Summary
Canonical correlation analysis seeks linear axes that reveal the joint structure of two matrices. Potentially, CCA could be a valuable technique for ordination and analysis of dual matrices of community and environmental measurements. Performance of CCA was tested with simulated and real vegetational data. CCA was found to have stringent requirements for linearity, and consequently to have little value for ordination. Indirect ordination of community data by reciprocal averaging, followed by interpretation of environmental relationships of the axes, should generally be more effective.
Similar content being viewed by others
References
Aart, P.J.M.van der & N., Smeenk-Enserink. 1975. Correlations between distributions of hunting spiders (Lycosidae, Ctenidae) and environmental characteristics in a dune area. Neth. J. Zool. 25: 1–45.
Austin, M.P. 1968. An ordination study of a chalk grassland community. J. Ecol. 56: 739–757.
Austin, M.P., P.S., Ashton & P., Greig-Smith. 1972. The application of quantitative methods to vegetation survey. III. A re-examination of rain forest data from Brunei. J. Ecol. 60: 305–324.
Barkham, J.P. & J.M., Norris. 1970. Multivariate procedures in an investigation of vegetation and soil relations of two beech woodlands, Cotswold Hills, England. Ecology 51: 630–639.
Beals, E.W. 1973. Ordination: mathematical elegance and ecological naïveté. J. Ecol. 61: 23–25.
Cassie, R.M. 1969. Multivariate analysis in ecology. Proc. N.Z. Ecol. Soc. 16: 53–57.
Cassie, R.M. & A.D., Michael. 1968. Fauna and sediments of an intertidal mud flat: a multivariate analysis. J. Exp. Mar. Biol. Ecol. 2. 1–23.
Dagnelie, P. 1960. Contribution à l'étude des communautés végétales par l'analyse factorielle. (Engl. Summ.) Bull. Serv. Carte phytogéo gr., Paris, Sér. B 5: 7–71, 93–195.
Eberhardt, E., D., Kopp & H., Passarge. 1967. Standorte und Vegetation des Kirchleerauer Waldes im Schweizerischen Mittelland. (Engl. and French summs.) In ‘Vegetations-und bodenkundliche Methoden der forstlichen Standortskartierung’, ed. H., Ellenberg. Veröff. Geobot. Inst. Rübel, Zürich 39: 13–134, 280–281, 290–291.
Frehner, H.-K. 1967. Kartierung der Waldgesellschaften des V. aargauischen Forstkreises Zofingen nach der Methode von Braun-Blanquet. (Engl. and French summs.) In ‘Vegetations- und bodenkundliche Methoden der forstlichen Satndortskarierung’, ed. H., Ellenberg. Veroff. Geobot. Inst. Rübel, Zürich 39: 135–147, 281–282, 291–292.
Gauch, H.G. 1973. The relationship between sample, similarity and ecological distance. Ecology 54: 618–622.
Gauch, H.G. & R.H., Whittaker. 1972. Comparison of ordination techniques. Ecology 53: 868–875.
Gauch, H.G. & R.H., Whittaker. 1976. Simulation of community patterns. Vegetatio 33: 13–16.
Gauch, H.G., R.H. Whittaker & T.R. Wentworth. 1976. A comparative study of reciprocal averaging and other ordination techniques. J. Ecol. (in press).
Goff, F.G. & G., Cottam. 1967. Gradient analysis: the use of species and synthetic indices. Ecology 48: 793–806.
Goldstein, R.A. & D.F., Grigal. 1972a. Computer programs for the ordination and classification of ecosystems. Ecological Sciences Division Publication No. 417, Oak Ridge National Laboratory, Oak Ridge, Tennessee.
Goldstein, R.A. & D.F., Grigal. 1972b. Definition of vegetation structure by canonical analysis. J. Ecol. 60: 277–284.
Goodall, D.W. 1954. Objective methods for the classification of vegetation. III. An eassay in the use of factor analysis. Austral. J. Bot. 2: 304–324.
Goodall, D.W. 1973. Sample similarity and species correlation. (Germ. summ.) In ‘Ordination and Classification of Communities’ ed. R.H., Whittaker. Handb. Veget. Sci. 5: 105–156. Junk, The Hague.
Hill, M.O. 1973. Reciprocal averaging: an eigenvector method of ordination. J. Ecol. 61: 237–249.
Hughes, R.E. & D.V., Lindley. 1955. Application of biometric methods to problems of classification in ecology. Nature, Lond. 175: 806–807.
Jeglum, J.K., C.F., Wehrhahn & J.M.A., Swan. 1971. Comparisons of environmental ordinations with principal component vegetational ordinations for sets of data having different degrees of complexity. (French summ.) Can. J. For. Res. 1: 99–112.
Kercher, J.R. & R.A. Goldstein. 1976. Vegetation analysis by canonical correlation of species and environmental parameters. (Manuscript).
Loucks, O.L. 1962. Ordinating forest communities by means of environmental scalars and phytosociological indices. Ecol. Monogr. 32: 137–166.
Morrison, D.F. 1967. Multivariate statisical methods. McGraw-Hill, New York.
Orlóci, L. 1975. Multivariate analysis in vegetation research. Junk, The Hague.
Pielou, E.C. 1969. An introduction to mathematical ecology. Wiley-Interscience, New York.
Rogers, D.J. 1970. A preliminary ordination study of forest vegetation in the Kirchleerau area of the Swiss Midland. (Germ. summ.) Ber. Geobot. Inst. Rübel, Zürich, 1969, 40: 28–78.
Service, J. 1972. A user's guide to the statistical analysis systems. Student Supply Stores, North Carolina State University, Raleigh, North Carolina.
Webb, L.J., J.G., Tracey, W.T., Williams & G.N., Lance. 1971. Prediction of agricultural potential from intact forest vegetation. J. Appl. Ecol. 8: 99–121.
Wentworth, T.R. 1976. The vegetation of limestone and granite soils in the mountains of Southeastern Arizona. Ph.D. thesis, Cornell University.
Westman, W.E. 1971. Production, nutrient circulation, and vegetation-soil relations of the pygmy forest region of northern California. Ph.D. thesis, Cornell University.
Westman, W.E. 1975. Edaphic climax pattern of the pygmy forest region of California. Ecol. Monogr. 45: 109–135.
Whittaker, R.H. 1954. Plant populations and the basis of plant indication (Germ. summ.) Angew. Pflsoziol. (Wien), Festschr. Aichinger 1: 183–206.
Whittaker, R.H. 1956. Vegetation of the Great Smoky Mountains. Ecol. Monogr. 26: 1–80.
Whittaker, R.H. 1967. Gradient analysis of vegetation. Biol. Rev. 42: 207–264.
Whittaker, R.H. 1972. Convergences of ordination and classification. (Germ. summ.) In ‘Grundfragen und Methoden in der Pflanzensoziologie’ eds. E. van der Maarel & R. Tüxen. Ber. Symp. int. Ver. Vegetationskunde, Rinteln, 1970: 39–57.
Author information
Authors and Affiliations
Additional information
This research was supported by a grant from the National Science Foundation. We appreciate preparation of the manuscript and aid with computations from S.B. Conley, C.E. French, Jr. and B.D. Lanyon.
Rights and permissions
About this article
Cite this article
Gauch, H.G., Wentworth, T.R. Canonical correlation analysis as an ordination technique. Vegetatio 33, 17–22 (1976). https://doi.org/10.1007/BF00055295
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00055295