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On non-linear species response models in ordination

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Summary

Ordination techniques are plagued by the non-linearity of vegetation data. The purpose of ordination is discussed and considered to be the process of arranging samples (or species) in relation to one or more environmental gradients or abstract axes that may represent such gradients, the arrangement to be ecologically significant. The appropriateness of various models of vegetation to current ordination techniques is considered, particularly the gaussian species response curve. Two alternatives are suggested based on β-functions and an ecological response curve model incorporating competition between species.

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References

  • Aart, P.J.M.van der. 1973. Distribution analysis of wolfspiders (Araneae, Lycosidae) in a dune area by means of principal component analysis. Neth. J. Zool. 23: 266–329.

    Google Scholar 

  • Aart, P.J.M.van der & N., Smeenk-Enserink. 1975. Correlations between distributions of hunting spiders (Lycosidae, Ctenidea) and environmental characteristics in a dune area. Neth. J. Zool. 25: 1–45.

    Google Scholar 

  • Anderson, A.J.B. 1971. Ordination methods in ecology. J. Ecol. 59: 713–726.

    Google Scholar 

  • Austin, M.P. 1972. Models and analysis of descriptive vegetation data. In J.N.R. Jeffers (ed.): Mathematical Models in Ecology. Symp. Brit. Ecol. Soc. 12: 61–86.

  • Austin, M.P. 1977. Performance of four ordination techniques assuming three different non-linear species response models Vegetatio 33: 43–49.

    Google Scholar 

  • Austin, M.P. & P., Greig-Smith. 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 

  • Austin, M.P. & I., Noy-Meir. 1971. The problem of non-linearity in ordination: experiments with two gradient models. J. Ecol. 59: 762–773.

    Google Scholar 

  • Bradley, J.V. 1968. Distribution-free Statistical Tests. Prentice-Hall, Englewood Cliffs, New Jersey.

    Google Scholar 

  • Bray, J.R. & J.T., Curtis. 1957. An ordination of the upland forest communities of southern Wisconsin. Ecol. Monogr. 27: 325–349.

    Google Scholar 

  • Clifford, H.T. & W., Stephenson. 1975. An Introduction to Numerical Classification. Academic Press. London.

    Google Scholar 

  • Curtis, J.T. 1959. The Vegetation of Wisconsin: an Ordination of Plant Communities. Univ. Wisconsin Madison.

    Google Scholar 

  • Dale, M.B. 1975. On objectives of methods of ordination. Vegetatio 30: 15–32.

    Google Scholar 

  • Ellenberg, H. 1954. Über einige Forschritte der kausalen Vegetationskunde. Vegetatio 5–6: 199–211.

    Google Scholar 

  • Fasham, M.J.R. 1976. A comparison of nonmetric multidimensional scaling, principal components and reciprocal averaging for the ordination of simulated coenoclines. (manuscript).

  • Gauch, H.G.Jr. 1973. The relationship between sample similarity and ecological data. Ecology 55: 1377–1381.

    Google Scholar 

  • 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 

  • Gauch, H.G.Jr. & R.H., Whittaker, 1972a. Coenocline simulation. Ecology 53: 446–451.

    Google Scholar 

  • Gauch, H.G.Jr. & R.H., Whittaker. 1972b. Comparison of ordination techniques. Ecology 53: 868–875.

    Google Scholar 

  • Gauch, H.G., R.H. Whittaker, & T.R. Wentworth. 1976. A comparative study of reciprocal averaging and other ordination techniques. J. Ecol. (in press).

  • Gittins, R. 1969. The application of ordination techniques. In I.H. Rorison (ed.); Ecological Aspects of the Mineral Nutrition of Plants Symp. Brit. Ecol. Soc. 1968, 9: 37–66.

  • Goodall, D.W. 1954. Vegetational classification and vegetational continua. (Germ. summ.) Angew. Pflanzensoziol. [Wien], Festschr. Aichinger 1: 168–182.

    Google Scholar 

  • Gower, J.C. 1966. Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika 53: 325–338.

    Google Scholar 

  • Groenewoud, H.van 1965. Ordination and classification of Swiss and Canadian coniferous forests by various biometric and other methods. (Germ. summ.) Ber. Geobot. Inst. ETH, Stiftg Rübel, Zürich, 1964, 36: 28–102.

    Google Scholar 

  • Hill, M.O. 1973. Reciprocal averaging: an eigenvector method of ordination. J. Ecol. 61: 237–249.

    Google Scholar 

  • Hill, M.O. 1974. Correspondence analysis: a neglected multivariate method. J. Roy. Stat. Soc., Ser. C, 23: 340–354.

    Google Scholar 

  • 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 

  • 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.

    Google Scholar 

  • Kessel, S.R. & R.H. Whittaker. 1976. Comparisons of three ordination techniques. Vegetatio (in press).

  • LaFrance, C.R. 1972. Sampling and ordination characteristics of computer-simulated individualistic communities. Ecology 53: 387–397.

    Google Scholar 

  • Loetsch, F., F. Zöhner, & K.E. Haller. 1973. Forest Inventory, Vol. 2. München. BLV.

