Ecological Application of Ordination Techniques in the
Literature
(and why it is especially good
for restoration ecology)
and Using
PCORD v. 4.10©
John Doudna
This webpage is not intended
to teach about the mathematics or theory of ordination. Rather, it is a summary
of some of the uses of ordination and its application in a single software
package, PC-ORD. Many other software
programs are available, and are linked on the
For background information on a variety of tests, try these websites:
A brief Introduction to Ordination
A Comprehensive
Treatment of Ordination
If you are looking for detailed information on particular Ordination techniques, try these websites:
An Introduction to Correspondence Analysis
An Introduction to Canonical Correlation and PCA
A Comprehensive
Treatment of Ordination
If you are looking for a list of different software packages, try these websites:
A Comprehensive
Treatment of Ordination
For a lot of detailed information, try this website:
A Comprehensive Treatment of
Ordination
In order to better understand
the study areas where ordination is used I performed a search in the Web of
Science electronic database. Below is a
brief summary of the returns I got using various search parameters. The search was done in April of 2005.
n Searches:
1. Principal Components Analysis or Correspondence Analysis or Multidimensional Scaling = 1800 results, 1/3 ecology
2. Above + community = 254 results, 70-80% ecology
3. 2 + restoration = 7 results, all ecology
4. 1 + restoration = 14 results, all ecology
5. Principal Components Analysis = 88, less than 6 ecology
6. Correspondence Analysis = 24, ~80% ecology
7. Multidimensional Scaling = 199, at least half ecology
My main intent with the survey was to determine what proportion of all ordinations was being done in the field of ecology, and also the predominant ordination technique that has been used in recent years. I found that the use of Non-Metric Multidimensional Scaling has become the predominant ordination technique used in the most recent studies. Correspondence Analysis and Principal Components Analysis are used less, but still make up a portion of the ordinations performed even in very recent studies. See the above websites for a thorough explanation of the issues with these tests, and why scientists have begun to use them less.
Some of the major areas within ecology that use ordination are:
n Genetics
n Community studies trying to understand composition by environmental variables (soil chemistry, rainfall, etc.)
n Plant and animal communities related to environmental toxins/stressors (pollution, global climate change)
n Plant and animal communities after restoration (which is the focus for the rest of the page)
Ordination in Restoration Ecology
n Ordination tests are a good suite of tests for restoration, since one’s goal could likely be restoring the community to its former composition, or at least away from the un-restored composition. With reference data from undisturbed sites or historic data, you can determine if the restoration has moved the composition of the community closer to that of its historic composition or to the composition of reference sites. An ordination plot can be a powerful graphical aid in demonstrating the success or failure of a restoration project.
n You can also look for environmental variables that are correlated to successful/unsuccessful restorations, and figure out why some have failed. (If you have collected environmental data). This will give you information for future efforts, and increase the understanding of which variables influence community composition.
n Tests can be done to detect significance of difference in scores on axes and significance of an axes correlation with other metrics (like diversity). This allows for a more thorough assessment of the results. One can analyze the results, and not have to simply display and try to interpret them from visual inspection.
Within my literature survey, I found 8 studies that had recently used ordination to analyze community composition after restoration. These studies compared the species composition of restored sites to un-restored and/or undisturbed sites. A brief summary of the studies follows.
n Of 8 studies, 2 were DCA, 1 was CCA, 1 was CA, and 4 were NMDS
n Almost always includes some other tests (outside of the ordination set) (e.g. comparing species richness, diversity and overall abundance)
The following two figures are from two of the papers using ordination to analyze restoration impacts on disturbed sites.
Fig. 1. An example of ordinations plotted against
two major axes and site categories delineated by lines. (Longcore,
Travis. 2003. Terrestrial Arthropods as Indicators of
Ecological Restoration Success in Coastal Sage Scrub (
This first figure is
an example of ordination plots showing the sites plotted on two axes. The ordination was a detrended
correspondence analysis, and the sites with the same treatment level are
outline for clarity. The solid line
represents the composition of terrestrial arthropods on restored sites, and the
other two are un-restored and un-disturbed sites. The initial indication is that the
restoration has not been very successful at restoring communities of
arthropods, and may have had a negative impact on them. This is a typical figure given in the text of
published papers using ordination tests.
One additional note, the different plots illustrate another common
approach when using ordination: including only data on certain species thought
to be more important as indicator species.
This allows for different runs of the test to detect similarities or
differences in composition based on a particular group.
