Ordination Analysis

by

David J. Gibson

• LAST REVIEWED: 14 December 2021
• LAST MODIFIED: 23 May 2012
• DOI: 10.1093/obo/9780199830060-0003

Introduction

Ordination is a multivariate method of gradient analysis and data reduction in which the distribution of samples, often sample plots characterized by the abundance of individual species or life forms, or the value of environmental variables, is arranged in a few dimensions based on eigenanalysis or the similarity (often dissimilarity) among samples (i.e., a resemblance, correlation, or covariance matrix). The method allows hypotheses to be generated about the relationship between the species composition of a site and potentially explanatory characteristics of the environment. Since its introduction in the ecological literature in the early 1950s, ecologists have embraced several approaches to ordination analysis, which are listed here. There is often controversy in the literature about which method to use; whether or not to use direct or indirect, or constrained or unconstrained approaches; and which software to use.

General Overviews

Ordination analysis has been reviewed many times since it became a popular method of analyzing community data. Care should be taken with the older “classic” reviews such as Greig-Smith 1983, as they do not include discussion of the most recent developments in analytical approaches. Some overviews of ordination methods, such as Zuur, et al. 2007, are written to accompany particular software packages. Ludwig and Reynolds 1988 is a straightforward account suitable for advanced undergraduates; Manly 2005 is more advanced, whereas Legendre and Legendre 1998 is encyclopedic. McGarigal, et al. 2000 provides one of the more recent general overviews of ordination. In all of these sources, ordination analysis is discussed in one or more chapters as part of a wider coverage of multivariate methods in ecology. Quinn and Keough 2002 provides an overview of ordination analyses in their text on experimental design. Ordination Methods for Ecologists is a comprehensive online overview.

• Greig-Smith, Peter. 1983. Quantitative plant ecology. 3d ed. Oxford: Blackwell.

  Since the publication of the first edition in 1957, this book became the standard text. Although the third edition is now dated, chapter 8 remains a thorough presentation of the statistical background for ordination methods.

• Legendre, Pierre, and Louis Legendre. 1998. Numerical ecology. 2d ed. Amsterdam: Elsevier.

  Encyclopedic and indispensible book that includes coverage of Principal Components Analysis (PCA), Principal Coordinate Analysis (PCoA, Metric Multidimensional Scaling), Nonmetric Multidimensional Dimensional Scaling (NMDS), and correspondence analysis (see Correspondence Analysis [CA] and Reciprocal Averaging [RA]) in a chapter on ordination. The statistical background to each method is thoroughly covered. Suitable for advanced students and experienced researchers with a good statistical background.

• Ludwig, John A., and James F. Reynolds. 1988. Statistical ecology: A primer on methods and computing. New York: Wiley.

  Very clearly written introduction suitable for undergraduate and graduate students and others new to the field. Worked examples are presented illustrating each method using a number of datasets.

• Manly, Bryan F. J. 2005. Multivariate statistical methods: A primer. 3d ed. Boca Raton, FL: Chapman & Hall/CRC.

  General overview written for nonmathematicians, but nevertheless emphasizing the statistical basis of several methods of ordination analysis including Principal Components Analysis (PCA), Canonical Correspondence Analysis (CCA), and Nonmetric Multidimensional Dimensional Scaling (NMDS). Suitable for advanced undergraduates or graduate students with a basic background in statistics.

• McGarigal, Kevin, Sam Cushman, and Susan Stafford. 2000. Multivariate statistics for wildlife ecology research. New York: Springer.

  DOI: 10.1007/978-1-4612-1288-1

  Chapter 2 of this book is a thorough overview of ordination analysis albeit with an emphasis on Principal Components Analysis (PCA).

• Ordination Methods for Ecologists.

  Comprehensive online source covering just about every aspect of ordination methods including a link for signing up to ORDNEWS, an active LISTSERV discussion group.

• Quinn, Gerry P., and Michael J. Keough. 2002. Experimental design and data analysis for biologists. Cambridge, UK: Cambridge Univ. Press.

  General textbook on experimental design that includes a useful overview of correspondence analysis (see Correspondence Analysis [CA] and Reciprocal Averaging [RA]), Canonical Correspondence Analysis (CCA), Principal Components Analysis (PCA), Principal Coordinate Analysis (PCoA, Metric Multidimensional Scaling), Nonmetric Multidimensional Dimensional Scaling (NMDS), and Redundancy Analysis (RDA, Constrained PCA, Canonical Redundancy Analysis) suitable for graduate students and general researchers.

• Zuur, Alain F., Elena N. Ieno, and Graham M. Smith. 2007. Analysing ecological data. New York: Springer.

  The principal methods of ordination are covered in four chapters offering clear advice on using each method. Familiarity with basic statistics is necessary. For advanced undergraduates or graduate students; chapter 3 includes recommendations for instructors. Available online as an e-book from the publisher. Accompanies the Brodgar software package (see Software Packages).