  • McIntosh, R.P. 1967. The continuum concept of vegetation. Bot. Rev. 33: 130–187.

    Google Scholar 

  • Monk, C.D. 1965. Southern mixed hardwood forest of north central Florida. Ecol. Mongr. 35: 335–354.

    Google Scholar 

  • Mueller-Dombois, D. & H., Ellenberg. 1974. Aims and Methods of Vegetation Ecology. John Wiley & Sons, New York.

    Google Scholar 

  • Mueller-Dombois, D. & H.P., Sims. 1966. Response of three grasses to two soils and a water table depth gradient. Ecology 47: 644–648.

    Google Scholar 

  • Noy-Meir, I. 1974a. Multivariate analysis of the semiarid vegetation in south-eastern Australia. II. Vegetation catenae and environmental gradients. Aust. J. Bot. 22: 115–140.

    Google Scholar 

  • Noy-Meir, I. 1974b. Catenation: quantitative methods for the definition of coenoclines. Vegetatio 29: 89–99.

    Google Scholar 

  • Noy-Meir, I. & R.H., Whittaker. 1976. Continuous multivariate methods in community analysis: some problems and developments. Vegetatio 33:

  • Noy-Meir, I. & M.P., Austin. 1970. Principal component ordination and simulated vegetation data. Ecology 51: 551–552.

    Google Scholar 

  • Noy-Meir, I., D., Walker, & W.T., Williams. 1975. Data transformations in ecological ordination. II. On the meaning of data standardization. J. Ecol. 63: 779–800.

    Google Scholar 

  • Orlóci, L. 1973. Ordination by resemblance matrices. (Germ. summ.) In R.H., Whittaker (ed.). Ordination and Classification of Communities. Han db. Veget. Sci. 5: 249–286. Dr. W. Junk B. V., The Hague.

    Google Scholar 

  • Orlóci, L. 1975. Multivariate Analysis in Vegetation Research. Dr. W. Junk b.v., The Hague. 276 pp.

    Google Scholar 

  • Poincaré, H. 1912. Calcul des probabilités. 2nd ed. Gauthier-Villars, Paris.

    Google Scholar 

  • Ramensky, L.G. 1930. Zur Methodik der vergleichenden Bearbeitung und Ordnung von Pflanzenlisten und anderen Objecten, die durch mehrere, verschiedenartige wirkende Faktoren bestimmt werden. Beitr. Biol. Pflanz. 18: 269–304.

    Google Scholar 

  • Swan, J.M.A. 1970. An examination of some ordination problems by use of simulated vegetation data. Ecology 51: 89–102.

    Google Scholar 

  • Westman, W.E. 1975. Edaphic climax pattern of the pygmy forest region of California. Ecol. Monogr. 45: 109–135.

    Google Scholar 

  • Whittaker, R.H. 1956. Vegetation of the Great Smoky Mountains. Ecol. Monogr. 26: 1–80.

    Google Scholar 

  • Whittaker, R.H. 1967. Gradient analysis of vegetation. Biol. Rev. 42: 207–264.

    Google Scholar 

  • Whittaker, R.H. 1973a. Introduction. (Germ. summ.) In R.H., Whittaker (ed.). Ordination and Classification of Communities. Handb. Veget. Sci. 5: 3–6. Dr. W. Junk b.v., The Hague.

    Google Scholar 

  • Whittaker, R.H. 1976b. Direct gradient analysis. (Germ. summ.) In R.H., Whittaker (ed.): Ordination and Classification of Communities. Handb. Veget. Sci. 5: 7–51. Dr. W. Junk b.v., The Hague.

    Google Scholar 

  • Whittaker, R.H. & C.W., Fairbanks, 1958. A study of plankton copepod communities in the Columbia Basin, southeastern Washington. Ecology 39: 46–65.

    Google Scholar 

  • Whittaker, R.H. & H.G., GauchJr. 1973. Evaluation of ordination techniques. (Germ. Summ.) In R.H., Whittaker (ed.): Ordination and Classification of Communities. Handb. Veget. Sci. 5: 287–321. Dr. W. Junk b.v., The Hague.

    Google Scholar 

  • Whittaker, R.H. & H.G., GauchJr. 1976. Evaluation of ordination techniques. In R.H., Whittaker (ed.): Ordination of Plant Communities. Dr. W. Junk b.v., The Hague (in press).

    Google Scholar 

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Authors and Affiliations

  1. Division of Land Use Research, CSIRO, Canberra, Australia

    M. P. Austin

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  1. M. P. Austin
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This study is an extended version of a paper given at the International Botanical Congress in Leningrad, 1975. Some of the ordination tests reported here were carried out at Cornell University with support from a National Science Foundation grant. I am indebted to I. Noy-Meir for the tests of parametric mapping and M. Fasham for those on non-metric multidimensional scaling. The manuscript has benefited very considerably from the comments of and discussions with R.H. Whittaker and H.G. Gauch, Jr. together with those of R. Cunningham and A. Nichols.

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Austin, M.P. On non-linear species response models in ordination. Vegetatio 33, 33–41 (1976). https://doi.org/10.1007/BF00055297

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