Landscape Ecology

, Volume 14, Issue 1, pp 17–33 | Cite as

Scaling properties in landscape patterns: New Zealand experience

  • Vladimir I. Nikora
  • Charles P. Pearson
  • Ude Shankar


In this paper we present a case study of spatial structure in landscape patterns for the North and South Islands of New Zealand. The aim was to characterise quantitatively landscape heterogeneity and investigate its possible scaling properties. The study examines spatial heterogeneity, in particular patchiness, at a range of spatial scales, to help build understanding on the effects of landscape heterogeneity on water movement in particular, and landscape ecology in general.

We used spatial information on various landscape properties (soils, hydrogeology, vegetation, topography) generated from the New Zealand Land Resource Inventory. To analyse this data set we applied various methods of fractal analyses following the hypothesis that patchiness in selected landscape properties demonstrates fractal scaling behaviour at two structural levels: (1) individual patches; and (2) mosaics (sets) of patches.

Individual patches revealed scaling behaviour for both patch shape and boundary. We found self-affinity in patch shape with Hurst exponent H from 0.75 to 0.95. We also showed that patch boundaries in most cases were self-similar and in a few cases of large patches were self-affine. The degree of self-affinity was lower for finer patches. Similarly, when patch scale decreases the orientation of patches tends to be uniformly distributed, though patch orientation on average is clearly correlated with broad scale geological structures. These results reflect a tendency to isotropic behaviour of individual patches from broad to finer scales. Mosaics of patches also revealed fractal scaling in the total patch boundaries, patch centers of mass, and in patch area distribution. All these reflect a special organisation in patchiness represented in fractal patch clustering. General relationships which interconnect fractal scaling exponents were derived and tested. These relationships show how scaling properties of individual patches affect those for mosaics of patches and vice-versa. To explain similarity in scaling behaviour in patchiness of different types we suggest that the Self-Organised Criticality concept should be used. Also, potential applications of our results in landscape ecology are discussed, especially in relation to improved neutral landscape models.

landscape patchiness scaling fractal dimensions self-similarity self-affinity neutral landscape models 


