Evolutionary Ecology

, Volume 12, Issue 3, pp 309–330 | Cite as

Scale-dependent foraging and patch choice in fractal environments

  • Mark E. Ritchie
Article

Abstract

Many spatially complex environments are fractal, and consumers in these environments face scale-dependent trade-offs between encountering high densities of small resource patches versus low densities of large resource patches. I address the effects of these trade-offs on foraging by incorporating scale-dependent encounter of resources in fractal landscapes into classical optimal foraging theory. This model is then used to predict optimal scales of perception (foraging scale) and patch choice in response to spatial features of landscapes. The model predicts that, for a given density of resources, landscapes with greater extent and fractal dimension and that contain patchy (low fractal dimension) resources favour large foraging scales and specialization on a small proportion of resource patches. Fragmented (low fractal dimension) landscapes of small extent with dispersed (high fractal dimension) resources favour smaller foraging scales and generalists that use a large proportion of available resource patches. These predictions synthesize the results of other spatially explicit consumer–resource models into a simple framework and agree reasonably well with results of several empirical studies. This study thus places optimal foraging theory in a spatial context and suggests evolutionary mechanisms of consumers' responses to important spatial phenomena (e.g. habitat fragmentation, resource aggregation).

foraging fractal geometry landscape resources scale 

References

  1. Alexander, S. and Orbach, R. (1982) Density of states on fractals: ‘Fractons’. J. Phys. Lett. 43, L625–631.Google Scholar
  2. Askins, R.A., Lynch, J.F. and Greenberg, R. (1990) Population declines in migratory birds in eastern North America. Curr. Ornith. 7, 1–57.Google Scholar
  3. Barnsley, M. (1988) Fractals Everywhere. Academic Press, New York.Google Scholar
  4. Belovsky, G.E. (1984) Moose and snowshoe hare competition and a mechanistic explanation from foraging theory. Oecologia (Berl.) 61, 150–159.CrossRefGoogle Scholar
  5. Belovsky, G.E. (1986) Generalist herbivore foraging and its role in competitive interactions. Am. Zool. 26, 51–69.Google Scholar
  6. Biondini, M.E. and Grygiel, C.E. (1994) Landscape distribution of organisms and the scaling of soil resources. Am. Nat. 143, 1026–1054.CrossRefGoogle Scholar
  7. Brown, J.S., Kotler, B.P. and Mitchell, W.A. (1994) Foraging theory, patch use, and the structure of a Negev desert granivore community. Ecology 75, 2286–2300.CrossRefGoogle Scholar
  8. Butler, M.J. (1988) In situ observations of bluegill (Lepomis macrochirus) foraging behavior: The effects of habitat complexity, group size, and predators. Copeia 1988, 939–944.CrossRefGoogle Scholar
  9. Cain, M.L., Eccleston, J. and Kareiva, P. (1985) The influence of food plant dispersion on caterpillar searching success. Ecol. Entomol. 10, 1–7.Google Scholar
  10. Campbell, B.D., Grime, J.P. and Mackey, J.M.L. (1991) A trade-off between scale and precision in resource foraging. Oecologia 87, 532–538.CrossRefGoogle Scholar
  11. Charnov, E.L. (1976) Optimal foraging: The marginal value theorem. Theor. Pop. Biol. 9, 129–136.CrossRefGoogle Scholar
  12. Chesson, P.L. (1994) Multispecies competition in variable environments. Theor. Pop. Biol. 45, 227–276.CrossRefGoogle Scholar
  13. Chesson, P.L. and Murdoch, W.W. (1986) Aggregation of risk: Relationships among host-parasitoid models. Am. Nat. 127, 696–715.CrossRefGoogle Scholar
  14. Comins, H.N. and Hassell, M.P. (1979) The dynamics of optimally foraging predators and parasitoids. J. Anim. Ecol. 48, 335–351.CrossRefGoogle Scholar
  15. Crist, T.O. and Wiens, J.A. (1994) Scale effects of vegetation on forager movement and seed harvesting by ants. Oikos 69, 37–46.Google Scholar
