Landscape Ecology

, Volume 8, Issue 3, pp 201–211 | Cite as

Lacunarity indices as measures of landscape texture

  • Roy E. Plotnick
  • Robert H. Gardner
  • Robert V. O'Neill


Lacunarity analysis is a multi-scaled method of determining the texture associated with patterns of spatial dispersion (i.e., habitat types or species locations) for one-, two-, and three-dimensional data. Lacunarity provides a parsimonious analysis of the overall fraction of a map or transect covered by the attribute of interest, the degree of contagion, the presence of self-similarity, the presence and scale of randomness, and the existence of hierarchical structure. For self-similar patterns, it can be used to determine the fractal dimension. The method is easily implemented on the computer and provides readily interpretable graphic results. Differences in pattern can be detected even among very sparsely occupied maps.


lacunarity landscape texture spatial analysis fractals 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Allain, C. and Cloitre, M. 1991. Characterizing the lacunarity of random and deterministic fractal sets. Physical Review A 44: 3552–3558.Google Scholar
  2. Comins, H.N. and Noble, I.R. 1985. Dispersal, variability, and transient niches; species coexistence in a uniformly variable environment. Am. Nat. 126: 706–723.Google Scholar
  3. Elliot, J.M. 1977. Some Methods for the Statistical Analysis of Samples of Benthic Invertebrates. Freshwater Biological Association, Scientific Publication no. 25.Google Scholar
  4. Feder, J. 1988. Fractals. Plenum, New York.Google Scholar
  5. Forman, R.T.T. and Godron, M. 1986. Landscape Ecology. John Wiley and Sons, NY.Google Scholar
  6. 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
  7. Gardner, R.H. and O'Neill, R.V. 1991. Pattern, process and predictability: The use of neutral models for landscape analysis. pp 289–307. In: Turner, M.G. and Gardner, R.H., eds. Quantitative Methods in Landscape Ecology. The analysis and interpretation of landscape heterogeneity. Ecological Studies Series, Springer-Verlag, New York.Google Scholar
  8. Gardner, R.H., O'Neill, R.V., and Turner, M.G. Ecological implications of landscape fragmentation. Proceedings of the Cary Conference. In Press.Google Scholar
  9. Gefen, Y., Meir, Y., and Aharony, A. 1983. Geometric implementation of hypercubic lattices with noninteger dimensionality by use of low lacunarity fractal lattices. Physical Review Letters, 50: 145–148.Google Scholar
  10. Gefen, Y., Aharony, A. and Mandelbrot, B.B. 1984. Phase transitions on fractals: III. Infinitely ramified lattices. Journal Physics A: Mathematical and General, 17: 177–1289.Google Scholar
  11. Getis, A. and Franklin, J. 1987. Second-order neighborhood analysis of mapped point patterns. Ecology, 68: 473–477.Google Scholar
  12. Geritz, S.A.H., Metz, J.A.J., Klinkhamer, P.G.L. and De Jong, T.J. 1987. Competition in safe sites. Theor. Pop. Biol. 33: 161–180.Google Scholar
  13. Gosz J.R. 1992. Fundamental ecological characteristics of landscape boundaries, pp 9–30. In: The Role of Landscape Boundaries in the Management and Restoration of Changing Environments, M.M. Holland, P.G. Risser and R.J. Naiman (eds.), Chapman and Hall, NY.Google Scholar
  14. Greig-Smith, P. 1964. Quantitative Plant Ecology. 2nd ed., Butterworths, London.Google Scholar
  15. Kareiva, P. 1986. Patchiness, dispersal, and species interactions: consequences for communities of herbivorous insects. Pages 192–206, in J. Diamond and T.J. Case, eds. Community ecology. Harper and Row, New York.Google Scholar
  16. Kareiva, P. 1990. Population dynamics in spatially complex environments: theory and data. Phil. Trans. R. Soc. Lond. B 330: 175–190.Google Scholar
  17. Kaye, B.H. 1989. A Random Walk Through Fractal Dimensions. VCH Publishers, New York.Google Scholar
  18. 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
  19. Lin, B. and Yang, Z.R. 1986. A suggested lacunarity expression for Sierpinski carpets. Journal Physics A: Mathematical and General, 19: L49-L52.Google Scholar
  20. Mandelbrot, B.B. 1983. The Fractal Geometry of Nature. W.H. Freeman, New York.Google Scholar
  21. Milne, B.T. 1992. Spatial aggregation and neutral models in fractal landscapes. Amer. Nat. 139: 32–57.Google Scholar
  22. Morisita, M., 1959. Measuring the dispersion of individuals and analysis of distributional patterns. Mem. Fac. Sci. Kyushu Univ. Serie E (Biology) 2: 215–235.Google Scholar
  23. O'Neill, R.V., Krummel J.R., Gardner, R.H., Sugihara, G., Jackson, B., DeAngelis, D.L., Milne, B.T., Turner, M.G., Zygmunt, B., Christensen, S.W., Dale, V.H., Graham, R.L. 1988a. Indices of landscape pattern. Landscape Ecology 1: 153–162.Google Scholar
  24. O'Neill, R.V., Milne, B.T., Turner, M.G., and Gardner, R.H. 1988b. Resource utilization scales and landscape pattern. Landscape Ecology 2: 63–69.Google Scholar
  25. O'Neill, R.V., Gardner, R.H., Turner, M.G. A hierarchical neutral model for landscape analysis. Landscape Ecology, In Press.Google Scholar
  26. Pacala, S.W. 1987. Neighborhood models of plant population dynamics. III Models with spatial heterogeneity in the physical environment. Theor. Pop. Biol. 31: 359–392.Google Scholar
  27. Palmer, M.W. 1992. The coexistence of species in fractal landscapes. American Naturalist, 139: 375–397.Google Scholar
  28. Pielou, E.C. 1969. An Introduction to Mathematical Ecology. Wiley-Interscience, New York.Google Scholar
  29. Turner, M.G., and Gardner, R.H. 1991. Quantitative Methods in Landscape Ecology: An Introduction, pp 3–14. In: Turner, M.G. and R.H. Gardner, eds. Quantitative Methods in Landscape Ecology. The analysis and interpretation of landscape heterogeneity. Ecological Studies Series, Springer-Verlag, New York.Google Scholar
  30. Voss, R. 1988. Fractals in nature: from characterization to simulation, pp 22–70. In: Peitgen, H. and D. Saupe, eds. The Science of Fractal Images. Springer-Verlag, New York.Google Scholar
  31. Wiens, J.A. and Milne, B.T. 1989. Scaling of ‘landscapes’ in landscape ecology, or landscape ecology from a beetle's perspective. Landscape Ecology 3: 87–96.Google Scholar

Copyright information

© SPB Academic Publishing bv 1993

Authors and Affiliations

  • Roy E. Plotnick
    • 1
  • Robert H. Gardner
    • 2
  • Robert V. O'Neill
    • 2
  1. 1.Department of Geological SciencesUniversity of Illinois at ChicagoChicagoUSA
  2. 2.Environmental Sciences DivisionOak Ridge National LaboratoryOak RidgeUSA

Personalised recommendations