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Applications of Fractal Geometry in Wildlife Biology

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Wildlife and Landscape Ecology

Abstract

Unlike simple physical systems, such as frictionless pendula and leaking buckets, ecosystems possess complexities that have limited biologists’ ability to describe, predict, and manage natural resources. Complexity can be addressed with tools to assess spatial pattern over vast expanses (e.g., geographic information systems and remote sensing), to uncover persistent interactions over space and time (Cressie 1991 Deutsch and Journel 1992), and to discover simplicity in the face of chaotic changes (Tilman and Wedin 1991 Solé et al. 1992 Kauffman 1993 Plotnick and McKinney 1993 Peak, Chapter 3). Techniques to unravel spatial and temporal complexity involve purposeful manipulation of the scale of observation to discover how phenomena change steadily, and predictably, with scale.

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References

  • Allee, W.C. 1931. Animal aggregations: A study in general sociology. University of Chicago Press, Chicago, Illinois, USA.

    Book  Google Scholar 

  • Allen, T.F.H., and T.B. Starr. 1982. Hierarchy. University of Chicago Press, Chicago, Illinois, USA.

    Google Scholar 

  • Allen, T.F.H., and T.W. Hoekstra. 1992. Toward a unified ecology. Columbia University Press, New York, New York, USA.

    Google Scholar 

  • Barnsley, M. 1988. Fractals everywhere. Academic Press, New York, New York, USA.

    Google Scholar 

  • Blueweiss, L., H. Fox, V. Kudzma, D. Nakashima, R. Peters, and S. Sams. 1978. Relationships between body size and some life history parameters. Oecologia (Berlin) 37:257–272.

    Article  Google Scholar 

  • Brody, S. 1945. Bioenergetics and growth. Reinhold Publishing Company, Baltimore, Maryland, USA.

    Google Scholar 

  • Brown, J.H. 1995 Macroecology. University of Chicago Press, Chicago, Illinois, USA.

    Google Scholar 

  • Brown, J.H., P.A. Marquet, and M.L. Taper. 1993. Evolution of body size: conse-quences of an energetic definition of fitness. American Naturalist 142:573–584.

    Article  PubMed  CAS  Google Scholar 

  • Burrough, P.A. 1986. Principles of geographical information systems for land re-sources. Assessment. Clarendon Press, Oxford, UK.

    Google Scholar 

  • Clements, F.E. 1905. Research methods in ecology. The University Publishing Company, Lincoln, Nebraska USA.

    Google Scholar 

  • Crawford, E.C. Jr., and R.C. Lasiewski. 1968. Oxygen consumption and respiratory evaporation of the emu and rhea. Condor 70:333–339.

    Article  Google Scholar 

  • Cressie, N.A.C. 1991. Statistics for spatial data. J. Wiley & Sons Inc., New York, New York, USA.

    Google Scholar 

  • Cresswick, R.J., H.A. Farach, and C.P. Poole, Jr. 1992. Introduction to renormalization group methods in physics. J. Wiley & Sons Inc., New York, New, Yrok, USA.

    Google Scholar 

  • Damuth, J. 1981 Population size and body size in mammals. Nature 290:699–700.

    Article  Google Scholar 

  • Delcourt, H.R., and P.A. Delcourt. 1988. Quaternary landscape ecology: relevant scales in space and time. Landscape Ecology 2:23–44.

    Article  Google Scholar 

  • Deutsch, C.V., and A.G. Journel. 1992. GSLIB: Geostatistical software library and user’s guide. Oxford University Press, Oxford, UK.

    Google Scholar 

  • Erickson, R.O. 1945. The Clematis fremontii var. Riehlii population in the Ozarks. Annals of the Missouri Botanical Garden 32:413–460.

    Article  Google Scholar 

  • Evans, D.L., and Z. Zhu. 1993. AVHRR for forest mapping: national applications and global implications. p. 76–79 in A. Lewis, editor. Looking to the future with an eye on the past: proceedings of the 1993 ACMS/ASPRS. American Society of Photogrammetry and Remote Sensing.

    Google Scholar 

  • Feder, J. 1988. Fractals. Plenum Press, New York, New York, USA.

    Google Scholar 

  • Feller, W. 1951. The asymptotic distribution of the range of sums of independent random variables. Annals of Mathematical Statistics 22:427.

    Article  Google Scholar 

  • Forman, R.T.T. 1995. Land mosaics. Cambridge University Press. Cambridge, UK.

