WHAT IF THE RESULTS ARE UNINTERPRETABLE?
It is rare to have a completely uninterpretable CCA diagram. However,
when it does occur, it tends to be for one of the following reasons:
Errors in the input files
Because the input formats for CANOCO are fairly awkward, it is common to
have errors in the files. Common errors include listing species, site,
or environmental variable names in the wrong order, mistakes in the format
statement, misalignment in a column, etc. Fortunately, CANOCO will alert
you to a number of errors (e.g. if the number or names of entities do not
match), and the results of other errors will be obvious (e.g. nonsensical
species names). Errors in coding or ordering species can be detected in
CANOCO output if rare species have high weights and common species have
low weights. However, some errors remain elusive, and can best be found
by repeatedly proofing the files.
In CANOCO for Windows, the facility for input of spreadsheet data, WCanoImp,
has reduced potential sources of error substantially. However, incorrect
selection of the data matrix in the data clipboard, inclusion of nonnumeric
characters, and (frequently) forgetting to transpose the data matrix when
necessary, can cause new problems. When running CANOCO for Windows
on a new data matrix, I recommend selecting the options to delete species,
samples, and environmental variables (even if you have no intention to
delete them). This is so that you can see the names of species, samples,
and environmental variables and thereby determine whether they were imported
correctly.
Misspecifying environmental variables
If a categorical variable is treated as a single numerical variable, you
are bound to get nonsensical results. Instead, you need to create
a series of dummy variables. See Environmental
variables in constrained ordination. For example, if you have
five management types, you should represent them by five 1/0 variables,
rather than one variable with values of one through five (unless those
types represent a logical sequence).
Disjoint data matrix
A disjoint matrix occurs when a plot (or group of plots) shares absolutely
no species with the remaining plots. This can lead to unpredictable and
uninterpretable results. Disjoint data matrices are readily detected in
DCA and CA, because the first eigenvalue equals 1.0, and because the disjoint
groups are clumped at opposite ends of the first axis. However, these warning
signs are not exhibited in CCA. It is often advisable to perform both CA
and a CCA on a data set, even if for no other purpose than to detect disjoint
matrices. Usually, interpretation becomes much easier once the disjoint
groups are removed. However, this should only be done for exploratory research.
Outliers
Even if it is not truly disjoint, it is possible for a single plot or a
small group of plots to be so unique that they influence the rest of the
analysis, making the detection of gradients difficult. Whether or not this
is a problem is largely a matter of taste - an extreme group is a real
pattern, and is probably caused by real processes. However, there is no
harm in removing such groups during exploratory analysis, if it is desirable
to detect more subtle patterns within the larger group.
Linear response
This is the old advice I used to give:
"As previously stated, CCA assumes that species have unimodal responses
to environmental gradients. However, if a very short gradient is sampled,
it is possible that species appear to have a linear response to environmental
gradients. In such cases, it is advisable to use Redundancy Analysis (RDA)
instead of CCA. RDA is available in CANOCO. The subject of when it is best
to use linear methods such as RDA instead of unimodal methods such as CCA
has not yet been thoroughly studied. A few guidelines are offered by ter
Braak and Prentice (1988)."
However, ter Braak and Smilauer (1998) stress that CA and CCA have two
faces: a 'unimodal face' and a 'linear face'. A linear assumption
is perfectly fine with CA/CCA as long as you are interested in relative
abundances. For example, CA/CCA will not be able to detect a gradient
along which all species simultaneously increase in abundance. PCA/RDA
would not only detect such a gradient, but would most likely make it the
first axis.
Low variation
It is possible that there is such low variation among plots, that there
is no power for CCA, RDA, or other methods to explain this variation with
the available environmental variables. This situation probably only occurs
when the data are already a result of a classification procedure, and all
the plots consist of one association or vegetation type.
Important variables missing
If there is a dominant environmental gradient in nature, but it is not
correlated with any of the measured environmental variables, then the CCA
diagram will not reflect this gradient. This is actually a desirable property
of CCA; being a direct gradient analysis technique, it only reflects relationships
with the existing variables. A dominant but unmeasured gradient can be
detected if the first CA eigenvalue is much larger than the first CCA eigenvalue.
You may be wrong
An ecologist should always be prepared for surprises. It is possible that
CCA is revealing the true patterns of vegetation structure, and that these
patterns were not previously suspected. Sharing ordination results with
colleagues can help bring about a fuller understanding of ecological patterns.
CANODRAW error
The computer program CANODRAW, which produces publication-quality graphics
from CANOCO output, is an extremely versatile and powerful tool. It utilizes
the data input files for CANOCO as well. However, it is not a FORTRAN Program,
and it sometimes reads these FORTRAN input files incorrectly. It seems
to have particular problems with the FORTRAN formatting statement "X",
which means skip a certain number of spaces. If you have reasonably elaborate
FORTRAN formatting statements in your input file, and get nonsensical results
from CANODRAW, check your raw CANOCO output. If the latter appears normal,
chances are you are running into a formatting error. The only solution
I know for this problem is to reconstruct your data files so that they
have very simple FORTRAN formatting codes.
References cited
(see also suggested references for self-education)
ter Braak, C. J. F., and I. C. Prentice. 1988. A theory of gradient
analysis. Adv. Ecol. Res. 18:271-313.
ter Braak, C. J. F., and P. Smilauer. 1998. CANOCO Reference Manual
and User's Guide to Canoco for
Windows: Software for Canonical Community Ordination (version 4). Microcomputer
Power (Ithaca, NY USA)
352 pp.
This page was created and is maintained by Michael
Palmer.
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