Environmental and Ecological Statistics

, Volume 6, Issue 3, pp 275–290 | Cite as

Twist number statistics as an additional measure of habitat perimeter irregularity

  • J. BogaertEmail author
  • P. Van Hecke
  • R. Moermans
  • I. Impens


Individual habitats are altered by the surrounding landscape matrix. Quantitative analysis of habitat boundary is therefore necessary. A shape index is proposed based on the perimeter twist number; twists divide the patch perimeter in seperate segments. Using Principal Components Analysis, the shape index is compared with fractal dimension (per-patch calculation based on area and perimeter) and with four shape (compactness) indices based upon pixel geometry, next to area and perimeter statistics. The analysis is executed with simulated data based on percolation maps. The proposed index can be used as a complementary shape descriptor because of (i) its independence of fractal dimension, (ii) its restricted correlation with only one compactness index and (iii) its ability to identify habitats characterized by limes divergens and a high interior-edge ratio.

fractal dimension habitat boundary landscape ecology limes convergens and divergens percolation map principal components analysis 


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  1. Baker, W.L. and Cai, Y. (1992) The r.le programs for multiscale analysis of landscape structure using the GRASS geographical information system. Landscape Ecology, 7(4), 291–302.Google Scholar
  2. Bogaert, J. and Impens, I. (1998) An improvement on area-perimeter ratios for interior-edge evaluation of habitats. In Proceedings of the 10th Portuguese Conference on Pattern Recognition, F. Muge, R.C. Pinto and M. Piedade (eds), IST, Lisbon, Portugal, March 26–27, pp. 55–61.Google Scholar
  3. Bribieska, E. (1997) Measuring 2-D shape compactness using the contact perimeter. Computers and Mathematics with Applications, 33(11), 1–9.Google Scholar
  4. Burrough, P.A. (1981) Fractal dimensions of landscapes and other environmental data. Nature, 294, 240–2.Google Scholar
  5. Chrisman, N. (1997) Exploring geographic information systems, John Wiley & Sons, New York.Google Scholar
  6. De Cola, L. (1989) Fractal analysis of a classified Landsat scene. Photogrammetric Engineering & Remote Sensing, 55(5), 601–1.Google Scholar
  7. Farina, A. (1998) Principles and methods in landscape ecology, Chapman & Hall, London.Google Scholar
  8. Forman, R.T.T. (1981) Interaction among landscape elements: a core of landscape ecology. In Perspectives in landscape ecology, contributions to research, planning and management of our environment, S.P. Tjallingii and A.A. de Veer (eds), Proceedings of the International Congress organized by the Netherlands Society for Landscape Ecology, Veldhoven, The Netherlands, April 6–11. Center for Agricultural Publishing and Documentation, Wageningen. pp. 35–48.Google Scholar
  9. Forman, R.T.T. (1997) Land mosaics. The ecology of landscapes and regions, Cambridge University Press.Google Scholar
  10. Forman, R.T.T. and Godron, M. (1986) Landscape ecology, John Wiley & Sons, New York.Google Scholar
  11. Frohn, R.C. (1998) Remote sensing for landscape ecology: new metric indicators for monitoring, modeling and assessment of ecosystems, Lewis Publishers, CRC Press LLC, Boca Raton, Florida.Google Scholar
  12. Game, M. (1980) Best shape for nature reserves. Nature, 287, 630–2.Google Scholar
  13. Groom, M.J. and Schumaker, N. (1993) Evaluating landscape change: patterns of worldwide deforestation and local fragmentation. In Biotic interactions and global change, P.M. Kareiva, J.G. Kingsolver and R.B. Huey (eds), Sinauer Associates Inc, Sunderland, Massachusetts. pp. 24–44.Google Scholar
  14. Guttmann, A.J. (1982) On the number of lattice animals embeddable in the square lattice. Journal of Physics A: Mathematical, Nuclear and General, 15, 1987–9.Google Scholar
  15. Jackson, J.E. (1991) A user's guide to principal components, John Wiley & Sons, New York.Google Scholar
