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 (no longer an issue with Canoco 5)
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. Šmilauer. 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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