Canonical Correspondence Analysis

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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

1987a).

7.2

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

samples.

Also see

Copyright 2004 PISCES Conservation Ltd