Spatial Interpolation Methods for Interpretation of Ordination Diagrams

  • M. Hauser
  • L. Mucina
Chapter
Part of the Handbook of vegetation science book series (HAVS, volume 11)

Abstract

Spatial interpolation methods are very popular in geosciences. Among these, trend surface analysis (TSA), inverse-distance interpolation, splines, and kriging are the most commonly used. Although vegetation science handles many spatial aspects of ecological data, these methods have experienced less appreciation. TSA and kriging interpolations are discussed in the present paper. Detailed formulations of the techniques are given, and their advantages and flaws briefly discussed. Two example data sets are used to elucidate the applications of these methods in the interpretation of ordination diagrams.

Keywords

Random Function Nugget Effect Ordination Diagram Trend Surface Spatial Interpolation Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Austin, M.P. 1977. Use of ordination and other multivariate descriptive methods to study succession. Vegetatio 35: 165–175.CrossRefGoogle Scholar
  2. Birks, H.J.B. 1987. Recent methodological developments in quantitative descriptive biogeography. Ann. Zool. Fennici, Helsinki 24: 165–178.Google Scholar
  3. Braun-Blanquet, J. 1964. Pflanzensoziologie. Grundzüge der Vegetationskunde. 3. Aufl. Springer-Verlag, Wien.Google Scholar
  4. Burden, R.L. and J.D. Faires. 1985. Numerical analysis. 3rd ed. Prindle, Weber and Schmidt, Boston.Google Scholar
  5. Burrough, P.R. 1987. Spatial aspects of ecological data. In: Jongman, R.H.G., ter Braak, C.J.F. and van Tongeren, O.F.R. (eds.), Data Analysis in Community and Landscape Ecology, pp. 213–251. Pudoc, Wageningen.Google Scholar
  6. Cliff, A.D. and J.K. Ord. 1981. Spatial Processes: Models and Applications. Pion, London.Google Scholar
  7. Dargie, T.C.D. 1984. On the integrated interpretation of indirect site ordinations: a case study using semi-arid vegetation in southeastern Spain. Vegetatio 55: 37–55.CrossRefGoogle Scholar
  8. Delhomme, J.P. 1978. Kriging in the hydrosciences. Adv. Water Res. 1:251–266.CrossRefGoogle Scholar
  9. Digby, P.G.N, and R.A. Kempton. 1987. Multivariate Analysis of Ecological Communities. Chapman and Hall, London.CrossRefGoogle Scholar
  10. Ellenberg, H. 1979. Zeigerwerte der Gefäßpflanzen Mitteleuropas. Verlag Erich Goltze KG, Göttingen.Google Scholar
  11. Feoli, E. 1983. Predictive use of classification and ordination methods in plant community ecology. A summary with examples.: C. Ferrari, G. Gentile, S. Pignatti, and E. Poli Marchese (eds.), Le comunitè vegetali come indicatori ambientali. pp. 83–108. Regione Emilia-Romana and Societá Italiana di Fitosociologia, Bologna.Google Scholar
  12. Feoli-Chiapella, L. and E. Feoli. 1977. A numerical phytosociological study of the summits of the Majella massive (Italy). Vegetatio 34: 21–29.CrossRefGoogle Scholar
  13. Fortin, M.J., P. Drapeau and P. Legendre. 1989. Spatial autocorrelation and sampling design in plant ecology. Vegetatio 83: 209–222.CrossRefGoogle Scholar
  14. Gittins, R. 1968. Trend-surface analysis of ecological data. J. Ecol. 56: 845–869.CrossRefGoogle Scholar
  15. Grabherr, G. and L. Mucina. 1989. Übersicht der Wälder und Waldstandorte in Vorarlberg. Lebensraum Vorarlberg, Bregenz 3: 9–46.Google Scholar
  16. Hajdu, L.J. 1981. Graphical comparison of resemblance measures in phytosociology. Vegetatio 48: 47–59.CrossRefGoogle Scholar
  17. Hill, M.O. 1974. Correspondence analysis; a neglected multivariate method. Appl. Stat. 23: 340–353.CrossRefGoogle Scholar
  18. Jongman, R.H.G., C.J.F. ter Braak and O.F.R. van Tongeren. 1987. Data Analysis in Community and Landscape Ecology. Pudoc, Wageningen.Google Scholar
  19. Krige, D.G. 1966. Two dimensional weighted moving average trend surfaces for ore evaluation. J.S. Afr. Inst. Min. Metall. 66: 13–38.Google Scholar
  20. Legendre, L. and P. Legendre. 1983. Numerical Ecology. Elsevier, Amsterdam.Google Scholar
  21. Legendre, P. 1990. Quantitative methods and biogeographic analysis. In: D. Garbary, and G.R. South (eds.), Evolutionary Biogeography of the Marine Algae of the North Atlantic, pp. 1–25. Springer-Verlag, Berlin.Google Scholar
  22. Legendre, P. and M.J. Fortin. 1989. Spatial pattern and ecological analysis. Vegetatio 80: 107–138.CrossRefGoogle Scholar
  23. Legendre, P. and L. Legendre (eds.). 1987. Developments in Numerical Ecology. Springer-Verlag, Berlin.Google Scholar
  24. Ludwig, J.R. and J.F. Reynolds. 1988. Statistical Ecology. A Primer on Methods and Computing. J. Wiley and Sons, New York.Google Scholar
  25. Matheron, G. 1962. Traité de géostatistique appliquée. Tome 1. Editions Technip, Paris.Google Scholar
