Canonical Correspondence Analysis
environmental variables that correlate most strongly with the ordination axes.
CCA excels at representing community data sets where: (1) species responses are
unimodal (hump shaped), and (2) the important underlying environmental variables
have been measured.  Note that condition 1 causes problems for methods assuming
linear response curves (PCA) but causes no problems for CCA, according to ter Braak
(1986, 1994).  Condition 2 results from the environmental matrix being used to
constrain the ordination results, unlike any other ordination technique apart from
Canonical Correlation.  For this reason, CCA has been called a method for "direct
gradient analysis" (ter Braak 1986).
CCA is currently one of the most popular ordination techniques in community ecology.
It is, however, one of the most dangerous in the hands of people who do not take the
time to understand this relatively complex method.  The dangers lie  in several areas:
(1) Because it includes multiple regression of community gradients on environmental
variables, it is subject to all of the hazards of multiple regression.  Multicollinearity is
a particular problem and it is easy to believe that a relatively high coefficient of
multiple correlation implies a highly significant result which it may not. Further, it
must be remembered that the method uses linear regression, it is quite likely that the
response of the community to changes in an environmental variable may not be
linear. (2) As the number of environmental variables increases relative to the number
of observations, the results become increasingly dubious as the appearance of very
strong relationships becomes inevitable.  (3) Statistics indicating the "percentage of
variance explained" can be calculated in several ways, each for a different question,
but users frequently confuse these statistics when reporting their results.
CCA does not explicitly calculate a distance matrix.  But CCA, like CA and PCA, is
implicitly based on the chi squared distance measure where samples are weighted
according to their totals (Chardy et al. 1976; Minchin 1987a).  This gives high weight
to species whose total abundance in the data matrix is low, thus exaggerating the
distinctiveness of samples containing several rare species (Faith et al., 1987; Minchin
Selecting Environmental variables
The choice of environmental variables determines the outcome of CCA. For an
exploratory analysis, include all the variables that you think are important
determinants of the community. If there are other variables that you do not believe to
be important but are easy to measure, then these should also be included during an
exploratory analysis.  You can always subsequently remove superfluous variables that
add little to your insight or are difficult to interpret. Remember, if you are testing a
hypothesis about the influence of selected variables on a community then the post 
hoc removal of variables until you get an interesting result is not the way to proceed.
The number of environmental variables can range from 1 to more than the number of
samples. If only 1 environmental variable is used then there is only one canonical axis
and it is not possible to produce a 2 dimensional graph. You can, if desired, produce a
2 dimensional image in which the second axis is the first residual axis.  If you have at
least as many environmental variables as you have samples then your ordination is
no longer constrained, and a simple correspondence analysis would result. When
using ECOM, the number of environmental variables must be less than the number of
Also see
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