91
ECOM II
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





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