Compositional dissimilarity as a robust measure of ecological distance
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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.
- Anderberg M. R. 1973. Cluster analysis for applications. Academic Press, New York.
- Austin M. P. 1976. Performance of four ordination techniques assuming three different non-linear species response models. Vegetation 33: 43–49.
- Austin M. P., 1980. Searching for a model for use in vegetation analysis. Vegetatio 42: 11–21.
- Austin M. P., 1985. Continuum concept, ordination methods, and niche theory. Ann. Rev. Ecol. Syst. 16: 39–61.
- Austin M. P., 1987. Models for the analysis of species' response to environmental gradients. Vegetatio 69: 35–45.
- 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.
- Austin M. P. & Noy Meir I., 1971. The problem of nonlinearity in ordination. Experiments with two-gradient models. J. Ecol. 59: 763–773.
- Beals E. W., 1973. Ordination: mathematical elegance and ecological naivete. J. Ecol. 61: 23–35.
- Beals E.W., 1984. Bray Curtis ordination: an effective strategy for analysis of multivariate ecological data. Adv. Ecol. Res. 14: 1–55.
- 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.
- Borg I. & Lingoes J. C., 1980. A model and algorithm for multidimensional scaling with external constraints on the distances. Psychometrika 45: 25–38.
- Bray J. R. & Curtis J. T., 1957. An ordination of the upland forest communities of southern Wisconsin. Ecol. Monogr. 27: 325–349.
- 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.
- Clymo R. S., 1980. Preliminary survey of the peat-bog Hummell Knowe Moss using various numerical methods. Vegetatio 42: 129–148.
- Faith D. P., 1984. Patterns of sensitivity of association measures in numerical taxonomy. Math. Biosci. 69: 199–207.
- 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.
- 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.
- GauchJr H. G., 1973. The relationship between sample similarity and ecological distance. Ecology 54: 618–622.
- GauchJr H.G., & Whittaker R. H., 1972. Comparison or ordination techniques. Ecology 53: 868–875.
- 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.
- Gauch H. G., Whittaker R. H. & Singer S. B., 1981. A comparative study of non-metric ordinations. J. Ecol. 69: 135–152.
- Gower J. C., 1966. Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika 53: 325–338.
- Gower J. C., 1967. Multivariate analysis and multidimensional geometry. The Statistician 17: 13–28.
- Gower J. C., 1971. A general coefficient of similarity and some of its properties. Biometrics 23: 623–637.
- Greig-Smith P., 1983. Quantitative plant ecology. 3rd ed. Blackwell, Oxford.
- Hajdu L. J. 1981. Graphical comparison of resemblance measures in phytosociology. Vegetatio 48: 47–59.
- Ihm P. & VanGroenewoud H., 1975. A multivariate ordering of vegetation data based on Gaussian type gradient response curves. J. Ecol. 63: 767–777.
- Kendall D. G., 1970. A mathematical approach to seriation. Philos. Trans. R. Soc. London A 269: 125–135.
- Kruskal J. B., 1964a. Multidimensional scaling by optimizing goodness-of-fit to a non-metric hypothesis. Psychometrika 29: 1–27.
- Kruskal J. B., 1964b. Non-metric multidimensional scaling: A numerical method. Psychometrika 29: 115–129.
- 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.
- Lance G. N. & Williams W. T., 1967. Mixed data classificatory programs. I. Agglomerative systems. Aust. Comput. J. 1: 15–20.
- Minchin P. R., 1987a. An evaluation of the relative robustness of techniques for ecological ordination. Vegetatio 69: 89–107.
- Minchin, P. R., 1987b. Simulation of multidimensional community patterns: towards a comprehensive model. Vegetatio (in press).
- Noy Meir I. & Austin M. P., 1970. Principal component ordination and simulated vegetational data. Ecology 51: 551–552.
- 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.
- Orlóci L., 1967. An agglomerative method for classification of plant communities. J. Ecol. 55: 193–206.
- Orlóci L., 1974. Revisions for the Bray and Curtis ordination. Can. J. Bot. 52: 1773–1776.
- Orlóci L., 1978. Multivariate analysis in vegetation research. 2nd ed. Junk, The Hague.
- Orlóci L., 1980. An algorithm for predictive ordination. Vegetatio 42: 23–25.
- Prentice I. C., 1977. Non-metric ordination methods in ecology. J. Ecol. 65: 85–94.
- Prentice I. C., 1980. Vegetation analysis and order invariant gradient models. Vegetatio 42: 27–34.
- Shepard R. N., 1962a. Analysis of proximities: Multidimensional scaling with an unknown distance function. I. Psychometrika 27: 125–140.
- Shepard R. N., 1962b. The analysis of proximities: multidimensional scaling with an unknown distance function. II. Psychometrika 27: 219–246.
- Shepard R. N., 1974. Representation of structure in similarity data-problems and prospects. Psychometrika 39: 373–421.
- Sibson R., 1972. Order invariant methods for data analysis. J. R. Statist. Soc. B 34: 311–349.
- 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.
- Sokal R. R. & Sneath P. H. A., 1963. Principles of numerical taxonomy. Witt. Freeman and Co., San Francisco.
- Swan J. M. A., 1970. An examination of some ordination problems by use of simulated vegetational data. Ecology 51: 89–102.
- Torgerson W. S., 1952. Multidimensional scaling: I. Theory and method. Psychometrika 17: 401–419.
- Whittaker R. H., 1952. A study of summer foliage insect communities in the Great Smoky Mountains. Ecol. Monogr. 22: 1–44.
- Williamson M. H., 1978. The ordination of incidence data. Ecology 66: 911–920.
- Compositional dissimilarity as a robust measure of ecological distance
Volume 69, Issue 1-3 , pp 57-68
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- Dissimilarity measure
- Ecological distance
- Hybrid multidimensional scaling
- Multidimensional scaling