An Introduction to Ordination
Connie Clark



Ordination is a collective term for multivariate techniques which adapt a multi-dimensional swarm of data points in such a way that when it is projected onto a two dimensional space any intrinsic pattern the data may possess becomes apparent upon visual inspection (Pielou, 1984). Basically, ordination serves to summarize community data (such as species abundance data) by producing a low-dimensional ordination space in which similar species and samples are plotted close together, and dissimilar species and samples are placed far apart.

Generally, ordination techniques are used to describe relationships between species composition patterns and the underlying environmental gradients which influence these patterns (asking, what factors structure the community?). For example, if you wanted to examine the distribution patterns of tree species in the Sierra Nevada Mt. Range, ordination could be used to determine which species are commonly found associated with one another, and how the species composition of the community changes with increase in elevation. Recently, use of ordination techniques have expanded to include analysis of dietary overlap (Schluter and Grant, 1982), and to explore patterns of within species morphological differences with geographic distance between populations (Alisauskas, 1998).


Data
Commonly, data interpreted using ordination are collected in a species by sample data matrix, similar to the matrix presented below. Sample data may include measures of density, biomass, frequency, importance values, presence/absence, or any number of abundance measures.

E7000 E6580 E6000 E5400 E5000 E4000 E2850 E1800
ABMA

88.6

144.4

21.7

52.2

0

0

0

0

ABCO

211.4

149.3

243.2

190.5

102.4

12.4

18.7

0

ACMA

0

0

0

0

0

13.1

5.5

0

ARME

0

0

0

0

0

0

0

34.9

CADE

0

0

0

3

65

33.8

36.4

28.7

CONU

0

0

0

0

0

0

0

11

LIDE

0

0

0

0

0

2.4

0

136.6

PICO

0

0

11.2

2.2

0

0

14.7

0

PILA

0

0

0

4

0

0

0

12.9

PIPO

0

0

0.8

3.5

10

85.1

23.5

64.4

PIJE

0

6.4

9.8

28.1

16.7

0

0

0

PSME

0

0

0

17.1

105.5

48.8

125

5.5

QUCH

0

0

0

0

0

52.2

19.6

0

QUWI

0

0

0

0

0

10

7.7

0

QUKE

0

0

0

0

0

47.5

46.4

0

The above is a relatively simple data set. However, it is easy to imagine that a true data set may encounter dozens of species over hundreds of samples. Complex sample by species matrices represent dozens to hundreds of dimensions which are impossible to visualize or interpret. Even graphed, species response curves of large community data sets can be nearly impossible to interpret. (As they resemble a mess of overlapping peaks and depressions as shown here.)
 

Ordination can help us find structure in these complicated data sets. By using various mathematical calculations (which will not be discussed here), ordination techniques will identify similarity between species and samples. Results are then projected onto two dimensions in such a way that species and samples most similar to one another will be close together, and species and samples most dissimilar from one another will appear farther apart (as shown below).


 

Ordination techniques:

There are several different ordination techniques, all of which differ slightly, in the mathematical approach used to calculate species and sample similarity/dissimiarity. Rather than reinventing the wheel by discussing each of these techniques in depth, I will offer only a brief description of the most commonly used methods here. Further details can be found in the following suggested references:

    Gauch, H. G., Jr. 1982. Multivariate Analysis in Community Structure. Cambridge University Press, Cambridge

    Causton, D. R. 1988. An introduction to vegetation analysis. Unwin Hyman, London.

    Kent, M., and P. Coker. 1992. Vegetation description and analysis: a practical approach. Belhaven Press, London.

    Pielou, E. C. 1984. The Interpretation of Ecological Data: A Primer on Classification and Ordination. Wiley, New York

    Okland, R. H. 1990. Vegetation ecology: theory, methods and applications with reference to Fennoscandia.
    Sommerfeltia Supplement 1:1-233.

    Jongman, R. H. G., C. J. F. ter Braak, and O. F. R. van Tongeren, editors. 1987. Data Analysis in Community and Landscape Ecology. Pudoc, Wageningen, The Netherlands.

    Analysis of Ecological Communities. Chapman and Hall, London.

