, Volume 69, Issue 1–3, pp 57–68 | Cite as

Compositional dissimilarity as a robust measure of ecological distance

  • Daniel P. Faith
  • Peter R. Minchin
  • Lee Belbin


The robustness of quantitative measures of compositional dissimilarity between sites was evaluated using extensive computer simulations of species' abundance patterns over one and two dimensional configurations of sample sites in ecological space. Robustness was equated with the strength over a range of models, of the linear and monotonic (rank-order) relationship between the compositional dissimilarities and the corresponding Euclidean distances between sites measured in the ecological space. The range of models reflected different assumptions about species' response curve shape, sampling pattern of sites, noise level of the data, species' interactions, trends in total site abundance, and beta diversity of gradients.

The Kulczynski, Bray-Curtis and Relativized Manhattan measures were found to have not only a robust monotonic relationship with ecological distance, but also a robust linear (proportional) relationship until ecological distances became large. Less robust measures included Chord distance, Kendall's coefficient, Chisquared distance, Manhattan distance, and Euclidean distance.

A new ordination method, hybrid multidimensional scaling (HMDS), is introduced that combines metric and nonmetric criteria, and so takes advantage of the particular properties of robust dissimilarity measures such as the Kulczynski measure.


Dissimilarity measure Ecological distance Hybrid multidimensional scaling Multidimensional scaling Nonmetric Ordination Robustness Simulation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderberg M. R. 1973. Cluster analysis for applications. Academic Press, New York.Google Scholar
  2. Austin M. P. 1976. Performance of four ordination techniques assuming three different non-linear species response models. Vegetation 33: 43–49.Google Scholar
  3. Austin M. P., 1980. Searching for a model for use in vegetation analysis. Vegetatio 42: 11–21.Google Scholar
  4. Austin M. P., 1985. Continuum concept, ordination methods, and niche theory. Ann. Rev. Ecol. Syst. 16: 39–61.Google Scholar
  5. Austin M. P., 1987. Models for the analysis of species' response to environmental gradients. Vegetatio 69: 35–45.Google Scholar
  6. Austin M. P. & Greig-Smith P., 1968. The application of quantitative methods to vegetation survey. II. Some methodological problems of data from rain forest. J. Ecol. 56: 827–844.Google Scholar
  7. 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
  8. Beals E. W., 1973. Ordination: mathematical elegance and ecological naivete. J. Ecol. 61: 23–35.Google Scholar
  9. Beals E.W., 1984. Bray Curtis ordination: an effective strategy for analysis of multivariate ecological data. Adv. Ecol. Res. 14: 1–55.Google Scholar
  10. Belbin, L., Faith, D. P. & Minchin, P. R., 1984. Some algorithms contained in the numerical taxonomy package NTP CSIRO Division of Water and Land Resources, Canberra Technical Memorandum 84/23.Google Scholar
  11. Borg I. & Lingoes J. C., 1980. A model and algorithm for multidimensional scaling with external constraints on the distances. Psychometrika 45: 25–38.Google Scholar
  12. Bray J. R. & Curtis J. T., 1957. An ordination of the upland forest communities of southern Wisconsin. Ecol. Monogr. 27: 325–349.Google Scholar
  13. Chardy P., Glemarc M. & Laurec A., 1976. Application of inertia methods to benthic marine ecology: practical implications of the basic options. Estuarine Coastal Mar. Sci. 4: 179–205.Google Scholar
  14. Clymo R. S., 1980. Preliminary survey of the peat-bog Hummell Knowe Moss using various numerical methods. Vegetatio 42: 129–148.Google Scholar
  15. Faith D. P., 1984. Patterns of sensitivity of association measures in numerical taxonomy. Math. Biosci. 69: 199–207.Google Scholar
  16. Faith D. P., Minchin P. R. & Belbin L., 1985. Parsimony and falsification in ecology: toward an assumption-free approach to the study of species' response to gradients. Stud. Plant Ecol. 16: 31–32.Google Scholar
  17. Fasham M. J. R., 1977. A comparison of non-metric multidimensional scaling, principal components and reciprocal averaging for the ordination of simulated coenoclines and coenoplanes. Ecology 58: 551–561.Google Scholar
  18. GauchJr H. G., 1973. The relationship between sample similarity and ecological distance. Ecology 54: 618–622.Google Scholar
  19. GauchJr H.G., & Whittaker R. H., 1972. Comparison or ordination techniques. Ecology 53: 868–875.Google Scholar
