, Volume 69, Issue 1–3, pp 89–107 | Cite as

An evaluation of the relative robustness of techniques for ecological ordination

  • Peter R. Minchin


Simulated vegetation data were used to assess the relative robustness of ordination techniques to variations in the model of community variation in relation to environment. The methods compared were local nonmetric multidimensional scaling (LNMDS), detrended correspondence analysis (DCA), Gaussian ordination (GO), principal components analysis (PCA) and principal co-ordinates analysis (PCoA). Both LNMDS and PCoA were applied to a matrix of Bray-Curtis coefficients. The results clearly demonstrated the ineffectiveness of the linear techniques (PCA, PCoA), due to curvilinear distortion. Gaussian ordination proved very sensitive to noise and was not robust to marked departures from a symmetric, unimodal response model. The currently popular method of DCA displayed a lack of robustness to variations in the response model and the sampling pattern. Furthermore, DCA ordinations of two-dimensional models often exhibited marked distortions, even when response surfaces were unimodal and symmetric. LNMDS is recommended as a robust technique for indirect gradient analysis, which deserves more widespread use by community ecologists.


Detrended correspondence analysis Gaussian ordination Indirect gradient analysis Non-metric multidimensional scaling Ordination Principal components analysis Principal co-ordinates analysis Robustness Simulated data 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Austin M. P., 1976. Performance of four ordination techniques assuming different non-linear species response models. Vegetatio 33: 43–49.Google Scholar
  2. Austin M. P., 1980. Searching for a model for use in vegetation analysis. Vegetatio 42: 11–21.Google Scholar
  3. Austin M. P., 1985. Continuum concept, ordination methods and niche theory. Ann. Rev. Ecol. Syst. 16: 39–61.Google Scholar
  4. Austin M. P., 1987. Models for the analysis of species' response to environmental gradients. Vegetatio 69: 35–45.Google Scholar
  5. Austin M. P., 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.Google Scholar
  6. Austin M. P. & Noy-Meir I., 1971. The problem of nonlinearity in ordination: experiments with two-gradient models. J. Ecol. 59: 763–773.Google Scholar
  7. Beatty S. W., 1984. Influence of microtopography and canopy species on spatial patterns of forest understorey plants. Ecology 65: 1406–1419.Google Scholar
  8. Bradfield G. E. & Scagel A., 1984. Correlations among vegetation strata and environmental variables in subalpine sprucefir forests — southeast British Columbia. Vegetatio 55: 105–114.Google Scholar
  9. Brown M. J., Ratkowsky D. A. & Minchin P. R., 1984. A comparison of detrended correspondence analysis and principal co-ordinates analysis using four sets of Tasmanian vegetation data. Aust. J. Ecol. 9: 273–279.Google Scholar
  10. Chardy P., Glemarec M. & Laurec A., 1976. Application of inertia methods to benthic marine ecology: practical implications of the basic options. Estuar. Coast. Mar. Sci. 4: 179–205.Google Scholar
  11. Clymo R. S., 1980. Preliminary survey of the peat-bog Hummell Knowe Moss using various numerical methods. Vegetatio 42: 129–148.Google Scholar
  12. 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.Google Scholar
  13. DelMoral R., 1980. On selecting indirect ordination methods. Vegetatio 42: 75–84.Google Scholar
  14. Faith D. P., Minchin P. R. & Belbin L., 1987. Compositional dissimilarity as a robust measure of ecological distance. Vegetatio 69: 57–68.Google Scholar
  15. Fasham M. J. R., 1977. A comparison of nonmetric multidimensional scaling, principal components analysis and reciprocal averaging for the ordination of simulated coenoclines and coenoplanes. Ecology 58: 551–561.Google Scholar
  16. Feoli E. & Feoli Chiapella L., 1980. Evaluation of ordination methods through simulated coenoclines: some comments. Vegetatio 42: 35–41.Google Scholar
  17. Fewster P. H. & Orlóci L., 1983. On choosing a resemblance measure for non-linear predictive ordination. Vegetatio 54: 27–35.Google Scholar
  18. Field J. G., Clarke K. R. & Warwick R. M., 1982. A practical strategy for analysing multispecies distribution patterns. Mar. Ecol. Prog. Ser. 8: 37–52.Google Scholar
  19. Gauch H. G., 1973. The relationship between sample similarity and ecological distance. Ecology 54: 618–622.Google Scholar
  20. Gauch H. G., 1979. Catalog of the Cornell ecology programs series. 11th ed. Ecology and Systematics, Cornell University, Ithaca, New York.Google Scholar
  21. Gauch H. G., 1982. Multivariate analysis in community ecology. Cambridge University Press, London and New York.Google Scholar
  22. Gauch H. G., Chase G. B. & Whittaker R. H., 1974. Ordination of vegetation samples by Gaussian species distributions. Ecology 55: 1382–1390.Google Scholar
  23. Gauch H. G. & Whittaker R. H., 1972a. Coenocline simulation. Ecology 53: 446–451.Google Scholar
  24. Gauch H. G. & Whittaker R. H., 1972b. Comparison of ordination techniques. Ecology 53: 868–875.Google Scholar
  25. Gauch H. G. & Whittaker R. H., 1976. Simulation of community patterns. Vegetatio 33: 13–16.Google Scholar
  26. Gauch H. G., Whittaker R. H. & Singer S. B., 1981. A comparative study of nonmetric ordinations. J. Ecol. 69: 135–152.Google Scholar