  16. Crist, T.O., Guertin, P.S., Wiens, J.A. and Milne, B.T. (1992) Animal movement in heterogeneous landscapes: An experiment with Eleodes beetles in shortgrass prairie. Funct. Ecol. 6, 536–544.CrossRefGoogle Scholar
  17. Crowder, L.B. and Cooper, W.E. (1982) Habitat structural complexity and the interaction between bluegills and their prey. Ecology 63, 1802–1813.CrossRefGoogle Scholar
  18. Diehl, S. (1993) Effects of habitat structure on resource availability, diet and growth of benthivorous perch, Perca fluviatilis. Oikos 67, 403–414.Google Scholar
  19. Doak, D.F., Marino, P.C. and Kareiva, P.M. (1992) Spatial scale mediates the influence of habitat fragmentation on dispersal success: Implications for conservation. Theor. Pop. Biol. 41, 315–336.CrossRefGoogle Scholar
  20. Dunbrack, R.L. and Dill, L.M. (1984) Three-dimensional prey reaction field of the juvenile coho salmon (Oncorhynchus kisutch). Can. J. Fish. Aquat. Sci. 41, 1176–1182.CrossRefGoogle Scholar
  21. Figiel, C.R. and Semlitsch, R.D. (1991) Effects of nonlethal injury and habitat complexity on predation in tadpole populations. Can. J. Fish. Aquat. Sci. 69, 830–834.Google Scholar
  22. Frontier, S. (1987) Applications of fractal theory to ecology. In Developments in Numerical Ecology (P. Legendre and L. Legendre, eds), pp. 335–378. Springer-Verlag, Berlin.Google Scholar
  23. Gardner, R.H., O'Neill, R.V., Turner, M.G. and Dale, V.H. (1989) Quantifying scale-dependent effects of animal movement with simple percolation models. Landscape Ecol. 3, 217–227.CrossRefGoogle Scholar
  24. Hassell, M.P. (1978) The Dynamics of Arthropod Predator-Prey Systems. Princeton University Press, Princeton, NJ.Google Scholar
  25. Hassell, M.P. and May, R.M. (1974) Aggregation in predators and insect parasites and its effect on stability. J. Anim. Ecol. 43, 567–594.CrossRefGoogle Scholar
  26. Hassell, M.P. and Pacala, S.W. (1990) Heterogeneity and the dynamics of host-parasitoid interactions. Phil. Trans. Roy. Soc. Lond. B 330, 203–220.Google Scholar
  27. Hassell, M.P., May, R.M., Pacala, S.W. and Chesson, P.L. (1991) The persistence of host-parasitoid associations in patchy environments. I. A general criterion. Am. Nat. 138, 568–583.CrossRefGoogle Scholar
  28. Hastings, H.M. and Sugihara, G. (1993) Fractals: A User's Guide for the Natural Sciences. Oxford University Press, New York.Google Scholar
  29. Holling, C.S. (1959) Some characteristics of simple types of predation and parasitism. Can. Entomol. 91, 385–398.CrossRefGoogle Scholar
  30. Holling, C.S. (1992) Cross-scale morphology, geometry and dynamics of ecosystems. Ecol. Monogr. 62, 447–502.CrossRefGoogle Scholar
  31. Holt, R.D. (1984) Spatial heterogeneity, indirect interactions, and the coexistence of prey species. Am. Nat. 124, 377–406.CrossRefGoogle Scholar
  32. Hutchinson, G.E. and MacArthur, R.H. (1959) A theoretical ecological model of size distributions among species of animals. Am. Nat. 93, 117–125.CrossRefGoogle Scholar
  33. Ives, A.R. (1992) Continuous time models of host-parasitoid interactions. Am. Nat. 140, 1–29.CrossRefPubMedGoogle Scholar
  34. Joern, A.R. (1983) Small-scale displacements of grasshoppers (Orthoptera: Acrididae) within arid grasslands. J. Kansas Entomol. Soc. 56, 131–139.Google Scholar
  35. Johnson, A.R., Milne, B.T. and Wiens, J.A. (1992) Diffusion in fractal landscapes: Simulations and experimental studies of Tenebrionid beetle movements. Ecology 73, 1968–1983.CrossRefGoogle Scholar
  36. Kaiser, H. (1983) Small scale spatial heterogeneity influences predation success in an unexpected way: Model experiments on the functional response of predatory mites (Acarina). Oecologia (Berl.) 56, 249–256.CrossRefGoogle Scholar
