- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Robustness of optimal random searches in fragmented environments

M. E. Wosniack1,*, M. C. Santos1,†, E. P. Raposo2,‡, G. M. Viswanathan3,4,§, and M. G. E. da Luz1,∥

  • 1Departamento de Física, Universidade Federal do Paraná, C.P. 19044, 81531-980 Curitiba-PR, Brazil
  • 2Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife-PE, Brazil
  • 3Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, 59078-970 Natal-RN, Brazil
  • 4National Institute of Science and Technology of Complex Systems, Universidade Federal do Rio Grande do Norte, 59078-970 Natal-RN, Brazil

  • *wosniack@fisica.ufpr.br
  • †msantos@fisica.ufpr.br
  • ‡ernesto@df.ufpe.br
  • §gandhi@dfte.ufrn.br
  • ∥luz@fisica.ufpr.br
PDF

Phys. Rev. E 91, 052119 – Published 13 May, 2015

DOI: https://doi.org/10.1103/PhysRevE.91.052119

Abstract

The random search problem is a challenging and interdisciplinary topic of research in statistical physics. Realistic searches usually take place in nonuniform heterogeneous distributions of targets, e.g., patchy environments and fragmented habitats in ecological systems. Here we present a comprehensive numerical study of search efficiency in arbitrarily fragmented landscapes with unlimited visits to targets that can only be found within patches. We assume a random walker selecting uniformly distributed turning angles and step lengths from an inverse power-law tailed distribution with exponent μ. Our main finding is that for a large class of fragmented environments the optimal strategy corresponds approximately to the same value μopt≈2. Moreover, this exponent is indistinguishable from the well-known exact optimal value μopt=2 for the low-density limit of homogeneously distributed revisitable targets. Surprisingly, the best search strategies do not depend (or depend only weakly) on the specific details of the fragmentation. Finally, we discuss the mechanisms behind this observed robustness and comment on the relevance of our results to both the random search theory in general, as well as specifically to the foraging problem in the biological context.

View figure in article

Article Text

References (59)

