, Volume 42, Issue 1–3, pp 27–34 | Cite as

Vegetation analysis and order invariant gradient models

  • I. C. Prentice


An ideal ordination method would have known properties with respect to an explicit, order invariant ecological response model defined in more than one dimension. The Curtis-McIntosh model (each species weakly unimodal) is a good general-purpose model of a single gradient, but not current method is guaranteed to dispose samples from such a gradient along a straight line. There is some theoretical justification for using reciprocal averaging (RA), or local non-metric multidimensional scaling (NMDS) with Kendall's simple similarity coefficient, but the former tends to produce arches rather than straight lines and the latter can produce erratic curves (as illustrated here by applying the method to simulated coenocline data). The non-metric method is nevertheless shown to perform well (a) with high beta-diversity plant distribution data and (b) with simulated coenoplane data, where its performance is better than that of RA. Results with coenoclines and coenoplanes concur with those of Fasham (1977) who tested NMDS with a different coefficient. Local scaling is shown to be preferable to global, and primary tie treatment to secondary, in tests on coenocline and coenoplane data. A possible alternative non-metric approach is mentioned.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderson, A.J.B. 1971. Ordination methods in ecology. J. Ecol. 59: 713–726.Google Scholar
  2. Austin, M.P. 1976a. On non-linear species response models in ordination. Vegetatio 33: 33–41.Google Scholar
  3. Austin, M.P. 1976b. Performance of four ordination techniques assuming three different non-linear species response models. Vegetatio 33: 43–49.Google Scholar
  4. Birks, H. J. B. 1976. The distribution of European pteridophytes: a numerical analysis. New Phytol. 77: 257–287.Google Scholar
  5. Carroll, J.D. 1972. Individual differences and multidimensional scaling. In R.N., Shepard, A.K., Romney & S.B., Nerlove (eds.): Multidimensional Scaling. Volume 1. Theory, p. 105–155. Seminar Press, New York.Google Scholar
  6. Curtis, J.T. & R.P., McIntosh. 1951. An upland forest continuum in the prairie-forest border region of Wisconsin. Ecology 32: 476–496.Google Scholar
  7. Dale, M.B. 1975. On objectives of methods of ordination. Vegetatio 30: 15–32.Google Scholar
  8. Fasham, M.J.R. 1977. A comparison of nonmetric multidimensional scaling, principal components and reciprocal averaging for the ordination of simulated coenoclines, and coenoplanes. Ecology 58: 551–561.Google Scholar
  9. Gauch, H.G.Jr. & R.H., Whittaker. 1972. Coenocline simulation. Ecology 53: 446–451.Google Scholar
  10. Gauch, H.G.Jr. & R.H., Whittaker. 1976. Simulation of community patterns. Vegetatio 33: 13–16.Google Scholar
  11. Gauch, H.G.Jr., G.B., Chase & R.H., Whittaker. 1974. Ordination of vegetation samples by Gaussian species distribution. Ecology 55: 1382–1390.Google Scholar
  12. Gauch, H.G.Jr., R.H., Whittaker & T.R., Wentworth. 1976. A comparative study of reciprocal averaging and other ordination techniques. J. Ecol. 65: 157–174.Google Scholar
  13. Hill, M.O. 1973. Reciprocal averaging; an eigenvector method of ordination. J. Ecol. 61: 237–249.Google Scholar
  14. Hill, M.O. 1974. Correspondence analysis: a neglected multivariate method. J. Roy. Statist. Soc. Ser. C (Applied Statistics) 23: 340–354.Google Scholar
  15. Hill, M.O., R.G.H., Bunce & M.W., Shaw. 1975. Indicator species analysis, a divisive polythetic method of classification, and its application to a survey of native pinewoods of Scotland. J. Ecol. 63: 597–614.Google Scholar
  16. Ihm, P. & H.van, Groenewoud. 1975. A multivariate ordering of vegetation data based on Gaussian type gradient response curves. J. Ecol. 63: 767–777.Google Scholar
  17. Kendall, D.G. 1971. Seriation from abundance matrices. In F.R., Hodson, D.G., Kendall and P., Tăutu (eds.). Mathematics in the Archaeological and Historical Sciences, p. 215–251. Edinburgh University Press, Edinburgh.Google Scholar
  18. Kruskal, J.B. 1964a. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika 29: 1–27.Google Scholar
  19. Kruskal, J.B. 1964b. Nonmetric multidimensional scaling: a numerical method. Psychometrika 29: 115–129.Google Scholar
  20. Lefkovitch, L.P. 1976. Hierarchical clustering from principal co-ordinates: an efficient method for small to very large number of objects. Mathematical Biosciences 31: 157–174.Google Scholar
  21. Lingoes, J.C. 1972. A general survey of the Guttman-Lingoes program series. In R.N., Shepard, A.K., Romney & S.B., Nerlove (eds.): Multidimensional Scaling. Volume 1. Theory, p. 49–68. Seminar Press, New York.Google Scholar
  22. Noy-Meir, I. & R.H., Whittaker. 1978. Recent developments in continuous multivariate techniques. In R.H., Whittaker (ed.): Ordination of Plant Communities, p. 337–378. Junk, The Hague.Google Scholar
  23. Prentice, I.C. 1977. Non-metric ordination methods in ecology. J. Ecol. 65: 85–94.Google Scholar
  24. Sammon, J.W.Jr. 1969. A nonlinear mapping for data structure analysis. IEEE Transactions on Computers C-18: 401–409.Google Scholar
  25. Sibson, R. 1971. Some thoughts on sequencing methods. In F.R., Hodson, D.G., Kendall and P., Tăutu (eds.): Mathematics in the Archaeological and Historical Sciences p. 263–266. Edinburgh University Press, Edinburgh.Google Scholar
  26. Sibson, R. 1972. Order invariant methods for data analysis. J. Roy. Statist. Soc. Ser. B 34: 311–349.Google Scholar

Copyright information

© Dr. W. Junk b.v. Publishers 1980

Authors and Affiliations

  • I. C. Prentice
    • 1
  1. 1.Department of Plant BiologyThe UniversityNewcastle upon TyneUnited Kingdom

Personalised recommendations