  16. Johnson, G.D., Tempelman, A., and Patil, G.P. (1995) Fractal based methods in ecology: a review for analysis at multiple spatial scales. Coenoses, 10(2–3), 123–31.Google Scholar
  17. Kenkel, N.C. and Walker, D.J. (1996) Fractals in the biological sciences. Coenoses, 11(2), 77–10.Google Scholar
  18. Kovach, W.L. (1993) MVSP—A MultiVariate Statistical Package for IBM-PC's (version 2.1), Kovach Computing Services, Pentraeth, Wales, U.K.Google Scholar
  19. Krummel, J.R., Gardner, R.H., Sugihara, G., O'Neill, R.V., and Coleman, P.R. (1987) Landscape patterns in a distributed environment. Oikos, 48, 321–4.Google Scholar
  20. Lagro, J. (1991) Assessing patch shape in landscape mosaics. Photogrammetric Engineering & Remote Sensing, 57(3), 285–93.Google Scholar
  21. Lam, N.S.N. (1990) Description and measurement of Landsat TM images using fractals. Photogrammetric Engineering & Remote Sensing, 56(2), 187–95.Google Scholar
  22. Lovejoy, S. (1982) Area-perimeter relation for rain and cloud areas. Science, 216, 185–7.Google Scholar
  23. Mandelbrot, B.B. (1967) How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science, 156, 636–8.Google Scholar
  24. Mandelbrot, B.B. (1977) Fractals: form, chance and dimension, W.H. Freeman and Co., San Francisco.Google Scholar
  25. Manly, B.F.J. (1991) Randomization and Monte Carlo methods in biology, Chapman and Hall, London.Google Scholar
  26. McGarigal, K. and Marks, B.J. (1993) FRAGSTATS: spatial pattern analysis program for quantifying landscape structure (version 1.0), Oregon State University, Forest Science Department, Corvallis.Google Scholar
  27. Milne, B.T. (1988) Measuring the fractal geometry of landscapes. Applied Mathematics and Computation, 27, 67–79.Google Scholar
  28. Milne, B.T. (1991) Lessons from applying fractal models to landscape patterns. In Quantitative methods in landscape ecology, M.G. Turner and R.H. Gardner (eds), Springer-Verlag, New York, pp. 199–235.Google Scholar
  29. Olsen, E.R., Ramsey, R.D., and Winn, D.S. (1993) A modified fractal dimension as a measure of landscape diversity. Photogrammetric Engineering & Remote Sensing, 59(10), 1517–2.Google Scholar
  30. Patton, D.R. (1975) A diversity index for quantifying habitat “edge”. Wildlife Society Bulletin, 3(4), 171–3.Google Scholar
  31. Riiters, K.H., O'Neill, R.V., Hunsaker, C.T., Wickham, J.D., Yankee, D.H., Timmins, S.P., Jones, K.B., and Jackson, B.L. (1995) A factor analysis of landscape pattern and structure metrics. Landscape Ecology, 10(1), 23–39.Google Scholar
  32. Ripple, W.J., Bradshaw, G.A., and Spies, T.A. (1991) Measuring forest landscape patterns in the Cascade Range of Oregon, USA. Biological Conservation, 57, 73–88.Google Scholar
  33. Schumaker, N.H. (1996) Using landscape indices to predict habitat connectivity. Ecology, 77(4), 1210–25.Google Scholar
  34. Stauffer, D. (1985) Introduction to percolation theory, Taylor & Francis, London.Google Scholar
  35. Sugihara, G. and May, R.M. (1990) Applications of fractals in ecology. Trends in Ecology and Evolution, 5(3), 79–86.Google Scholar
  36. Turner, M.G. (1989) Landscape ecology: the effect of pattern on process. Annual Review of Ecology and Systematics, 20, 171–97.Google Scholar
  37. USA-CERL (1993) GRASS 4.1 User's Reference Manual, United States Army Corps of Engineers, Construction Engineering Research Laboratories, Champaign, Illinois.Google Scholar
  38. Van Leeuwen, C.G. (1965) The isomorphy of natural and anthropogeneous landscapes with regard to the environmental conditions in border areas. Gorteria, 2, 93–105 (in Dutch + English summary).Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • J. Bogaert
    • 1
    Email author
  • P. Van Hecke
    • 1
  • R. Moermans
    • 2
  • I. Impens
    • 1
  1. 1.Department of Biology, Research Group of Plant and Vegetation EcologyUniversity of AntwerpWilrijkBelgium
  2. 2.Biometric UnitAgricultural Research CenterMerelbekeBelgium

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