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Ordination: Mathematical Elegance and Ecological Naivete

Edward W. Beals
Journal of Ecology
Vol. 61, No. 1 (Mar., 1973), pp. 23-35
DOI: 10.2307/2258914
Stable URL: http://www.jstor.org/stable/2258914
Page Count: 13
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Ordination: Mathematical Elegance and Ecological Naivete
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Abstract

Principal components analysis, as a method of ordination to detect environmental influences, makes many unreal assumptions about ecological data. It does not take into account the normal-curve relationship between species success and environment, nor the ecological ambiguity of species absence in a stand. Furthermore, it uses an ecologically nonsensical centroid, and presumes a species-dimensional space. The latter is shown not to relate in any Euclidean way to environmental space. Each plant species in a pair of stands responds to the total environmental difference of those two stands, not to factors independent of those to which other species are responding. A model preferable to species-dimensional space is one which is defined by changes in vegetation from point to point (δ-vegetational space). The Bray and Curtis ordination, including the distance used, comes closer to this model than does principal components analysis. This is probably why the former method has given results that are equally satisfactory ecologically to those of more sophisticated methods, despite its alleged crudeness and frequently unwise choice of reference points. Refined techniques are being developed, which represent this vegetation model.

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