  27. Gibson N. & Kirkpatrick J. B., 1985. Vegetation and flora associated with localised snow accumulation at Mount Field West, Tasmania. Aust. J. Ecol. 10: 91–99.Google Scholar
  28. Goodall D. W. & Johnson R. W., 1982. Non-linear ordination in several dimensions. A maximum likelihood approach. Vegetatio 48: 197–208.Google Scholar
  29. Gower J. C., 1966. Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika 53: 325–338.Google Scholar
  30. Greig-Smith P., 1980. The development of numerical classification and ordination. Vegetatio 42: 1–9.Google Scholar
  31. Greig-Smith P., 1983. Quantitative plant ecology. 3rd ed. Blackwell, Oxford.Google Scholar
  32. 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
  33. Hill M. O. & Gauch H. G., 1980. Detrended correspondence analysis, an improved ordination technique. Vegetatio 42: 47–58.Google Scholar
  34. Hotelling H., 1933. Analysis of a complex of statistical variables into principal components. J. Ed. Psych. 24: 417–441 & 498–520.Google Scholar
  35. Ihm P. & VanGroenewoud H., 1975. A multivariate ordering of vegetation data based on Gaussian type gradient response curves. J. Ecol. 63: 767–777.Google Scholar
  36. Johnson R. W. & Goodall D. W., 1979. Maximum likelihood approach to non-linear ordination. Vegetatio 41: 133–142.Google Scholar
  37. Kruskal J. B., 1964a. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika 29: 1–27.Google Scholar
  38. Kruskal J. B., 1964b. Nonmetric multidimensional scaling: a numerical method. Psychometrika 29: 115–129.Google Scholar
  39. Loucks O. L., 1962. Ordinating forest communities by means of environmental scalars and phytosociological indices. Ecol. Monogr. 32: 137–166.Google Scholar
  40. Minchin, P. R., 1983. A comparative evaluation of techniques for ecological ordination using simulated vegetation data and an integrated ordination-classification analysis of the alpine and subalpine plant communities of the Mt Field Plateau, Tasmania. Ph.D. thesis, University of Tasmania.Google Scholar
  41. Minchin, P. R., 1987. Simulation of multidimensional community patterns: towards a comprehensive model. Vegetatio (in press).Google Scholar
  42. Mohler C. L., 1981. Effects of sample distribution along gradients on eigenvector ordination. Vegetatio 45: 141–145.Google Scholar
  43. Noy-Meir I. & Austin M. P., 1970. Principal-component ordination and simulated vegetational data. Ecology 51: 551–552.Google Scholar
  44. Oksanen J., 1983. Ordination of boreal heath-like vegetation with principal component analysis, correspondence analysis and multidimensional scaling. Vegetatio 52: 181–189.Google Scholar
  45. Orlóci L., 1974. On information flow in ordination. Vegetatio 29: 11–16.Google Scholar
  46. Orlóci L., 1978. Multivariate analysis in vegetation research. 2nd ed. Junk, The Hague.Google Scholar
  47. Orlóci L., 1980. An algorithm for predictive ordination. Vegetatio 42 23–25.Google Scholar
  48. Orlóci L., Kenkel N. C. & Fewster P. H., 1984. Probing simulated vegetation data for complex trends by linear and nonlinear ordination methods. Abstr. Bot. 8: 163–172.Google Scholar
  49. Prentice I. C., 1977. Non-metric ordination methods in ecology. J. Ecol. 65: 85–94.Google Scholar
  50. Prentice I. C., 1980. Vegetation analysis and order invariant gradient models. Vegetatio 42: 27–34.Google Scholar
  51. Robertson P. A., MacKenzie M. D. & Elliot L. F., 1984. Gradient analysis and classification of the woody vegetation for four sites in southern Illinois and adjacent Missouri. Vegetatio 58: 87–104.Google Scholar
  52. Rotenberry J. T. & Wiens J. A., 1980. Habitat structure, patchiness and avian communities in North American steppe vegetation: a multivariate analysis. Ecology 61: 1228–1250.Google Scholar
  53. Schönemann P. H. & Carroll R. M., 1970. Fitting one matrix to another under choice of a central dilation and a rigid motion. Psychometrika 35: 245–255.Google Scholar
  54. Sibson R., 1972. Order invariant methods for data analysis. J. Roy. Statist. Soc. B. 34: 311–349.Google Scholar
  55. Swan J. M. A., 1970. An examination of some ordination problems by use of simulated vegetational data. Ecology 51: 89–102.Google Scholar
  56. Van derMaarel E., 1980. On the interpretability of ordination diagrams. Vegetatio 42: 43–45.Google Scholar
  57. Van derMaarel E., Boot R., VanDorp D. & Rijntjes J., 1985. Vegetation succession on the dunes near Oostvoorne, The Netherlands; a comparison of the vegetation in 1959 and 1980. Vegetatio 58: 137–187.Google Scholar
  58. Walker J. & Peet R. K., 1983. Composition and species diversity of pine-wiregrass savannas of the Green Swamp, North Carolina. Vegetatio 55: 163–179.Google Scholar
  59. Whittaker R. H., 1960. Vegetation of the Siskiyou Mountains, Oregon and California. Ecol. Monogr. 30: 279–338.Google Scholar
  60. Whittaker R. H., 1967. Gradient analysis of vegetation. Biol. Rev. 42: 207–264.Google Scholar
  61. Whittaker R. H. & Gauch H. G., 1978. Evaluation of ordination techniques. In: R. H.Whittaker (ed.), Ordination of plant communities, pp. 227–336. Junk, The Hague.Google Scholar
  62. Young, F. W. & Lewyckyj, R., 1979. ALSCAL-4 User's Guide. Data Analysis and Theory Associates, P.O. Box 446, Carrboro, North Carolina.Google Scholar

Copyright information

© Dr W. Junk Publishers 1987

Authors and Affiliations

  • Peter R. Minchin
    • 1
  1. 1.CSIRO Division of Water and Land ResourcesCanberraAustralia

Personalised recommendations