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  1. Bak, P. 1996. How nature works. A science of self-organized criticality. Copernicus Press, New York.Google Scholar
  2. Bour, O. and Davy, P. 1997. Connectivity of random fault networks following a power law fault length distribution. Water Resources Research 33(7): 1567–1583.CrossRefGoogle Scholar
  3. Clausen, B. and Pearson, C.P. 1995. Regional frequency analysis of annual maximum streamflow drought. Journal of Hydrology 173: 111–130.CrossRefGoogle Scholar
  4. Duncan, M.J. 1991. Macro-porosity in New Zealand soils. Internal Report No WS1423, Hydrology Centre, Christchurch, New Zealand.Google Scholar
  5. ESRI 1992. Understanding GIS. The ARC/INFO Method. ESRI, Redlands, California.Google Scholar
  6. Feder, J. 1988. Fractals. Plenum, New York.Google Scholar
  7. Gardner, R.H., Milne, B.T., Turner, M.G. and O'Neill, R.V. 1987. Neutral models for the analysis of broad-scale landscape pattern. Landscape Ecology 1: 19–28.Google Scholar
  8. Gardner, R.H., O'Neill, R.V. and Turner, M.G. 1993. Ecological implications of landscape fragmentation. In Humans as components of ecosystems: subtle human effects and the ecology of populated areas. pp. 208–226. Edited by Pickett, S.T.A. and McDonnell, M.J. Springer-Verlag, New York.Google Scholar
  9. Goodchild, M.F. and Mark, D.M. 1987. The fractal nature of geographic phenomena. Annals of the Association of American Geographers 77(2): 265–278.Google Scholar
  10. Grassberger, P. and Procaccia, I. 1983. Characterisation of strange attractors. Physical Review Letters 50(5): 346–349.CrossRefGoogle Scholar
  11. Hastings, H.M. and Sugihara, G. 1993. Fractals. A user's guide for natural sciences. Oxford University Press, Oxford.Google Scholar
  12. Hutchinson, P.D. 1990. Regression estimation of low flow in New Zealand. Publication No. 22 of The Hydrology Centre, Christchurch, New Zealand.Google Scholar
  13. King, A.W. 1991. Translating models across scales in the landscape. In Quantitative Methods in Landscape Ecology. pp. 479–517. Edited by Turner, M.G. and Gardner, R.H. Springer-Verlag, New York.Google Scholar
  14. Krummel, J.R., Gardner, R.H., Sugihara, G., O'Neill, R.V. and Coleman, P.R. 1987. Landscape patterns in a disturbed environment. Oikos 48: 321–324.Google Scholar
  15. LaGro, J. 1991. Assessing patch shape in landscape mosaics. Photogammetric Engineering and Remote Sensing 57(3): 285–293.Google Scholar
  16. Liebovitch, L.S. and Toth, T. 1989. A fast algorithm to determine fractal dimensions by box-counting. Physics Letters A 141: 386CrossRefGoogle Scholar
  17. Levin, S.A., Powell, T.M. and Steele, J.H. (eds) 1993. Patch dynamics. Lecture Notes in Biomatematics. Springer-Verlag, Berlin.Google Scholar
  18. Mandelbrot, B.B. 1983. The fractal geometry of nature. W.H. Freeman and Company, New York.Google Scholar
  19. Matsushita, M. and Ouchi, S. 1989. On the self-affinity of various curves. Physica D 38: 246–251.Google Scholar
  20. McKerchar, A.I. 1991. Regional flood frequency analysis for small New Zealand basins. 1. Mean annual flood estimation. Journal of Hydrology (NZ) 30(2): 65–76.Google Scholar
  21. Milne, B.T. 1991. Lessons from applying fractal models to landscape patterns. In Quantitative Methods in Landscape Ecology. pp. 199–235. Edited by Turner, M.G. and Gardner, R.H. Springer-Verlag, New York.Google Scholar
  22. Milne, B.T. 1992. Spatial aggregation and neutral models in fractal landscapes. American Naturalist 139(1): 32–57.CrossRefGoogle Scholar
  23. Milne, B.T., Turner, M.G., Wiens, J.A. and Johnson, A.R. 1992. Interactions between the fractal geometry of landscapes and allometric herbivory. Theoretical Population Biology 41: 337–353.Google Scholar
  24. Moon, F.C. 1987. Chaotic vibrations. John Wiley, New York.Google Scholar
  25. Newsome, P.F.J. 1992. New Zealand land resource inventory.Arc/Info_Data Manual. Landcare Research, New Zealand.Google Scholar
  26. Nikora, V., Sapozhnikov, V. and Noever, D. 1993. Fractal geometry of individual river channels and its computer simulation. Water Resources Research 29(10): 3561–3568.CrossRefGoogle Scholar
  27. Ouchi, S. and Matsushita, M. 1989. Measurement of self-affinity on surfaces as a trial application of fractal geometry to landform analysis. Geomorphology 5(1/2): 115–130.Google Scholar
  28. Pearson, C.P. 1991. Regional flood frequency for small New Zealand basins. 2. Flood frequency groups. Journal of Hydrology (NZ) 30(2): 77–92.Google Scholar
  29. Pearson, C.P. 1995. Regional frequency analysis of low flows in New Zealand rivers. Journal of Hydrology (NZ) 33(2): 94–122.Google Scholar
  30. Puigdefabregas, J. and Sanchez, G. 1996. Geomorphological implications of vegetation patchiness on semi-arid slopes. In Advances in Hillslope Processes. pp. 1027–1060. Edited by Anderson M.G. and Brooks, S.M. John Wiley, London.Google Scholar
  31. Sapozhnikov, V. and Foufoula-Georgiou, E. 1995. Study of selfsimilar and self-affine objects using logarithmic correlation integral. Journal of Physics A: Math. Gen. 28: 559–571.Google Scholar
  32. Sarraille, J. and DiFalco, P. 1992. A program for calculating fractal dimensions. California State University, Stanislaus.Google Scholar
  33. Seyfried, M.S. and Wilcox, B.P. 1995. Scale and the nature of spatial variability: Field examples having implications for hydrologic modeling. Water Resources Research 31(1): 173–184.Google Scholar
  34. Schumaker, N.H. 1996. Using landscape indices to predict habitat connectivity. Ecology 77(4): 1210–1225.Google Scholar
  35. Turner, M.G. and Gardner, R.H. (eds.) 1991. Quantitative methods in landscape ecology. Springer-Verlag, New York.Google Scholar
  36. Turcotte, D.L. 1992. Fractals and chaos in geology and geophysics. Cambridge University Press, Cambridge.Google Scholar
  37. Wiens, J.A., Schooley, R.L. and Weeks, R.D. 1997. Patchy landscapes and animal movements: do beetles percolate? Oikos 78: 257–264.Google Scholar
  38. With, K.A., Gardner, R.H. and Turner, M.G. 1997. Landscape connectivity and population distributions in heterogeneous environments. Oikos 78: 151–169.Google Scholar
  39. With, K.A. and King, A.W. 1997. The use and misuse of neutral landscape models in ecology. Oikos 79: 219–229.Google Scholar
  40. Wu, J. and Levin, S.A. 1997. A patch-based spatial modelling approach: conceptual framework and simulation scheme. Ecological Modelling 101: 325–346.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Vladimir I. Nikora
    • 1
  • Charles P. Pearson
    • 1
  • Ude Shankar
    • 1
  1. 1.National Institute of Water and Atmospheric Research Ltd (NIWA)ChristchurchNew Zealand

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