    Google Scholar 

  • Frank, D.A., and R.S. Inouye. 1994. Temporal variation in actual evapo-transpiration of terrestrial ecosystems: patterns and ecological processes. Journal of Biogeography 21:401–411.

    Article  Google Scholar 

  • Gould, H., and J. Tobochnik. 1988. An introduction to computer simulation methods: applications to physical systems. Part 2. Addison-Wesley Publishing Company, Reading, Massachusetts, USA.

    Google Scholar 

  • Grassberger, P., and I. Procaccia. 1983. Measuring the strangeness of strange attractors. Physica D 9:189–208.

    Article  Google Scholar 

  • Gupta, V.K., and E.D. Waymire. 1989 Statistical self-similarity in river networks parameterized by elevation. Water Resources Research 25:463–476.

    Article  Google Scholar 

  • Harestad, A.S., and F.L. Bunnell. 1979. Home range and body weight: A reevaluation. Ecology 60:389–402.

    Article  Google Scholar 

  • Holling, C.S. 1992. Cross-scale morphology, geometry and dynamics of ecosystems. Ecological Monographs 62:447–502.

    Article  Google Scholar 

  • Hurlbert, S.H. 1984. Pseudoreplication and the design of ecological field experiments. Ecological Monographs 54:187–211.

    Article  Google Scholar 

  • Hurst, H.E. 1951. Long-term storage capacity of reservoirs. Transactions of the American Society Civil Engineers 116:770–808.

    Google Scholar 

  • Johnson, A.R., B.T. Milne, and J.A. Wiens. 1992. Diffusion in fractal landscapes: Simulations and experimental studies of Tenebrionid beetle movements. Ecology 73:1968–1983.

    Article  Google Scholar 

  • Kauffman, S.A. 1993. The origins of order. Oxford University Press, Oxford, UK.

    Google Scholar 

  • Keitt, T.H., and A.R. Johnson. 1995. Spatial heterogeneity and anomalous kinetics: Emergent patterns in diffusion-limited predator-prey interactions. Journal of Theoretical Biology 172:127–139.

    Article  Google Scholar 

  • Krummel, J.R., R.H. Gardner, G. Sugihara, R.V. O’Neill, and P.R. Coleman. 1987. Landscape pattern in a disturbed environment. Oikos 48:321–324.

    Article  Google Scholar 

  • Levin, S.A. 1992. The problem of pattern and scale in ecology. Ecology 73:1942–1968.

    Article  Google Scholar 

  • Loehle, C., and B.-L. Li. 1996. Statistical properties of ecological and geologic fractals. Ecological Modelling 85:271–284.

    Article  Google Scholar 

  • MacArthur, R.H. 1972. Geographical ecology. Princeton University Press, Princeton, New Jersey, USA.

    Google Scholar 

  • Magnuson, J.J. 1990. Long-term ecological research and the invisible present. BioScience 40:495–501.

    Article  Google Scholar 

  • Mandelbrot, B.B. 1982. The fractal geometry of nature. W.H. Freeman and Co., New York, New York, USA.

    Google Scholar 

  • Mandelbrot, B.B., and J.R. Wallis. 1969. Some long-run properties of geophysical records. Water Resources Research 5:321–340.

    Article  Google Scholar 

  • Mangel, M., and F.R. Adler. 1994. Construction of multidimensional clustered patterns. Ecology 75:1289–1298.

    Article  Google Scholar 

  • Milne, B.T. 1991a. Lessons from applying fractal models to landscape patterns. Pp. 199–235 in M.G. Turner, and R.H. Gardner, editors. Quantitative methods in landscape ecology. Springer-Verlag, New York, New York, USA.

    Google Scholar 

  • Milne, B.T. 1991b. The utility of fractal geometry in landscape design. Landscape and Urban Planning 21:81–90.

    Article  Google Scholar 

  • Milne, B.T. 1992a. Spatial aggregation and neutral models in fractal landscapes. American Naturalist 139:32–57.

    Article  Google Scholar 

  • Milne, B.T. 1992b. Indications of landscape condition at many scales. Pp. 883–895 in D.H. McKenzie, D.E. Hyatt, and V.J. McDonald, editors. Ecological indicators. Vol. 2. Elsevier Applied Science, London, UK and New York, New York, USA.

    Google Scholar 

  • Milne, B.T. 1993. Pattern analysis for landscape evaluation and characterization. Pp. 131–143 in M.E. Jensen, and P.S. Bourgeron, compilers. Ecosystem management: principles and applications. United States Department of Agriculture, Forest Service Pacific Northwest Research Station General Technical Report PNWGTR-318. Portland, Oregon, USA.