  26. Matheron, G. 1971. The Theory of Regionalized Variables and its Applications. Cah. Centre Morphol. Mathem. de Fontainebleu.Google Scholar
  27. Miles, J., W. Schmidt and E. van der Maarel (eds.). 1988. Temporal and Spatial Patterns of Vegetation Dynamics. Kluwer, Dordrecht.Google Scholar
  28. Mucina, L. 1982. Numerical classification and ordination of ruderal plant communities (Sisymbrietalia, Onopordetalia) in the western part of Slovakia. Vegetatio 48: 267–275.CrossRefGoogle Scholar
  29. Mucina, L. 1989. Syntaxonomy of the Onopordum acanthium communities in temperate and continental Europe. Vegetatio 81: 107–115.CrossRefGoogle Scholar
  30. Mucina, L. and M.B. Dale (eds.). 1989. Numerical Syntaxonomy. Kluwer, Dordrecht.Google Scholar
  31. Mucina, L. and S. Poláčik. 1982. Principal components analysis and trend surface analysis of a small-scale pattern in a transition mire. Vegetatio 48: 165–173.CrossRefGoogle Scholar
  32. Mucina, L. and E. van der Maarel. 1989. Twenty years of numerical syntaxonomy. Vegetatio 81: 1–15.CrossRefGoogle Scholar
  33. Mucina, L., V. Čík and P. Slavkovský. 1988. Trend surface analysis and splines for pattern determination in plant communities. Coenoses 3: 89–105.Google Scholar
  34. Mucina, L. and G. Grabherr. Ecology of montane and subalpine woods in Vorarlberg, western Austria. (In preparation).Google Scholar
  35. Nichols, S. 1977. On the interpretation of principal components analysis in ecological contexts. Vegetatio 34: 191–197.CrossRefGoogle Scholar
  36. Orlóci, L. 1978. Multivariate Analysis in Vegetation Research. 2nd ed. Dr. W. Junk, The Hague.Google Scholar
  37. Peet, R.F., R.G. Knox, J.S. Case and R.B. Allen. 1988. Putting things in order: the advantages of detrended correspondence analysis. Am. Nat. 131: 924–934.CrossRefGoogle Scholar
  38. Persson, S. 1981. Ecological indicator values as an aid in the interpretation of diagrams. J. Ecol. 69: 71–84.CrossRefGoogle Scholar
  39. Pickett, S.T.A. and J. Kolasa. 1989. Structure of theory in vegetation science. Vegetatio 83: 7–15.CrossRefGoogle Scholar
  40. Pielou, E.C. 1984. The Interpretation of Ecological Data. A Primer on Classification and Ordination. J. Wiley and Sons, New York.Google Scholar
  41. Podani, J. 1988. SYN-TAX III. User’s manual. Abstr. Bot., Budapest 12: 1–183.Google Scholar
  42. Ripley, B.D. 1981. Spatial Statistics. J. Wiley and Sons, New York.CrossRefGoogle Scholar
  43. ter Braak, C.J.F. 1987. CANOCO — a FORTRAN program for canonical community ordination by (partial) (detrended) (canonical) correspondence analysis, principal components analysis and redundancy analysis (version 2.1). TNO Institute of Applied Computer Science, Wageningen.Google Scholar
  44. ter Braak, C.J.F. and C.W.H. Looman. 1987. Regression. In: Jongman, R.H.G., C.J.F. ter Braak and O.F.R. van Tongeren O.F.R. (eds.), Data Analysis in Community and Landscape Ecology, pp. 29–77. Pudoc, Wageningen.Google Scholar
  45. Unwin, D. 1975. An introduction to trend surface analysis. Concepts Tech. Mod. Geogr. 5: 1–40.Google Scholar
  46. Upton, G.J. and B. Fingleton. 1985. Spatial Data Analysis by Example. Volume 1. Point pattern and quantitative data. J. Wiley and Sons, Chichester.Google Scholar
  47. van der Maarel, E. 1969. On the use of ordination models in phytosociology. Vegetatio 19: 21–46.CrossRefGoogle Scholar
  48. van der Maarel, E. 1979. Transformation of cover-abundance values in phytosociology and its effects on community similarity. Vegetatio 39: 97–114.CrossRefGoogle Scholar
  49. van der Maarel, E. 1980. On the interpretability of ordination diagrams. Vegetatio 42: 43–45.CrossRefGoogle Scholar
  50. van der Maarel, E. 1989. Theoretical vegetation science on the way. Vegetatio 83: 1–6.CrossRefGoogle Scholar
  51. van der Maarel, E., I. Espejel and P. Moreno-Casasola. 1987. Two-step vegetation analysis based on very large data sets. Vegetatio 68: 139–143.CrossRefGoogle Scholar
  52. van Groenewoud, H. 1965. Ordination and classification of Swiss and Canadian coniferous forests by various biometric and other methods. Ber. Geobot. Inst. ETH, Stiftung Rübel 36: 28–102.Google Scholar
  53. Wartenberg, D. 1985. Canonical trend surface analysis: a method for describing geographic patterns. Syst. Zool. 34: 259–279.CrossRefGoogle Scholar
  54. Wartenberg, D., S. Ferson and F.J. Rohlf. 1987. Putting things in order: a critique of detrended correspondence analysis. Am. Nat. 129: 434–448.CrossRefGoogle Scholar
  55. Watson, D.F. 1982. ACORD: Automatic contouring of raw data. Comp. Geosci. 8: 97–101.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • M. Hauser
    • 1
  • L. Mucina
    • 1
  1. 1.Dept. of Vegetation Ecology & Biological ConservationUniversity of ViennaViennaAustria

Personalised recommendations