-based Model of Hunter-gatherer Population Dynamics. Journal of Anthropological Archaeology 7(4):329-372.CrossRefGoogle Scholar
  9. ben-Avraham, D. and Havlin, S. (2000). Diffusion and Reactions in Fractals and Disordered Systems. Cambridge University Press, Cambridge.Google Scholar
  10. Boyer, D., Miramontes, O., Ramos-Fernández, G., Mateos, J. L., and Cocho, G. (2004). Modeling the Searching Behavior of Social Monkeys. Physica A 342:329-335.CrossRefGoogle Scholar
  11. Charnov, E. L. (1976). Optimal Foraging, the Marginal Value Theorem. Theoretical Population Biology 9(2):129-136.CrossRefGoogle Scholar
  12. Charnov, E. L. and Orians, G. H. (1973). Optimal Foraging: Some Theoretical Expectations. Unpublished MS. Available at <>
  13. Cole, B. J. (1995). Fractal Time in Animal Behavior: the Movement Activity of Drosophila. Animal Behavior 50:1317-1324.CrossRefGoogle Scholar
  14. da Luz, M. G. E., Buldyrev, S. V., Havlin, S., Raposo, E. P., Stanley, H. E., and Viswanathan, G. M. (2001). Improvements in the Statistical Approach to Random Lévy Flight Searches. Physica A 295:89-92.CrossRefGoogle Scholar
  15. Fisher, R. A. (1937). The Wave of Advance of Advantageous Genes. Annals of Eugenics 7:355-369.Google Scholar
  16. Green, Richard F. (1987). Stochastic Models of Optimal Foraging. In Kamil, A. C., Krebs, J. R., and Pullman, H. R. (eds.), Foraging Behavior. Plenum Press, New York, pp. 273-302.Google Scholar
  17. Harpending, H. (1976). Regional Variation in !Kung Populations. In Lee, R. B. and DeVore, I. (eds.), Kalahari Hunter-Gatherers. Harvard University Press, Cambridge, pp. 152-165.Google Scholar
  18. Hawkes, K. and O’Connell, J. (1981). Affluent Hunters? Some Comments in Light of the Alyawara Case. American Anthropologist 83:622-626.CrossRefGoogle Scholar
  19. Hawkes, K. and O’Connell, J. (1985). Optimal Foraging Models and the Case of the ! Kung. American Anthropologist 87:401-405.CrossRefGoogle Scholar
  20. Hoddle, Mark S. (2003). The Effect of Prey Species and Environmental Complexity on the Functional Response of Franklinothrips orizabensis: A Test of the Fractal Foraging Model. Ecological Entomology 28:309-318.CrossRefGoogle Scholar
  21. Johnson, Jerald B. and Kristian S. Omland (2004). Model Selection in Ecology and Evolution. TRENDS in Ecology and Evolution 19(2):101-108.CrossRefGoogle Scholar
  22. Kelly, R. L. (1995). The Foraging Spectrum: Diversity in Hunter-Gatherer Lifeways. Smithsonian Institution Press, Washington.Google Scholar
  23. Lee, R. B. (1979). The !Kung San: Men, Women, and Work in a Foraging Society. Cambridge University Press, Cambridge.Google Scholar
  24. Lee, R. B. (1993). The Dobe Ju/’hoansi. Harcourt Brace, New York.Google Scholar
  25. Lee, R. B. and DeVore, I. (eds.) (1976). Kalahari Hunter-Gatherers: Studies of the !Kung San and their Neighbors. Harvard University Press, Cambridge.Google Scholar
  26. Liebovitch, L. S. (1998). Fractals and Chaos Simplified for the Life Sciences. Oxford University Press, New York.Google Scholar
  27. Liebovitch, L. S. and Scheurle, D. (2000). Two Lessons from Fractals and Chaos. Complexity 5(4):34-43.CrossRefGoogle Scholar
  28. Liebovitch, L. S. and Todorov, A. T. (1996). Fractal Dynamics of Human Gait: Stability of Long-Range Correlations in Stride Interval Fluctuations. Journal of Applied Physiology 80:1446-1447.CrossRefGoogle Scholar
  29. Liebovitch, L. S., Fischbarg, J., and Koniarek, J. (1987). Ion Channel Kinetics: A Model Based on Fractal Scaling Rather Than Multistate Markov Processes. Mathematical Biosciences 84:37-68.CrossRefGoogle Scholar
  30. Liebovitch, L. S., Todorov, A. T., Zochowski, M., Scheurle, D., Colgin, L., Wood, M. A., Ellenbogen, K. A., Herre, J. M., and Bernstein, R. C. (1999). Nonlinear Properties of Cardiac Rhythm Abnormalities. Physical Review E 59(3):3312-3319.CrossRefGoogle Scholar
