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Continuous multivariate methods in community analysis: Some problems and developments

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Summary

The early development of indirect ordination techniques in ecology was along two main lines: the Wisconsin approach, which led to the development and wide use of polar ordination (PO), and the multivariate Euclidean approach, which led to wide use of principal component analysis (PCA). Several methodological problems then emerged for both techniques: the basis of axis definition, the R/Q dichotomy, the choice of similarity measure and data transformation, the treatment of discontinuities, and the distortion due to nonlinearity and its effects on axis interpretation.

Developments in the last few years have contributed significantly towards the solutions of these problems:

  1. (1)

    The procedures of axis selection in PO have been modified so as to allow for either similarities in the full assemblage of samples (as in PCA), or choice of end points by known environmental relations (as in direct gradient analysis).

  2. (2)

    The duality between the R and Q similarity matrices in PCA, and the simultaneous site and species ordination in reciprocal averaging, turn the decision between R and Q techniques into a merely technical point.

  3. (3)

    Some systematic relations have been recognized within the large array of similarity measures used in ordination, and rational guidelines for choices among them can be suggested.

  4. (4)

    Non-centered PCA and reciprocal averaging (correspondence analysis) have proved to be useful in describing compositional variation that includes discontinuities.

  5. (5)

    Divergent solutions have been developed to cope with the problem of nonlinearity and axis interpretation: (a) The range of beta-diversity within which linear ordination methods do not cause too severe coenocline distortion has been defined. (b) Transformations of data and similarity measures (and in particular double standardization) have been shown to reduce distortion due to non-linearity in ordination techniques assuming linear structure. (c) Some new methods of nonlinear ordination (catenation) have been fairly successful in detecting coenoclines in simulated and real data. No single answer to the problems of indirect ordination has emerged, but these various solutions make the problems generally manageable.

Some continuous multivariate techniques have been developed in which individual axes are interpretable as noda, with axes and noda defining a structure of overlapping groups of sites connected by continuous variation. These techniques provide a further link between ordination and classification.

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Authors and Affiliations

  1. Department of Botany, Hebrew University, Jerusalem, Israel

    I. Noy-Meir

  2. Ecology and Systematics, Cornell University, 14853, Ithaca, New York, USA

    R. H. Whittaker

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  1. I. Noy-Meir
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  2. R. H. Whittaker
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This paper results from independent research on ordination by the first author while he was a Research Student at the Australian National University in Canberra, where he benefited from the advice and help of W. T. Williams and Donald Walker, and by the second author and H. G. Gauch at Cornell University with support by the National Science Foundation. The structure of the paper is based on a seminar given by the first author at the Centre d'Études Phytosociologiques et Écologiques at Montpellier in October 1974. Discussions with M. P. Austin. M. B. Dale, Eilif Dahl, and László Orlóci, and exchange of manuscripts and ideas with François Romane, M. O. Hill, M. P. Austin, and M. J. Fasham have helped to clarify some of the problems and to bring this review up to date.

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Noy-Meir, I., Whittaker, R.H. Continuous multivariate methods in community analysis: Some problems and developments. Vegetatio 33, 79–98 (1977). https://doi.org/10.1007/BF00205904

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