Fig. 2. An example of a canonical
correspondence analysis. The
graph indicates the relation of the sites to environmental attributes. (Kee Dae Kim, Eun Ju Lee and Kang-Hyun Cho. 2004.
The Plant Community of Nanjido, A Representative Landfill in
Figure 2 is an
example of Canonical Correspondence Analysis.
This allows for a graphical representation of the relationship between a
sampling point or site and the environmental variables that were collected. The result is an interpretable graphic of the
relatedness of points based on each of the characteristics. One can begin to determine the influence of
each variable on the separation of the sampling points, which may be
responsible for the differences in community composition.
Follow-up tests for ordination procedures include
All of these tests are possible in PCORD v.4.10©.
Using PCORD v.4.10©
Matrix format:
|
# rows |
Row Name (e.g. sites) |
|
|
|
# columns |
Column Name (e.g. species) |
|
|
|
|
Data Type (Q=quantitative, C =
categorical, M = mixed) for each
column of data |
Data Type (Q=quantitative, C =
categorical, M = mixed) for each
column of data |
Data Type (Q=quantitative, C =
categorical, M = mixed) for each
column of data |
|
|
column variable name |
column variable name |
column variable name |
|
sample name |
data |
data |
data |
|
sample name |
data |
data |
data |
|
sample name |
data |
data |
data |
PCORD gives you many options for modifying your data through relativizations, standardizations, and modification of data. These are all done outside the actual ordination analysis, and could quite easily be misused if proper care is not taken to ensure the validity of modifications made. Also, the final interpretation of the data must take into account the modifications that were made.
Once the data set is input and ready for analysis, PCORD allows you to run all major ordination techniques.
Those listed in the menu are: Bray-Curtis, Detrended Correspondence Analysis, Non-metric Multidimensional Scaling, Non-metric Multidimensional Scaling Scores, Principal Components Analysis, Reciprocal Averaging (Correspondence Analysis), Canonical Correspondence Analysis, and Weighted Averaging. For the last two, an additional matrix is necessary to assign additional values or weights to the data.
Under the “graph” menu, you can select to graph the ordination, a dendrogram, a species-area curve to determine sufficiency of sampling intensity, and an NMS scree plot to determine the number of axes to use.
Under the “group” menu, you can run a cluster analysis to determine groups, an MRPP to test multivariate difference between pre-defined groups, TWINSPAN, tests to detect indicator species for a pre-defined group, or a Mantel test to test the relationship between multiple distance matrices for the same set of samples (e.g. before and after a fire).
Some screen shots from the program
Below is an analysis of terrestrial arthropods collected on restored, un-restored and un-disturbed coastal sand dunes in July, 2004. The output is a detrended correspondence analysis.
This next shot is the same
data analyzed with PCA (with the points centered on the origin).
This next shot is the same
data analyzed with Non-metric Multidimensional Scaling (this time the program
determined that a one-dimensional graphing was sufficient to represent the
ranks of the sites).
If you look closely at the distribution of points, or even
not-so-closely with NMS, you can see that based on the ordination technique
used, you can derive very different comparisons between the points. The DCA suggests that point HBC is very
different in composition from the rest of the sampling points. Most sampling points from the same locality
(those beginning with the same two letters) are clustered fairly close to each
other. Other than that, there does not
appear to be much structure to the points.
The results of the PCA suggest that sampling point SBR is very different
from the rest of the points. Site HBC
can now be found in the main swarm of data points. It also appears that there might be three
sets of points:
These interpretation difficulties are why it is very important to use the data generated (yes, the actual numbers), to develop a final analysis of the data, and not simply try to interpret the graphical representation. This is one of the main areas where papers using ordination seem to fall short in their results and discussion sections.
One nice option in PCORD, which may give a researcher additional information for discussing the interpreted relatedness of the sampling points is the ability to create a cluster dendrogram.
In summary, PCORD is a very straightforward software program, with a
lot of options. However, without proper
knowledge of the techniques and mathematics, it can easily be mis-used. I would
recommend a basic understanding of the principles and techniques of the tests
you wish to run before using the software.
There are a lot of readable texts on the topic (see below for some
options). Other sources can be found at
the sites mentioned earlier on this page.
Texts
Gauch, H. G., Jr. 1982. Multivariate Analysis in Community
Structure. Cambridge University Press, Cambridge.
Legendre, P., and L. Legendre. 1998.
Numerical Ecology, 2nd English Edition. Elsevier, Amsterdam.
Pielou, E. C. 1984. The Interpretation
of Ecological Data: A Primer on Classification and Ordination. Wiley,