  37. Kareiva, P. (1987) Habitat fragmentation and the stability of predator-prey interactions. Nature 326, 388–390.CrossRefGoogle Scholar
  38. Kareiva, P. (1990) Population dynamics in spatially complex environments: Theory and data. Phil. Trans. Roy. Soc. Lond. B 330, 175–190.Google Scholar
  39. Kareiva, P. and Perry, R. (1989) Leaf overlap and the ability of ladybird beetles to search among plants. Ecol. Entomol. 14, 127–129.Google Scholar
  40. Keitt, T.H. and Johnson, A.R. (1995) Spatial heterogeneity and anomalous kinetics: Emergent patterns in di.usion-limited predatory-prey interaction. J. Theor. Biol. 172, 127–139.CrossRefGoogle Scholar
  41. Kotliar, N.B. and Wiens, J.A. (1990) Multiple scales of patchiness and patch structure: A hierarchical framework for the study of heterogeneity. Oikos 59, 253–260.Google Scholar
  42. Krummel, J.R., Gardner, R.H., Sugihara, G. and O'Neill, R.V. (1987) Landscape patterns in a disturbed environment. Oikos 48, 321–324.Google Scholar
  43. Levin, S. (1992) The problem of pattern and scale in ecology. Ecology 73, 1943–1967.CrossRefGoogle Scholar
  44. Lundberg, P. and Astrom, M. (1990) Functional response of optimally foraging herbivores. J. Theor. Biol. 144, 367–377.Google Scholar
  45. MacArthur, R.H. (1972) Geographical Ecology. Princeton University Press, Princeton, NJ.Google Scholar
  46. Mandelbrot, B.B. (1982) The Fractal Geometry of Nature. W.H. Freeman, San Francisco, CA.Google Scholar
  47. May, R.M. (1978) Host-parasitoid systems in patchy environments: A phenomenological model. J. Anim. Ecol. 47, 833–843.CrossRefGoogle Scholar
  48. McLaughlin, J.F. and Roughgarden, J. (1992) Predation across spatial scales in heterogeneous environments. Theor. Pop. Biol. 41, 277–299.CrossRefGoogle Scholar
  49. Milne, B.T. (1991) Lessons from applying fractal models to landscape patterns. In Quantitative Methods in Landscape Ecology (M.G. Turnel and R.H. Gardner, eds), pp. 199–235. Springer-Verlag, New York.Google Scholar
  50. Milne, B.T. (1992) Spatial aggregation and neutral models in fractal landscapes. Am. Nat. 139, 32–57.CrossRefGoogle Scholar
  51. Milne, B.T., Turner, M.G., Wiens, J.A. and Johnson, A.R. (1992) Interactions between fractal geometry of landscapes and allometric herbivory. Theor. Pop. Biol. 41, 337–353.CrossRefGoogle Scholar
  52. Morse, D.R., Lawton, J.H., Dodson, M.M. and Williamson, M.H. (1985) Fractal dimension of vegetation and the distribution of arthropod body lengths. Nature 314, 731–732.CrossRefGoogle Scholar
  53. Murdoch, W.W. (1977) Stabilizing e.ects of spatial heterogeneity in predator-prey systems. Theor. Pop. Biol. 11, 252–273.CrossRefGoogle Scholar
  54. Murdoch, W.W. and Stewart-Oaten, A. (1989) Aggregation by parasitoids and predators: Effects on equilibrium and stability. Am. Nat. 134, 288–310.CrossRefGoogle Scholar
  55. Nitecki, M.H. (ed.) (1984) Extinction. University of Chicago Press, Chicago, IL.Google Scholar
  56. O'Neill, R.V., Milne, B.T., Turner, M.G. and Gardner, R.H. (1988) Resource utilization scales and landscape pattern. Landscape Ecol. 2, 63–69.Google Scholar
  57. Pacala, S.W. and Hassell, M.P. (1991) The persistence of host-parasitoid systems in patchy environments. II. Evaluation of field data. Am. Nat. 138, 584–605.CrossRefGoogle Scholar
  58. Palmer, M.W. (1988) Fractal geometry: A tool for describing spatial patterns of plant communities. Vegetatio 75, 91–102.CrossRefGoogle Scholar
  59. Palmer, M.W. (1992) The coexistence of species in fractal landscapes. Am. Nat. 139, 375–397.CrossRefGoogle Scholar
  60. Pulliam, H.R. (1974) On the theory of optimal diets. Am. Nat. 108, 59–75.CrossRefGoogle Scholar
  61. Quinn, J.F. and Hastings, A. (1987) Extinction in subdivided habitats. Cons. Biol. 1, 198–208.CrossRefGoogle Scholar
  62. Rotenberry, J.T. and Wiens, J.A. (1980) Habitat structure, patchiness, and avian communities in North American steppe vegetation: A multivariate analysis. Ecology 61, 1228–1250.CrossRefGoogle Scholar