    Google Scholar 

  • Milne, B.T., and R.T.T. Forman. 1986. Peninsulas in Maine: woody plant diversity, distance, and environmental patterns. Ecology 67:967–974.

    Article  Google Scholar 

  • Milne, B.T., K. Johnston, and R.T.T. Forman 1989. Scale-dependent proximity of wildlife habitat in a spatially-neutral Bayesian model. Landscape Ecology 2:101–110.

    Article  Google Scholar 

  • Milne, B.T., M.G. Turner, J.A. Wiens, and A.R. Johnson. 1992. Interactions between the fractal geometry of landscapes and allometric herbivory. Theoretical Population Biology 41:337–353.

    Article  Google Scholar 

  • Milne, B.T., and A.R. Johnson. 1993. Renormalization relations for scale transformation in ecology. Pp. 109–128 in R.H. Gardner, editor. Some mathematical questions in biology: predicting spatial effects in ecological systems. American Mathematical Society, Providence, Rhode Island, USA.

    Google Scholar 

  • Milne, B.T., A.R. Johnson, T.H. Keitt, C.A. Hatfield, J.L. David, and P. Hraber. 1996. Detection of critical densities associated with piñon-juniper woodland ecotones. Ecology 77:805–821.

    Article  Google Scholar 

  • Morgan, F. 1988. Geometric measure theory. Academic Press. New York, New York, USA.

    Google Scholar 

  • Morse, D.R., J.H. Lawton, M.M. Dodson, and M.H. Williamson. 1985. Fractal dimension of vegetation and the distribution of arthropod body lengths. Nature 314:731–734.

    Article  Google Scholar 

  • Niklas, K.J. 1994. Plant allometry: the scaling of form and process. University of Chicago Press, Chicago, Illinois, USA.

    Google Scholar 

  • O’Neill, R.V., J.R. Krummel, R.H. Gardner, G. Sugihara, B. Jackson, D.L. DeAngelis, B.T. Milne, M.G. Turner, B. Zygmunt, S.W. Christensen, V.H. Dale, and R.L. Grahm. 1988. Indices of landscape pattern. Landscape Ecology 1:153–162.

    Article  Google Scholar 

  • Palmer, M.W. 1988. Fractal geometry: a tool for describing spatial patterns of plant communities. Vegetatio 75:91–102.

    Article  Google Scholar 

  • Pauly, D., and I. Tsukayama, editors. 1987. The Peruvian anchoveta and its upwelling ecosystem: three decades of change. Instituto de Mar del Peru, Callao, Peru.

    Google Scholar 

  • Peitgen, H.-O., and D. Saupe. 1988. The science of fractal images. Springer-Verlag, New York, New York, USA

    Google Scholar 

  • Pennycuick, C.J., and Kline, N.C. 1986. Units of measurement for fractal extent, applied to the coastal distribution of bald eagle nests in the Aleutian Islands, Alaska. Oecologia 68:254–258.

    Article  Google Scholar 

  • Peters, R.H. 1983. The ecological implications of body size. Cambridge University Press, Cambridge, UK.

    Book  Google Scholar 

  • Pielou, E.C. 1977. Mathematical ecology. J. Wiley & Sons, New York, New York, USA.

    Google Scholar 

  • Plotnick, R.E., and M.L. McKinney. 1993. Ecosystem organization and extinction dynamics. Palios 8:202–212.

    Article  Google Scholar 

  • Preston, F.A. 1962. The canonical distribution of commonness and rarity, Part I. Ecology 43:185–215,431–32.

    Google Scholar 

  • Pulliam, H.R., and B.J. Danielson. 1991. Sources, sinks, and habitat selection: a landscape perspective in population dynamics. American Naturalist 137:S50–S60.

    Article  Google Scholar 

  • Quinn, W.H., V.T. Neal, and S.E. Antunez de Mayolo. 1987. El Niño over the pastfour and a half centuries. Journal Geophysical Research 92:14449–14461.

    Article  Google Scholar 

  • Richardson, L.F. 1960. Statistics of deadly quarrels. E.Q. Wright and C.C. Lienau, editors. Boxwood Press, Pacific Grove, California, USA.

    Google Scholar 

  • Robards, F.C., and J.I. Hodges. 1976. Observations from 2760 bald eagle nests in southeast Alaska: progress report 1969–1976. United States Department of the Interior, Fish and Wildlife Service, Eagle Management Study. Juneau, Alaska, USA.