     

    Web Links

    The Ordination Webpage 


    Note: this web site comes highly recommended as it provides detailed yet simple explanations of most currently used ordination techniques (see the Indirect Gradient Analysis section of above mentioned web page). In the General Reference section of the web site, Palmer offers a fantastic glossary for terms used in ordination, and clarifies some common confusion in the terminology used to date. In addition, he provides links to other ordination sites and offers addresses for software links. In the Statistics and Background section of the site, read through Centroids and Inertia, Similarity, Distance and Difference, and Explorations in Coenspace for the conceptual background necessary in understanding ordination techniques. The Direct Gradient Analysis section will be of interest if you have specific environmental data collected in addition to abundance and species data. You may find this to be a stronger approach to the analysis of your data set. Ecological Data, Transformations and Standardization is for more advanced users who likely have an understanding of ordination and seek more advanced information regarding data manipulation.

    Principal Components Analysis (PCA)
    PCA was one of the earliest ordination techniques applied to ecological data. PCA uses a rigid rotation to derive orthogonal axes, which maximize the variance in the data set. Both species and sample ordinations result from a single analysis. Computationally, PCA is basically an eigenanalysis. The sum of the eigenvalues will equal the sum of the variance of all variables in the data set. PCA is relatively objective and provides a reasonable but crude indication of relationships.

    Reciprocal Averaging (RA) - Correspondence Analysis
    RA is an ordination technique related conceptually to weighted averages. However, computationally, RA is related to eigenvector ordinations. RA places sampling units and species on the same gradients, and maximizes variation between species and sample scores using a correlation coefficient. It serves as a relatively objective analysis of community data. Results are generally superior to the results from PCA. However, RA axis ends are compressed relative to the middle, and the second axis is often a distortion of the first axis, resulting in an arched effect.

    Detrended Correspondence Analysis (DCA)
    DCA is an eigenvector ordination technique based on Reciprocal Averaging, correcting for the arch effect produced from RA. Hill and Gauch (1980) report DCA results are superior to those of RA. Other ecologists criticize the detrending process of DCA. DCA is widely used for the analysis of community data along gradients. It has also been found effective for niche ordination of birds by foraging heights (Sabo 1980). DCA ordinates samples and species simultaneously. It is not appropriate for the analysis of a matrix of similarity values between community data (Gauch, 1982).

    Nonmetric Multidimensional Scaling (NMS)
    NMS actually refers to an entire related family of ordination techniques. These techniques use rank order information to identify similarity in a data set. NMS is a truly nonparametric ordination method which seeks to best reduce space portrayal of relationships. The verdict is still out on this type of ordination. Gauch (1982) claims NMS is not worth the extra computational effort, and that it gives effective results only for easy data sets with low diversity. Others hold NMS is extremely effective (Kenkel and Orloci, 1986, Bradfield and Kenkel, 1987).
     

    Appropriate uses of ordination:
    It is important to keep in mind that the purpose of ordination is to assist a researcher to find pattern in data sets that are otherwise too complicated to interpret. A good ordination technique will be able to identify the most important dimensions in a data set, and ignore the "noise", in order to show these patterns. However, ordination techniques should not be used in hypothesis driven analysis. They are meant as exploratory tools. Thus, post-hoc analysis is acceptable, and many different techniques can be tried on the same data set. No null hypothesis can be rejected, nor are p- values generated to test statistical significance. When p-values are offered, they can only be used as a rough guide or indicator of underlying processes that MAY BE explaining community patterns.
     

    Bibliography


    Alisauskas, R. T. 1998. Winter range expansion and relationships between landscape and morphometrics of midcontinent Lesser Snow Geese. Auk 115(4 ):851-862.

    Brandfield, G. E., and N. C. Kenkel. 1987. Nonlinear ordination using flexible shortest path adjustment of ecological distances. Ecology 68(3):750-753.

    Gauch, H. G., Jr. 1982. Multivariate Analysis in Community Structure. Cambridge University Press, Cambridge.

    Hill, M. O. and Gauch, H. G. 1980. Deterended correspondence analysis, an improved ordination technique. Vegetatio 42:47-58.

    Kenkel, N. C., and L. Orloci. 1986. Applying metric and nonmetric multidimensional scaling to ecological studies: some new results. Ecology 67:919-928.

    Pielou, E. C. 1984. The Interpretation of Ecological Data: A Primer on Classification and Ordination. Wiley, New York

    Sabo, S. R. 1980. Niche and habitat relations in subalpine bird communities of the White Mountains of New Hampshire. Ecological Monographw:50:241-259.

    Schluter. D., and P. R. Grant. 1982. The distribution of Geospiza difficilis on Galapagos islands: test of three hypotheses. Evolution 36:1213-1226
     
     

This page was last updated on 06/02/05