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The analysis of vegetation-environment relationships by canonical correspondence analysis

  • Cajo J. F. Ter Braak
Chapter
Part of the Advances in vegetation science book series (AIVS, volume 8)

Abstract

Canonical correspondence analysis (CCA) is introduced as a multivariate extension of weighted averaging ordination, which is a simple method for arranging species along environmental variables. CCA constructs those linear combinations of environmental variables, along which the distributions of the species are maximally separated. The eigenvalues produced by CCA measure this separation.

As its name suggests, CCA is also a correspondence analysis technique, but one in which the ordination axes are constrained to be linear combinations of environmental variables. The ordination diagram generated by CCA visualizes not only a pattern of community variation (as in standard ordination) but also the main features of the distributions of species along the environmental variables. Applications demonstrate that CCA can be used both for detecting species-environment relations, and for investigating specific questions about the response of species to environmental variables. Questions in community ecology that have typically been studied by ‘indirect’gradient analysis (i.e. ordination followed by external interpretation of the axes) can now be answered more directly by CCA.

Keywords

Canonical correspondence analysis Correspondence analysis Direct gradient analysis Ordination Species-environment relation Trend surface analysis Weighted averaging 
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References

  1. Austin, M. P., 1971. Role of regression analysis in plant ecology. Proc. Ecol. Soc. Austr. 6: 63–75.Google Scholar
  2. Austin, M. R, Cunningham, R. B. & Fleming, P. M., 1984. New approaches to direct gradient analysis using environmental scalars and statistical curve-fitting procedures. Vegetatio 55: 11–27.CrossRefGoogle Scholar
  3. Campbell, N. A. & Atchley, W. R., 1981. The geometry of canonical variate analysis. Syst. Zool. 30: 268–280.CrossRefGoogle Scholar
  4. Carleton, T. J., 1984. Residual ordination analysis: a method for exploring vegetation-environment relationships. Ecology 65: 469–477.CrossRefGoogle Scholar
  5. Cramer, W. & Hytteborn, H., 1987. The separation of fluctuation and long-term change in the vegetation dynamics of a rising sea-shore. Vegetatio 69: 157–167.CrossRefGoogle Scholar
  6. Dargie, T. C. D., 1984. On the integrated interpretation of indirect site ordinations: a case study using semi-arid vegetation in south-eastern Spain. Vegetatio 55: 37–55.CrossRefGoogle Scholar
  7. Finney, D. J., 1964. Statistical methods in biological assay. Griffin, London, 668 pp.Google Scholar
  8. Forsythe, W. L. & Loucks, O. L., 1972. A transformation for species response to habitat factors. Ecology 53: 1112–1119.CrossRefGoogle Scholar
  9. Gabriel, K. R., 1971. The biplot graphic display of matrices with application to principal component analysis. Biometrika 58: 453–467.CrossRefGoogle Scholar
  10. Gauch, H. G., 1982. Multivariate analysis in community ecology. Cambridge University Press, Cambridge.Google Scholar
  11. Gauch, H. G. & Stone, E. L., 1979. Vegetation and soil pattern in a mesophytic forest at Ithaca, New York. Am. Midl. Nat. 102: 332–345.CrossRefGoogle Scholar
  12. Gauch, H. G. & Wentworth, T. R., 1976. Canonical correlation analysis as an ordination technique. Vegetatio 33: 17–22.CrossRefGoogle Scholar
  13. Gittins, R., 1968. Trend-surface analysis of ecological data. J. Ecol. 56: 845–869.CrossRefGoogle Scholar
  14. Gittins, R., 1985. Canonical analysis. A review with applications in ecology. Springer Verlag, Berlin.Google Scholar
  15. Hill, M. O., 1973. Reciprocal averaging: an eigenvector method of ordination. J. Ecol. 61: 237–249.CrossRefGoogle Scholar
  16. Hill, M. O., 1979. DECORANA - A FORTRAN program for detrended correspondence analysis and reciprocal averaging. Ecology and Systematics, Cornell University, Ithaca, New York.Google Scholar
  17. Hill, M. O. & Gauch, H. G., 1980. Detrended correspondence analysis, an improved ordination technique. Vegetatio 42: 47–58.CrossRefGoogle Scholar
  18. Israels, A. Z., 1984. Redundancy analysis for qualitative variables. Psychometrika 49: 331–346.CrossRefGoogle Scholar
  19. Jolliffe, I. T., 1982. A note on the use of principal components in regression. Appl. Statist. 31: 300–303.CrossRefGoogle Scholar
  20. Loucks, O. L., 1962. Ordinating forest communities by means of environmental scalars and phytosociological indices. Ecol. Monogr. 32: 137–166.CrossRefGoogle Scholar
  21. Mardia, K. V., Kent, J. T. & Bibby, J. M., 1979. Multivariate analysis. Academic Press, London.Google Scholar
  22. Nishisato, S., 1980. Analysis of categorical data: dual scaling and its applications. University of Toronto Press, Toronto.Google Scholar
  23. Ter Braak, C. J. F., 1983. Principal components biplots and alpha and beta diversity. Ecology 64: 454–462.CrossRefGoogle Scholar
  24. Ter Braak, C. J. F., 1985a. Correspondence analysis of incidence and abundance data: properties in terms of a unimodal response model. Biometrics 41: 859–873.CrossRefGoogle Scholar
  25. Ter Braak, C. J. F., 1985b. CANOCO - A FORTRAN program for canonical correspondence analysis and detrended correspondence analysis. IWIS-TNO, Wageningen, The Netherlands.Google Scholar
  26. Ter Braak, C. J. F., 1986. Canonical correspondence analysis: a new eigenvector technique for multivariate direct gradient analysis. Ecology 67: 1167–1179.CrossRefGoogle Scholar
  27. Ter Braak, C. J. F. & Looman, C. W. N., 1986. Weighted averaging, logistic regression and the Gaussian response model. Vegetatio 65: 3–11.CrossRefGoogle Scholar
  28. Whittaker, R. H., 1967. Gradient analysis of vegetation. Biol. Rev. 42: 207–264.PubMedCrossRefGoogle Scholar
  29. Yarranton, G. A., 1970. Towards a mathematical model of limestone pavement vegetation. III. Estimation of the determinants of species frequencies. Can. J. Bot. 48: 1387–1404.CrossRefGoogle Scholar

Copyright information

© Dr W. Junk Publishers, Dordrecht 1987

Authors and Affiliations

  • Cajo J. F. Ter Braak
    • 1
    • 2
  1. 1.Statistics Department WageningenTNO Institute of Applied Computer ScienceWageningenThe Netherlands
  2. 2.Research Institute for Nature ManagementLeersumThe Netherlands

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