Studies by ourselves and others (Swan 1970, Austin & Noy-Meir 1972, Beals 1973, Hill 1973, 1974, Austin 1976a, b, Fasham 1977, Gauch Whittaker & Wentwarth 1977, Noy-Meir & Whittaker 1977, Orloci 1978, Gauch, Whittaker & Singer 1979) have found faults with all ordination techniques currently in use, at least when applied to ecological data specifying the occurrences of species in community samples. These faults certainly do not make existing techniques useless; but they mean that results must be interpreted with caution. Even with the best techniques, the underlying structure of the data is often poorly expressed.

Detrended correspondence analysis: an improved ordination technique

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.

Compositional dissimilarity as a robust measure of ecological distance

Canonical correspondence analysis (CCA) is introduced as a multivariate extension of weighted averaging ordination, which is a simple method for arranging species along environmental variables. CCA constructs those linear combinations of environmental variables, along which the distributions of the species are maximally separated. The eigenvalues produced by CCA measure this separation.

/pdf/the-analysis-of-vegetation-environment-relationships-by-1t1e62l921.pdf

The analysis of vegetation-environment relationships by canonical correspondence analysis

Canonical Correspondence Analysis (CCA) is quickly becoming the most widely used gradient analysis technique in ecology. The CCA algorithm is based upon Correspondence Analysis (CA), an indirect gradient analysis (ordination) technique. CA and a related ordination technique, Detrended Correspondence Analysis, have been crit- icized for a number of reasons. To test whether CCA suffers from the same defects, I simulated data sets with properties that usually cause problems for DCA. Results indicate that CCA performs quite well with skewed species distributions, with quantitative noise in species abundance data, with samples taken from unusual sampling designs, with highly intercorrelated environmental variables, and with situations where not all of the factors determining species composition are known. CCA is immune to most of the problems of DCA.

/pdf/putting-things-in-even-better-order-the-advantages-of-2h5hrpdm5q.pdf

Putting things in even better order: the advantages of canonical correspondence analysis'

The performance of a new biological water quality score system based on macroinvertebrates over a wide range of unpolluted running-water sites

SUMMARY Reciprocal averaging is a technique of indirect ordination, related both to weighted averages and to principal components analysis and other eigenvector techniques. A series of tests with simulated community gradients (coenoclines), simulated community patterns (coenoplanes), and sets of vegetation samples was used to compare ordination performance of reciprocal averaging (RA) with non-standardized and standardized principal components analysis (PCA) and polar or Bray-Curtis ordination (PO). Of these, non-standardized PCA is most vulnerable to effects of beta diversity, giving distorted ordinations of sample sets with three or more half-changes. PO and RA give good ordinations to five or more half-changes, and standardized PCA is intermediate. Sample errors affect all these techniques more at low than at high beta diversity, but PCA is most vulnerable to effects of sample errors. All three techniques could ordinate well a small (1-5 x 1-5 half-changes) simulated community pattern; and PO and RA could ordinate larger patterns (4 5 x 4-5 half-changes) well. PCA distorts larger community patterns into complex surfaces. Given a rectangular pattern (1-5 x 4-5 halfchanges), RA distorts the major axis of sample variation into an arch in the second axis of ordination. Clusters of samples tend to distort PCA ordinations in rather unpredictable ways, but they have smaller effects on RA, and none on PO. Outlier samples do not affect PO (unless used as endpoints), but can cause marked deterioration in RA and PCA ordinations. RA and PO are little subject to the involution of axis extremes that affects nonstandardized PCA. Despite the arch effect, RA is much superior to PCA at high beta diversities and on the whole preferable to PCA at low beta diversities. Second and higher axes of PCA and RA may express ecologically meaningless, curvilinear functions of lower axes. When curvilinear displacements are combined with sample error, axis interpretation is difficult. None of the techniques solves all the problems for ordination that result from the curvilinear relationships characteristic of community data. For applied ordination research consideration of sample set properties, careful use of supporting information to evaluate axes, and comparison of results of RA or PCA with PO and direct ordination are suggested.

https://www.jstor.org/stable/pdfplus/2259071.pdf

A comparative study of reciprocal averaging and other ordination techniques

Canonical correlation analysis seeks linear axes that reveal the joint structure of two matrices. Potentially, CCA could be a valuable technique for ordination and analysis of dual matrices of community and environmental measurements. Performance of CCA was tested with simulated and real vegetational data. CCA was found to have stringent requirements for linearity, and consequently to have little value for ordination. Indirect ordination of community data by reciprocal averaging, followed by interpretation of environmental relationships of the axes, should generally be more effective.

T. R. Wentworth

Papers

A comparative study of reciprocal averaging and other ordination techniques

Canonical correlation analysis as an ordination technique