, Volume 75, Issue 1–2, pp 91–102

Fractal geometry: a tool for describing spatial patterns of plant communities

  • Michael W. Palmer


Vegetation is a fractal because it exhibits variation over a continuum of scales. The spatial structure of sandrim, bryophyte, pocosin, suburban lawn, forest tree, and forest understory communities was analyzed with a combination of ordination and geostatistical methods. The results either suggest appropriate quadrat sizes and spacings for vegetation research, or they reveal that a sampling design compatible with classical statistics is impossible. The fractal dimensions obtained from these analyses are generally close to 2, implying weak spatial dependence. The fractal dimension is not a constant function of scale, implying that patterns of spatial variation at one scale cannot be extrapolated to other scales.


Geostatistics Gradient analysis Heterogeneity Homogeneity Ordination 


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  1. Auerbach M. & Shmida A. 1987. Spatial scale and the determinants of plant species richness. Trends Ecol. Evol. 2: 238–242.Google Scholar
  2. Burrough P. A. 1981. Fractal dimensions of landscapes and other environmental data. Nature 294: 240–242.Google Scholar
  3. Burrough P. A. 1983. Multiscale sources of spatial variation in soil. I. Application of fractal concepts to nested levels of soil variation. J. Soil Sci. 34: 577–597.Google Scholar
  4. Clark I. 1979. Practical geostatistics. Applied Science Publishers, London.Google Scholar
  5. Cliff A. D. & Ord J. K. 1981. Spatial processes: models and applications. Pion, London.Google Scholar
  6. Cook D. G. & Pocock S. J. 1983. Multiple regression in geographical mortality studies, with allowance for spatially correlated errors. Biometrics 39: 361–371.Google Scholar
  7. Culling W. E. H. 1986. Highly erratic spatial variability of soil-pH on Iping Common, West Sussex. Catena 13: 81–98.Google Scholar
  8. Dietvorst P., van der Maarel E. & van der Putten H. 1982. A new approach to the minimal area of a plant community. Vegetatio 50: 77–91.Google Scholar
  9. Fingleton B. 1986. Analyzing cross-classified data with inherent spatial dependence. Geogr. Anal. 18: 48–61.Google Scholar
  10. Gauch H. G. 1982. Noise reduction by eigenvector ordinations. Ecology 63: 1643–1649.Google Scholar
  11. Greig-Smith P. 1961. Data on pattern within plant communities. I. The analysis of pattern. J. Ecology 49: 695–702.Google Scholar
  12. Hill M. O. 1979. DECORANA: a FORTRAN program for detrended correspondence analysis and reciprocal averaging. Section of Ecology and Systematics CEP-40. Cornell University, Ithaca, New York.Google Scholar
  13. Hill M. O. & GauchJr H. G. 1980. Detrended correspondence analysis: an improved ordination technique. Vegetatio 42: 47–58.Google Scholar
  14. Hurlbert S. H. 1984. Pseudoreplication and the design of ecological field experiments. Ecol. Monogr. 54: 187–211.Google Scholar
  15. Journel A. G. & Huijbregts C. 1978. Mining geostatistics. Academic Press, London.Google Scholar
  16. Kershaw K. A. 1963. Pattern in vegetation and its causality. Ecology 44: 377–388.Google Scholar
  17. Krummel J. P., Gardner R. H., Sugihara G., O'Neill R. V. & Coleman P. R. 1987. Landscape patterns in a disturbed environment. Oikos 48: 321–324.Google Scholar
  18. Legendre, P., Sokal, R. R., Oden, N. L. & Vaudor, A. 1987. Analysis of variance with a tocorrelation in both the variable and the classification criterion. Proc. 1. Conf. Int. Fed. Classification Soc., Aachen, p. 110.Google Scholar
  19. Malanson G. P. 1985. Spatial autocorrelation and distributions of plant species on environmental gradients. Oikos 45: 278–280.Google Scholar
  20. Mandelbrot B. B. 1982. The fractal geometry of nature. Freeman, San Francisco.Google Scholar
  21. Olsvig-Whittaker L., Shachak M. & Yair A. 1983. Vegetation patterns related to environmental factors in a Negev Desert Watershed. Vegetatio 54: 153–165.Google Scholar
  22. Pennycuick C. J. & 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.Google Scholar
  23. Phillips J. D. 1985. Measuring complexity of environmental gradients. Vegetatio 64: 95–102.Google Scholar
  24. Robertson G. P. 1987. Geostatistics in ecology: interpolating with known variance. Ecology 68: 744–748.Google Scholar
  25. Sander L. M. 1986. Fractal growth processes. Nature 322: 789–793.Google Scholar
  26. Shmida A. & Ellner S. 1984. Coexistence of plant species with similar niches. Vegetatio 58: 29–55.Google Scholar
  27. Shmida A. & Wilson M. V. 1985. Biological determinants of species diversity. J. Biogeog. 12: 1–20.Google Scholar
  28. ter Braak, C. J. F. 1980. Binary mosaics and point quadrat sampling in ecology. Master's Thesis, University of Newcastle upon Tyne.Google Scholar
  29. ter Braak C. J. F. 1986. Canonical correspondence analysis: a new eigenvector technique for multivariate direct gradient analysis. Ecology 67: 1167–1179.Google Scholar
  30. ter Braak C. J. F. 1987. The analysis of vegetation-environment relationships by canonical correspondence analysis. Vegetatio 69: 69–77.Google Scholar
  31. Vlcek J. & Cheung E. 1986. Fractal analysis of leaf shapes. Can. J. For. Res. 16: 124–127.Google Scholar
  32. Wilkinson, G. N., Eckert, S. R., Hancock, T. W. & Mayo, O. 1983. Nearest neighbour (NN) analysis of field experiments. J. R. Statist. Soc. Ser. B.: 151–211.Google Scholar
  33. Wilson M. V. & Mohler C. L. 1983. Measuring compositional change along gradients. Vegetatio 54: 129–141.Google Scholar

Copyright information

© Kluwer Academic Publishers 1988

Authors and Affiliations

  • Michael W. Palmer
    • 1
  1. 1.Department of BotanyDuke UniversityDurhamUSA

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