  31. Liebovitch, L. S., Scheurle, D., Rusek, M., and Zochowski, M. (2001). Fractal Methods to Analyze Ion Channel Kinetics. Methods 24:359-375.CrossRefGoogle Scholar
  32. MacArthur, R. H. and Pianka, E. R. (1966). On Optimal Use of a Patchy Environment. American Naturalist 100(916):603-609.CrossRefGoogle Scholar
  33. Mandelbrot, B. B. (1983). The Fractal Geometry of Nature. W. H. Freeman and Company, New York.Google Scholar
  34. Mårell, A., Ball, J. P., and Hofgaard, A. (2002). Foraging and movement paths of female reindeer: insights from fractal analysis, correlated random walks, and Lévy flights. Canadian Journal of Zoology 80:854-865CrossRefGoogle Scholar
  35. Marshall, L. (1976). The !Kung of Nyae Nyae. Harvard University Press, Cambridge.Google Scholar
  36. Ramos-Fernández, G., Mateos, J. L., Miramontes, O., Cocho, G., Larralde, H., and Ayala-Orozco, B. (2003). Lévy Walk Patterns in the Foraging Movements of Spider Monkeys (Ateles geoffroyi). Behavioral Ecology and Sociobiology 55(3):223-230.Google Scholar
  37. Russell, Robert W., George L. Hunt, Kenneth O. Coyle, and R. Ted Cooney. (1992). Landscape Ecology 7(3):195-209.CrossRefGoogle Scholar
  38. Salmon, M. H. (1989). Efficient Explanations and Efficient Behavior. In Pinsky, V. and Wylie, A. (eds.), Critical Traditions in Contemporary Archaeology. Cambridge University Press, Cambridge, pp. 10-13.Google Scholar
  39. Shlesinger, M. F., Zaslavsky, G. M., and Klafter, J. (1993). Strange Kinetics. Nature 363:31-37.CrossRefGoogle Scholar
  40. Smith, E. A. (1991). Inujjuamiut Foraging Strategies: Evolutionary Ecology of an Arctic Hunting Economy. Aldine de Gruyter, New York.Google Scholar
  41. Stephens, D. W. and Eric L. Charnov (1982). Optimal Foraging: Some Simple Stochastic Models. Behavioral Ecology and Sociobiology 10:251-263.CrossRefGoogle Scholar
  42. Stephens, D. W. and Krebs, J. R. (1986). Foraging Theory. Princeton University Press, Princeton.Google Scholar
  43. Viswanathan, G. M., Afanasyev, V., Buldyrev, S. V., Murphy, E. J., Prince, P. A., and Stanley, H. E. (1996). Lévy Flight Search Patterns of Wandering Albatrosses. Nature 381:413-415.CrossRefGoogle Scholar
  44. Viswanathan, G. M., Buldyrev, S. V., Havlin, S., da Luz, M. G. E., Raposo, E. P., and Stanley, H. E. (1999). Optimizing the Success of Random Searches. Nature 401:911-914.CrossRefGoogle Scholar
  45. Viswanathan, G. M., Afanasyev, V., Buldyrev, S. V., Havlin, S., da Luz, M. G. E., Raposo, E. P., and Stanley, H. E. (2000). Lévy Flights in Random Searches. Physica A 282:1-12.CrossRefGoogle Scholar
  46. Viswanathan, G. M., Afanasyev, V., Buldyrev, S. V., Havlin, S., da Luz, M. G. E., Raposo, E. P., and Stanley, H. E. (2001). Lévy Flights Search Patterns of Biological Organisms. Physica A 295:85-88.CrossRefGoogle Scholar
  47. Viswanathan, G. M., Bartumeus, F., Buldyrev, S. V., Catalan, J., Fulco, U. L., Havlin, S., da Luz, M. G. E., Lyra, M. L., Raposo, E. P., and Stanley, H. E. (2002). Lévy Flight Random Searches in Biological Phenomena. Physica A 314:208-213.CrossRefGoogle Scholar
  48. Wijsman, E. M. and Cavalli-Sforza, L. L. (1984). Migration and Genetic Population Structure with Special Reference to Humans. Annual Review of Ecology and Systematics 15:279-301.CrossRefGoogle Scholar
  49. Yellen, J. E. (1977). Archaeological Approaches to the Present: Models for Reconstructing the Past. Academic Press, New York.Google Scholar
  50. Yellen, J. E. and Lee, R. B. (1976). The Dobe-/Du/da Environment: Background to a Hunting and Gathering Way of Life. In Lee, R. B. and DeVore, I. (eds.), Kalahari Hunter-Gatherers: Studies of the!Kung San and their Neighbors. Harvard University Press, Cambridge, pp. 27-46.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Clifford T. Brown
    • 1
  • Larry S. Liebovitch
    • 1
  • Rachel Glendon
    • 1
  1. 1.Department of AnthropologyFlorida Atlantic UniversityBoca RatonUSA

Personalised recommendations