  1. E. Bertin, A Concise Introduction to the Statistical Physics of Complex Systems (Springer, Berlin, 2012).
  2. Lévy Flights and Related Topics in Physics, edited by M. F. Shlesinger, G. Zaslavsky, and U. Frisch (Springer, Berlin, 1995).
  3. H. C. Berg, Random Walks in Biology (Princeton University Press, Princeton, NJ, 1983).
  4. D. W. Stephens and J. R. Krebs, Foraging Theory (Princeton University Press, Princeton, NJ, 1987).
  5. Dispersal, Individual, Movement and Spatial Ecology, edited by M. A. Lewis, P. K. Maini, and S. V. Petrovskii (Springer, Berlin, 2013).
  6. I. Peterson, The Jungle of Randomness: A Mathematical Safari (Wiley, New York, 1997).
  7. R. V. Solé and J. Bascompte, Self-Organization in Complex Ecosystems (Princeton University Press, Princeton, NJ, 2006).
  8. G. M. Viswanathan, M. G. E. da Luz, E. P. Raposo, and H. E. Stanley, The Physics of Foraging: An Introduction to Random Searches and Biological Encounters (Cambridge University Press, Cambridge, UK, 2011).
  9. T. M. Scanlon, K. K. Caylor, S. A. Levin, and I. Rodriguez-Iturbe, Nature (London) 449, 209 (2007).
  10. S. Kéfi, M. Rietkerk, C. L. Alados, Y. Pueyo, V. P. Papanastasis, A. ElAich, and P. C. de Ruiter, Nature (London) 449, 213 (2007).
  11. R. W. Russell, G. L. Hunt, K. O. Coyle, and R. T. Cooney, Landsc. Ecol. 7, 195 (1992).
  12. M. S. Hoddle, Ecol. Entomol. 28, 309 (2003).
  13. M. W. Palmer, Vegetatio 75, 91 (1988).
  14. B. T. Milne, Amer. Natur. 139, 32 (1992).
  15. M. E. Ritchie, Evol. Ecol. 12, 309 (1998).
  16. K. A. With and A. W. King, Conserv. Biol. 13, 314 (1999).
  17. K. A. With and A. W. King, Landsc. Ecol. 14, 73 (1999).
  18. K. A. With and D. M. Pavuk, Landsc. Ecol. 26, 1035 (2011).
  19. S. A. Levin, Ecology 73, 1943 (1992).
  20. P. Fauchald, Amer. Natur. 153, 603 (1999).
  21. P. Fauchald, K. E. Erikstad, and H. Skarsfjord, Ecology 81, 773 (2000).
  22. C. J. Johnson, M. S. Boyce, R. Mulders, A. Gunn, R. J. Gau, H. D. Cluff, and R. L. Case, Landsc. Ecol. 19, 869 (2004).
  23. D. W. Sims, E. J. Southall, N. E. Humphries, G. C. Hays, C. J. A. Bradshaw, J. W. Pitchford, A. James, M. Z. Ahmed, A. S. Brierley, M. A. Hindell, D. Morritt, M. K. Musyl, D. Righton, E. L. C. Shepard, V. J. Wearmouth, R. P. Wilson, M. J. Witt, and J. D. Metcalfe, Nature (London) 451, 1098 (2008).
  24. R. H. MacArthur and E. O. Wilson, The Theory of Island Biogeography (Princeton University Press, Princeton, NJ, 1967).
  25. I. Hanski, Metapopulation Ecology (Oxford University Press, Oxford, 1999).
  26. D. L. Hartl and A. G. Clark, Principles of Population Genetics (Sinauer Associates, Sunderland, 2006).
  27. R. Levins, Bull. Entomol. Soc. Am. 15, 237 (1969).
  28. M. A. M. de Aguiar, M. Baranger, E. M. Baptestini, L. Kaufman, and Y. Bar-Yam, Nature (London) 460, 384 (2009).
  29. D. B. Lindenmayer and J. Fischer, Habitat Fragmentation and Landscape Change: An Ecological and Conservation Synthesis (Island Press, Washington, DC, 2006); J. Fischer, D. B. Lindenmayer, and A. D. Manning, Front. Ecol. Environ. 4, 80 (2006).
  30. R. B. Primack, Essentials of Conservation Biology (Sinauer Associates, Sunderland, 2010).
  31. S. Benhamou, Ecology 88, 1962 (2007).
  32. A. M. Reynolds, Physica A 388, 561 (2009).
  33. F. Bartumeus and S. Levin, Proc. Natl. Acad. Sci. USA 105, 19072 (2008).
  34. C. E. Sparling, J.-Y. Goerges, S. L. Gallon, M. Fedak, and D. Thompson, Anim. Behav. 74, 207 (2007).
  35. K. A. Barton, B. L. Phillips, J. M. Morales, and J. M. L. Travis, Oikos 118, 309 (2009).
  36. A. S. Ferreira, E. P. Raposo, G. M. Viswanathan, and M. G. E. da Luz, Physica A 391, 3234 (2012).
  37. E. P. Raposo, F. Bartumeus, M. G. E. da Luz, P. J. Ribeiro-Neto, T. A. Souza, and G. M. Viswanathan, PLoS Comput. Biol. 7, e1002233 (2011).
  38. S. A. Sotelo-López, M. C. Santos, E. P. Raposo, G. M. Viswanathan, and M. G. E. da Luz, Phys. Rev. E 86, 031133 (2012).
  39. G. M. Viswanathan, S. V. Buldyrev, S. Havlin, M. G. E. da Luz, E. P. Raposo, and H. E. Stanley, Nature (London) 401, 911 (1999).
  40. R. N. Mantegna and H. E. Stanley, Phys. Rev. Lett. 73, 2946 (1994).
  41. E. P. Raposo, S. V. Buldyrev, M. G. E. da Luz, G. M. Viswanathan, and H. E. Stanley, J. Phys. A 42, 434003 (2009).
  42. F. Bartumeus, E. P. Raposo, G. M. Viswanathan, and M. G. E. da Luz, PLoS ONE 9, e106373 (2014).
  43. E. P. Raposo, S. V. Buldyrev, M. G. E. da Luz, M. C. Santos, H. E. Stanley, and G. M. Viswanathan, Phys. Rev. Lett. 91, 240601 (2003).
  44. C. P. Brooks, Ecology 87, 864 (2006).
  45. E. A. Marschall, P. L. Chesson, and R. A. Stein, Anim. Behav. 37, 444 (1989).
  46. H. Tuomisto, K. Ruokolainen, and M. Y. Halla, Science 299, 241 (2003).
  47. A. Zurbuchen, S. Cheesman, J. Klaiber, A. Mueller, S. Hein, and S. Dorn, J. Anim. Ecol. 79, 674 (2010).
  48. G. J. Russell, J. M. Diamond, T. M. Reed, and S. L. Pimm, J. Anim. Ecol. 75, 324 (2006).
  49. P. Turchin, Ecology 72, 1253 (1991).
  50. D. I. Bolnick, L. H. Yang, J. A. Fordyce, J. M. Davis, and R. Svanback, Ecology 83, 2936 (2002).
  51. J. A. Wiens, Ann. Rev. Ecol. Syst. 7, 81 (1976); The Princeton Guide to Ecology, edited by S. Levin (Princeton University Press, Princeton, NJ, 2009), Chaps. IV-1–IV-3.
  52. A. M. Reynolds and F. Bartumeus, J. Theor. Biol. 260, 98 (2009).
  53. K. A. Schmidt and J. S. Brown, Am. Natur. 147, 360 (1996).
  54. M. Kawata and H. Agawa, Ecol. Lett. 2, 210 (1999).
  55. G. A. Nevitt, Biol. Bull. 198, 245 (2000).
  56. J. D. Olden, R. L. Schooley, J. B. Monroe, and N. L. Poff, J. An. Ecol. 73, 1190 (2004).
  57. D. B. Lindenmayer and J. F. Franklin, Conserving Forest Biodiversity: A Comprehensive Multiscaled Approach (Island Press, Washington, DC, 2002).
  58. M. E. Wosniack, M. C. Santos, M. R. Pie, M. C. M. Marques, E. P. Raposo, G. M. Viswanathan, and M. G. E. da Luz, J. R. Soc. Interface 11, 20130887 (2014).
  59. K. R. Searle, N. T. Hobbs, B. A. Wunder, and L. A. Shipley, Behav. Ecol. 17, 315 (2006).

Outline

Information

Phys. Rev. E 91, 052119– Published 13 May, 2015
  • Received 26 February 2015

©2015 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation