Re: detrended correspondence analysis

From: Jean Thioulouse (
Date: Wed Nov 10 1999 - 14:41:53 MET

"Mark Weber" <> wrote :
>I have been reading about detrended correspondence analysis and detrended
>canonical correspondence in the ecological literature. What advantages do
>these types of analyses have over standard COA and CCA? Does ADE-4 have
>options within COA and CCA for these types of analyses?

The question was already asked by Sonia Said (in French) a while ago

Here is a short translation of the answer given by D. Chessel :

ADE-4 does not have options for detrended analyses.

COA has canonical analysis properties and a clear definition that is well
known since

Hirschfeld, H.O. (1935) A connection between correlation and contingency.
Proceedings of the Cambridge Philosophical Society, Mathematical and
Physical Sciences : 31, 520-524.


Williams, E.J. (1952) Use of scores for the analysis of association in
contingency tables. Biometrika : 39, 274-289.

These canonical properties can be used on samples x species tables, see

Thioulouse, J. & Chessel, D. (1992) A method for reciprocal scaling of
species tolerance and sample diversity. Ecology : 73, 670-680.

Within the limits of these basic properties, the results of COA do not
depend on software, and the use is clear and simple.

Unfortunately, these properties (double averaging) have a cost, which
is the arch effect. See Wartenberg, D., Ferson, S. & Ohlf, F.J. (1987)
Putting things in order : a critique of detrended correspondence analysis.
The American Naturalist : 129, 3, 434-448.

The ideal would be a universal double averaging procedure without arch
effect. This is not possible, and we think that it is better to give up
some purposes instead of introducing the convenient rescaling and
the numerical procedure of detrending, which are unclear and software

Of course the debate is still open.

Jean Thioulouse - Laboratoire de Biometrie et Biologie Evolutive
Universite Lyon 1 - Bat 711 - 69622 Villeurbanne Cedex -  France
Fax: (33) 4 78 89 27 19                  Tel: (33) 4 72 43 29 01

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