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calculated as a linear combination of the environmental variables) and WA  scores

(sites scores calculated as a weighted average of the species abundances) are

identical because the second matrix exerts no influence over the results (ter Braak

1994), since the large number of variables in the second matrix can support any

pattern found by the weighted averaging step with the species matrix.

Using a wide variety of real data sets, it is clear that the species environment

correlation is almost always high. It is usually [greater than] 0.6, and often much

higher. This seems to be true regardless of other criteria for performance of the

ordination, such as interpretability or proportion of variance in the species matrix that

is explained.

For these reasons, I conclude that (1) the species environment correlation is a poor

criterion for evaluating the success of an ordination, (2) the species environment

correlation should not be interpreted literally as a measure of the strength of the

relationship between species and the environment, and (3) the statistical significance

of the species environment correlation, even when it appears very high, should

always be checked with randomization tests.

The problems caused by large numbers of noisy environmental variables cannot be

alleviated by using a stepwise selection procedure, similar to that commonly used in

multiple regression. If the environmental data are noisy, stepwise selection will simply

pick out the best random variables, and the species environment correlation will still

be misleadingly high. As with multiple regression, the parsimony of the procedure is

set by the size of the pool of independent variables, not the number of independent

variables selected.

I recommend that the species environment correlation not be reported as such. If it is

reported at all, a more appropriate name would be the "LC WA correlation" to avoid

misleading the reader. If it is reported, it should be accompanied by a randomization

test for statistical significance. A better (but still imperfect) measure of the strength of

the relationship between species and environmental matrices is the proportion of

variance in the species data that is captured by the environmental data.

Copyright 2004  PISCES Conservation Ltd