Ordination Analysis
- LAST REVIEWED: 11 January 2024
- LAST MODIFIED: 11 January 2024
- DOI: 10.1093/obo/9780199830060-0003
- LAST REVIEWED: 11 January 2024
- LAST MODIFIED: 11 January 2024
- DOI: 10.1093/obo/9780199830060-0003
Introduction
Ordination is a method for reducing dimensions of multivariate data. Inference on high-dimensional data can be challenging, and reducing dimensions can make it more approachable. In biology, the lower-dimensional space is visually represented in an ordination diagram. Such a visualization allows the discussion of patterns in the distribution of samples and species or of other units under study. In community ecology ordination allows hypotheses to be generated, and tested, about the potential relationship between composition of an ecological community at a site and characteristics of the environment. Sparse data sets with few observations are a common occurrence in community ecology, and ordination helps to reduce the information burden of the analysis. Since its introduction in the ecological literature in the early 1950s, ecologists have embraced several approaches to ordination analysis, which are listed here.
Historical Background
Ordination methods were introduced to ecologists largely through the work of plant community ecologists. Curtis and McIntosh 1951 uses a compositional gradient analysis procedure based upon species adaptation values. Goodall 1954 introduces the term ordination to describe the arrangement of plant communities in a uni- or multidimensional order. The desire to objectively quantify the relationship among plant communities along environmental gradients arose from the work Whittaker 1956. Over the years many new ordination methods have been introduced (faster than that they could be tested, according to Gauch 1982), and considerable effort has been put into assessing the limitations of ordination methods, the appropriateness of data transformations before applying ordination, and the ability of different resemblance measures to as a measure of ecological distance; see for example Whittaker and Gauch 1973; Faith, et al. 1987; and Legendre and Gallagher 2001. Studies of limitations and appropriateness of ordination methods started with Greig-Smith 1957 and Austin and Orloci 1966. The result is a field with proponents of particular schools of ordination methods. For example, Kenkel 2006; Warton, et al. 2012; and Roberts 2020 all advocate for some groups of methods over others.
Austin, M. P., and L. Orloci. 1966. Geometric methods in ecology: II. An evaluation of some ordination techniques. Journal of Ecology 54:217–227.
DOI: 10.2307/2257668
An early comparison of ordination methods in which Polar Ordination (PO) and Principal Components Analysis (PCA) are evaluated.
Curtis, J. T., and R. P. McIntosh. 1951. An upland forest continuum in the prairie-forest border region of Wisconsin. Ecology 32:476–496.
DOI: 10.2307/1931725
The Polar Ordination (PO) method of ordination is introduced in this study of forest communities.
Faith, D. P., P. R. Minchin, and L. Belbin. 1987. Compositional dissimilarity as a robust measure of ecological distance. Vegetatio 69:57–68.
DOI: 10.1007/BF00038687
Computer simulations evaluated the robustness of various quantitative measures of compositional dissimilarity between sites, finding the Kulczynski, Bray-Curtis, and relativized Manhattan measures to be the best. Hybrid multidimensional scaling is introduced, which combines metric and nonmetric models.
Gauch, H. G. 1982. Multivariate analysis in community ecology. New York: Cambridge Univ. Press.
Classical community ecology reference. Encourages thinking of data and ordination in a geometrical fashion, placing emphasis on the different spaces that can be represented with ordination methods.
Goodall, D. W. 1954. Objective methods for the classification of vegetation: III. An essay in the use of factor analysis. Australian Journal of Botany 2:304–324.
DOI: 10.1071/BT9540304
Though the title of the article reads “factor analysis,” the study concerns principal component. The term “ordination” is proposed as an antonym to “classification” to describe principal component analysis and quantitative methods that can be used to arrange vegetational data in a multidimensional series.
Greig-Smith, P. 1957. Quantitative plant ecology. London: Butterworth’s Scientific Publications.
The first of three editions of this authoritative book (1957, 1964, 1983). The use of ordination analysis was in its infancy at this time, and the author’s presentation shows how the concept developed from earlier approaches of gradient analysis and the use of climax adaptation numbers.
Kenkel, N. C. 2006. On selecting an appropriate multivariate analysis. Canadian Journal of Plant Science 86.3: 663–676.
DOI: 10.4141/P05-164
Review study of Principal Components Analysis (PCA), Correspondence Analysis (CA), and Nonmetric Multidimensional Dimensional Scaling (NMDS), as well as various constrained ordination methods. Argues that algorithmic ordination methods should only be used when the assumptions of more statistically oriented ordination methods are violated.
Legendre, P., and E. D. Gallagher. 2001. Ecologically meaningful transformations for ordination of species data. Oecologia 129:271–280.
Instead of using distances to summarize data, this study considers transformations of data so that a good ordination is retrieved, while species effects remain available unlike in distance-based ordination methods.
Roberts, D. W. 2020. Comparison of distance‐based and model‐based ordinations. Ecology 101.1: e02908.
DOI: 10.1002/ecy.2908
NMDS and t-nearest Stochastic Neighbor Embedding (t-SNE) are compared to model-based ordination with real and simulated data. Concludes distance-based methods to be superior.
Warton, D. I., S. T. Wright, and Y. Wang. 2012. Distance‐based multivariate analyses confound location and dispersion effects. Methods in Ecology and Evolution 3.1: 89–101.
DOI: 10.1111/j.2041-210X.2011.00127.x
From a model-based perspective, distance measures often used in community ecology for ordination imply certain mean-variance relationships. The authors demonstrate this and argue that multivariate analysis based on such distances can perform poorly.
Whittaker, R. H. 1956. Vegetation of the Great Smoky Mountains. Ecological Monographs 26:1–80.
DOI: 10.2307/1943577
Foundational study that spurred the development of quantitative community ecology following the demonstration of vegetation continua with an elevational gradient.
Whittaker, R. H., and H. G. Gauch Jr. 1973. Evaluation of ordination techniques. In Ordination and classification of communities. Edited by R. H. Whittaker, 287–321. The Hague, The Netherlands: Junk.
DOI: 10.1007/978-94-010-2701-4_11
Comprehensive overview of ordination methods of the time focusing on Polar Ordination (PO) and Principal Components Analysis (PCA) compared using simulated coenoclines varying the levels of beta diversity.
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