  63. Savino, J.F. and Stein, R.M. (1982) Predator-prey interaction between largemouth bass and bluegills as influenced by simulated, submersed vegetation. Trans. Am. Fish. Soc. 111, 255–266.CrossRefGoogle Scholar
  64. Scheffer, M. and deBoer, R.J. (1995) Implications of spatial heterogeneity for the paradox of enrichment. Ecology 76, 2270–2277.CrossRefGoogle Scholar
  65. Schoener, T.W. (1971) The theory of feeding strategies. Ann. Rev. Ecol. Syst. 2, 368–404.CrossRefGoogle Scholar
  66. Shipley, L.A., Gross, J.E., Spalinger, D.E., Hobbs, N.T. and Wunder, B.A. (1994) The scaling of intake rate in mammalian herbivores. Am. Nat. 143, 1055–1082.CrossRefGoogle Scholar
  67. Spalinger, D.E. and Hobbs, N.T. (1992) Mechanisms of foraging in mammalian herbivores: New models of functional response. Am. Nat. 140, 325–348.CrossRefPubMedGoogle Scholar
  68. Sredl, M.J. and Collins, J.P. (1992) The interaction of predation, competition, and habitat complexity in structuring an amphibian community. Copeia 1992, 607–614.CrossRefGoogle Scholar
  69. Stephens, D.W. and Charnov, E.L. (1982) Optimal foraging: Some simple stochastic models. Behav. Ecol. Sociobiol. 10, 251–263.CrossRefGoogle Scholar
  70. Stephens, D.W. and Krebs, J.R. (1986) Foraging Theory. Princeton University Press, Princeton, NJ.Google Scholar
  71. Sugihara, G. and May, R.M. (1990) Applications of fractals in ecology. Trends Ecol. Evol. 5, 79–86.CrossRefGoogle Scholar
  72. Tilman, D. (1982) Resource Competition and Community Structure. Princeton University Press, Princeton, NJ.Google Scholar
  73. Tilman, D. (1994) Competition and biodiversity in spatially structured habitats. Ecology 75, 2–16.CrossRefGoogle Scholar
  74. Tilman, D., May, R.M., Lehman, C.L. and Nowak, M.A. (1994) Habitat destruction and the extinction debt. Nature 371, 65–66.CrossRefGoogle Scholar
  75. Turchin, P. (1991) Translating the foraging movements in heterogeneous environments into the spatial distribution of foragers. Ecology 72, 1253–1266.CrossRefGoogle Scholar
  76. Turner, M. (1989) Landscape ecology: The effect of pattern on process. Ann. Rev. Ecol. Syst. 20, 171–197.CrossRefGoogle Scholar
  77. 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
  78. Voss, R.F. (1986) Characterization and measurement of random fractals. Phys. Scripta T13, 27–32.Google Scholar
  79. Whitehead, H. and Walde, S.J. (1992) Habitat dimensionality and mean search distances of top predators: Implications for ecosystem structure. Theor. Pop. Biol. 42, 1–9.CrossRefGoogle Scholar
  80. Wiens, J.A. (1989) Spatial scaling in ecology. Funct. Ecol. 3, 385–397.CrossRefGoogle Scholar
  81. Wiens, J.A. and Milne, B.T. (1989) Scaling of ‘landscapes’ in landscape ecology, or, landscape ecology from a beetle's perspective. Landscape Ecol. 3, 87–96.CrossRefGoogle Scholar
  82. Wiens, J.A., Crist, T.O., With, K.A. and Milne, B.T. (1995) Fractal patterns of insect movement in microlandscape mosaics. Ecology 76, 663–666.CrossRefGoogle Scholar
  83. Williamson, M.H. and Lawton, J.H. (1991) Fractal geometry of ecological habitats. In Habitat Structure: The Physical Arrangement of Objects in Space (S.S. Bell, E.D. McCoy and H.R. Mushinsky, eds), pp. 69–86. Chapman and Hall, New York.Google Scholar
  84. With, K.A. (1994) Using fractal analysis to assess how species perceive landscape structure. Landscape Ecol. 9, 25–36.CrossRefGoogle Scholar
  85. With, K.A. and Crist, T.O. (1995) Critical thresholds in species' responses to landscape structure. Ecology 76, 2446–2459.CrossRefGoogle Scholar

Copyright information

© Chapman and Hall 1998

Authors and Affiliations

  • Mark E. Ritchie
    • 1
  1. 1.Department of Fisheries and Wildlife and Ecology CenterUtah State UniversityLoganUSA

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