    Google Scholar 

  • Root, T. 1988. Energy constraints on avian distributions and abundances. Ecology 69:330–339.

    Article  Google Scholar 

  • Rosenzweig, M.L. 1995. Species diversity in space and time. Cambridge University Press, Cambridge, Massachusetts, USA.

    Book  Google Scholar 

  • Rossi, R.E., D.J. Mulla, A.G. Journel, and E.H. Franz. 1992. Geostatistical tools for modelling and interpreting ecological dependence. Ecological Monographs 62:277–314.

    Article  Google Scholar 

  • Scheuring, I. 1991. The fractal nature of vegetation and the species-area relation. Theoretical Population Biology 39:170–177.

    Article  Google Scholar 

  • Scheuring, I., and R.H. Riedi. 1994. Application of multifractals to the analysis of vegetation pattern. Journal of Vegetation Science 5:489–495.

    Article  Google Scholar 

  • Schneider, D.C. 1994. Quantitative ecology: spatial and temporal scaling. Academic Press, San Diego, California, USA.

    Google Scholar 

  • Senft, R.L., M.B. Coughenour, D.W. Bailey, L.R. Rittenhouse, O.E. Sala, and D.M. Swift. 1987. Large herbivore foraging and ecological hierarchies. BioScience 37:789–799.

    Article  Google Scholar 

  • Simpson, G.G. 1964. Species density of North American recent mammals. Systematic Zoology 13:57–73.

    Article  Google Scholar 

  • SolĂ©, R.V., D. LĂłpez, M. Ginovart, and J. Valls. 1992. Self-organized criticality in Monte Carlo simulated ecosystems. Physics Letters A 172:56–61.

    Article  Google Scholar 

  • SolĂ©, R.V., and S.C. Manrubia. 1995. Are rainforests self-organized in a critical state? Journal of Theoretical Biology 173:31–40.

    Article  Google Scholar 

  • Sommerer, J.C., and E. Ott. 1993. Particles floating on a moving fluid: a dynamically comprehensible physical fractal. Science 259:335–339.

    Article  PubMed  CAS  Google Scholar 

  • Spalinger, D.E., and N.T. Hobbs. 1992. Mechanisms of foraging in mammalian herbivores: new models of functional response. American Naturalist 140:325–348.

    Article  PubMed  CAS  Google Scholar 

  • Stahl, W.R. 1962. Similarity and dimensional methods in biology. Science 137:205–212.

    Article  PubMed  CAS  Google Scholar 

  • Tilman, D., and D. Wedin. 1991. Oscillations and chaos in the dynamics of a perennial grass. Nature 353:653–655.

    Article  Google Scholar 

  • Turcotte, D.L. 1992. Fractals and chaos in geology and geophysics. Cambridge University Press, Cambridge, UK.

    Google Scholar 

  • Turner, M.G., R.V. O’Neill, R.H. Gardner, and B.T. Milne. 1989. Effects of changing spatial scale on the analysis of landscape pattern. Landscape Ecology 3:153–162.

    Article  Google Scholar 

  • Urban, D.L., R.V. O’Neill, and H.H. Shugart. 1987. Landscape ecology. BioScience 37:119–127.

    Article  Google Scholar 

  • Voss, R.F. 1988. Fractals in nature: from characterization to simulation. Pp. 21–70 in H.-O. Peitgen and D. Saupe, editors. The science of fractal images. Springer-Verlag, New York, New York, USA.

    Google Scholar 

  • Wiens, J.A. 1989. Spatial scaling in ecology. Functional Ecology 3:383–397.

    Article  Google Scholar 

  • Yamamura, N. 1976. A mathematical approach to spatial distribution and temporal succession in plant communities. Bulletin of Mathematical Biology 38:517–526.

    Google Scholar 

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Authors
  1. Bruce T. Milne
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Editors and Affiliations

  1. Utah Cooperative Fish and Wildlife Research Unit (U.S. Geological Survey—Biological Resources Devision) Department of Fisheries and Wildlife College of Natural Resources, Utah State University, Logan, UT, 84322-5290, USA

    John A. Bissonette

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Milne, B.T. (1997). Applications of Fractal Geometry in Wildlife Biology. In: Bissonette, J.A. (eds) Wildlife and Landscape Ecology. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1918-7_2

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  • DOI: https://doi.org/10.1007/978-1-4612-1918-7_2

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