Abstract
A method is described for fitting a model in which site characteristics are represented by a set of orthogonal axes, while the probability that a particular species will be present, and its quantity if it is present, are each related to the axes of the system by symmetrical hypersurfaces with an optimum, decreasing asymptotically to zero as conditions depart from the optimum. The method needs initial estimates of the positions of the sample sites within the axis system. Given these starting points, they can be progressively improved by an iterative procedure. Results are reported of an extensive series of tests using artificial data, and of an analysis of field data from brigalow woodland in Queensland.
Similar content being viewed by others
References
Austin M. P., 1976. On non-linear species response models in ordination. Vegetatio 33: 33–41.
Austin M. P. & Austin B. O., 1980. Behaviour of experimental plant communities along a nutrient gradient. J. Ecol. 68: 891–918.
Beals E. W., 1960. Forest bird communities in the Apostle Islands of Wisconsin. Wilson Bull. 72: 156–181.
Bray J. R. & Curtis J. T., 1957. An ordination of the upland forest communities of southern Wisconsin. Ecol. Monogr. 27: 325–349.
Czekanowski J., 1909. Zur differential Diagnose der Neander-talgruppe Korresp Bl, dt. Ges. Anthrop. 40: 44–47.
GauchJr. H. G. & Chase G. B., 1974. Fitting the gaussian curve to ecological data. Ecology 55: 1377–1381.
GauchJr. H. G., Chase G. B. & Whittaker R. H., 1974. Ordination of vegetation samples by gaussian species distributions. Ecology 55: 1382–1390.
GauchJr. H. G. & Whittaker R. H., 1972. Comparison of ordination techniques. Ecology 53: 868–875.
Hill M. O., 1973. Reciprocal averaging: an cigenvector method of ordination. J. Ecol. 61: 237–249.
Johnson, R. W., 1973. A study of some multiyariate methods for the analysis of botanical data. Ph. D. thesis. Utah State University.
Johnson R. W., 1980. Studies of a vegetation transeet through brigalow (Acacia harpophylla) forest in central Queensland. Austr. J. Ecol. 5: 287–307.
Johnson R. W., & Goodall D. W., 1980. A maximum likelihood approach to non-linear ordination. Vegetatio 41: 133–142.
McDonald R. P., 1962. A general approach to non-linear factor analysis. Psychometrika 27: 307–415.
Nelder J. A. & Mead R., 1965. A simplex method for function minimization. Computer J. 7: 308–313.
Orlóci L., 1968, Information analysis in phytosociology: partition, classification and prediction. J. Theor. Biol. 20: 271–284.
Webb A. A., 1971. Soil Survey of Brigalow Research Station. In Brigalow Research Station Soil and Vegetation Survey, p. 1–19, Queensland Department of Primary Industries, Brisbane.
Williams W. T., 1972. Partition of infermation. Austr. J. Bot. 20: 235–240.
Williams W. T., 1973. Partition of information: The CENT-PERC problem. Austr. J. Bot. 21: 277–281.
Williams W. T. & Dale M. B., 1962. Partition correlation matrices for heterogenous quantitative data. Nature, Lond. 196: 602.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Goodall, D.W., Johnson, R.W. Non-linear ordination in several dimensions. Vegetatio 48, 197–208 (1982). https://doi.org/10.1007/BF00055261
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00055261