TERMINOLOGY IN ORDINATION: Some common confusions

The recent proliferation of ordination techniques has unfortunately often lead to a confusion in terminology. In particular, the name of a technique is often confused with the name of the algorithm (i.e. mathematical method) or with the name of the computer package which performs the algorithm.   In several cases, more than one algorithm can reach the same solution. Also, most computer packages can perform more than one kind of ordination.  Therefore, it is crucial that proper terminology be adopted in the literature.

The acronym, name, computer programs, and algorithms of some of the major eigenanalysis-based ordination techniques. RA = Reciprocal Averaging, SVD = Singular Value Decomposition



type of analysis


Program or Package


Principal Components Analysis 


Eigenanalysis, SVD 



Correspondence Analysis 


RA, eigenanalysis, SVD 



Detrended Correspondence Analysis 


RA with detrending and rescaling 



Canonical Correspondence Analysis 


RA with regressions, eigenanalysis 



Detrended Canonical Correspondence Analysis 


RA with regressions and detrending 


Editors and reviewers need to be especially vigilant of such mistakes, which are quite prone to occur in legends.  For example, it is common to see legends in print such as "Fig. 1. a DECORANA ordination of hardwood forests in the study site" or "Table 2. eigenvalues and percent variance explained in a CANOCO  ordination of the fertilization experiment results".  Of course, the first example should be a DCA, as implemented with (presumably) DECORANA, and the second should be (presumably) a CCA as implemented with CANOCO.  The names of the programs should probably not appear in the legend, but instead should (in almost all occasions) be restricted to the methods section.

Another source of confusion is that Canonical Correspondence Analysis sounds very similar to Canonical Correlation Analysis, which is also often abbreviated CCA. Canonical Correlation Analysis resembles Canonical Correspondence Analysis in that it searches for the multivariate relationships between two data sets (e.g. an environmental data set and a species abundance data set); however, Canonical Correlation Analysis assumes linear responses of species to environmental variables. This assumption is likely to be violated in nature. Canonical Correspondence Analysis, like other correspondence analysis methods, assumes a more reasonable unimodal response curve (ter Braak and Prentice 1988).

The fact that Canonical Correlation Analysis assumes a linear model makes it easily confused with Redundancy Analysis (RDA).  However, these are different techniques: RDA assumes that one of the two sets of enviornmetnal variables can be considered the "independent variables", and the other set is considered the "dependent variables". Canonical Correlation Analysis puts both sets of variables on equal footing.  See ter Braak and Smilauer (1998) for more explanation.

The acronym "MDS" is also a cause of confusion.  It has been used to refer to metric multidimensional scaling (also known as Principal Coordinates Analysis or PCoA), Nonmetric multidimensional scaling (NMDS), or even as a blanket term describing distance-based ordination techniques as a whole.  Given these confusions, it is probably best to abandon the acronym.

Principal Coordinates Analysis (PCoA) is, understandably, frequently confused with Principal Components Analysis (PCA).  The confusion is enhanced by the fact that PCA is a special case of PCoA.

References cited

(see also suggested references for self-education)

ter Braak, C. J. F., and I. C. Prentice. 1988. A theory of gradient analysis. Adv. Ecol. Res. 18:271-313.

ter Braak, C. J. F., and P. Smilauer. 1998. CANOCO Reference Manual and User's Guide to Canoco for Windows: Software for Canonical Community Ordination (version 4). Microcomputer Power (Ithaca, NY USA) 352 pp.

This page was created and is maintained by Michael Palmer.
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