  20. GauchJr H. G., Whittaker R. H. & Wentworth T. R., 1977. A comparative study of reciprocal averaging and other ordination techniques. J. Ecol. 65: 157–174.Google Scholar
  21. Gauch H. G., Whittaker R. H. & Singer S. B., 1981. A comparative study of non-metric ordinations. J. Ecol. 69: 135–152.Google Scholar
  22. Gower J. C., 1966. Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika 53: 325–338.Google Scholar
  23. Gower J. C., 1967. Multivariate analysis and multidimensional geometry. The Statistician 17: 13–28.Google Scholar
  24. Gower J. C., 1971. A general coefficient of similarity and some of its properties. Biometrics 23: 623–637.Google Scholar
  25. Greig-Smith P., 1983. Quantitative plant ecology. 3rd ed. Blackwell, Oxford.Google Scholar
  26. Hajdu L. J. 1981. Graphical comparison of resemblance measures in phytosociology. Vegetatio 48: 47–59.Google Scholar
  27. 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
  28. Kendall D. G., 1970. A mathematical approach to seriation. Philos. Trans. R. Soc. London A 269: 125–135.Google Scholar
  29. Kruskal J. B., 1964a. Multidimensional scaling by optimizing goodness-of-fit to a non-metric hypothesis. Psychometrika 29: 1–27.Google Scholar
  30. Kruskal J. B., 1964b. Non-metric multidimensional scaling: A numerical method. Psychometrika 29: 115–129.Google Scholar
  31. Lamont B. B. & Grant K. J., 1979. A comparison of twenty-one measures of site dissimilarity. In: L.Orlóci, C. R.Rao & W. M.Stiteler (eds). Multivariate methods in ecological work pp. 101–126. International Co-operative Publishing House, Fairland, Maryland.Google Scholar
  32. Lance G. N. & Williams W. T., 1967. Mixed data classificatory programs. I. Agglomerative systems. Aust. Comput. J. 1: 15–20.Google Scholar
  33. Minchin P. R., 1987a. An evaluation of the relative robustness of techniques for ecological ordination. Vegetatio 69: 89–107.Google Scholar
  34. Minchin, P. R., 1987b. Simulation of multidimensional community patterns: towards a comprehensive model. Vegetatio (in press).Google Scholar
  35. Noy Meir I. & Austin M. P., 1970. Principal component ordination and simulated vegetational data. Ecology 51: 551–552.Google Scholar
  36. Noy Meir I., Walker D. & Williams W. T., 1975. Data transformations in ecological ordination. II. On the meaning of data standardization. J. Ecol. 63: 779–800.Google Scholar
  37. Orlóci L., 1967. An agglomerative method for classification of plant communities. J. Ecol. 55: 193–206.Google Scholar
  38. Orlóci L., 1974. Revisions for the Bray and Curtis ordination. Can. J. Bot. 52: 1773–1776.Google Scholar
  39. Orlóci L., 1978. Multivariate analysis in vegetation research. 2nd ed. Junk, The Hague.Google Scholar
  40. Orlóci L., 1980. An algorithm for predictive ordination. Vegetatio 42: 23–25.Google Scholar
  41. Prentice I. C., 1977. Non-metric ordination methods in ecology. J. Ecol. 65: 85–94.Google Scholar
  42. Prentice I. C., 1980. Vegetation analysis and order invariant gradient models. Vegetatio 42: 27–34.Google Scholar
  43. Shepard R. N., 1962a. Analysis of proximities: Multidimensional scaling with an unknown distance function. I. Psychometrika 27: 125–140.Google Scholar
  44. Shepard R. N., 1962b. The analysis of proximities: multidimensional scaling with an unknown distance function. II. Psychometrika 27: 219–246.Google Scholar
  45. Shepard R. N., 1974. Representation of structure in similarity data-problems and prospects. Psychometrika 39: 373–421.Google Scholar
  46. Sibson R., 1972. Order invariant methods for data analysis. J. R. Statist. Soc. B 34: 311–349.Google Scholar
  47. Sokal R. R. & Michener C. D., 1957. The effects of different numerical techniques on the phenetic classification of bees of the Hoplitis complex (Megachilidae). Proc. Linn. Soc. London 178: 59–74.Google Scholar
  48. Sokal R. R. & Sneath P. H. A., 1963. Principles of numerical taxonomy. Witt. Freeman and Co., San Francisco.Google Scholar
  49. Swan J. M. A., 1970. An examination of some ordination problems by use of simulated vegetational data. Ecology 51: 89–102.Google Scholar
  50. Torgerson W. S., 1952. Multidimensional scaling: I. Theory and method. Psychometrika 17: 401–419.Google Scholar
  51. Whittaker R. H., 1952. A study of summer foliage insect communities in the Great Smoky Mountains. Ecol. Monogr. 22: 1–44.Google Scholar
  52. Williamson M. H., 1978. The ordination of incidence data. Ecology 66: 911–920.Google Scholar

Copyright information

© Dr W. Junk Publishers 1987

Authors and Affiliations

  • Daniel P. Faith
    • 1
  • Peter R. Minchin
    • 1
  • Lee Belbin
    • 1
  1. 1.Division of Water and Land ResourcesCSIROCanberraAustralia

Personalised recommendations