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The Problem of Non-Linearity in Ordination: Experiments with Two-Gradient Models

M. P. Austin and I. Noy-Meir
Journal of Ecology
Vol. 59, No. 3 (Nov., 1971), pp. 763-773
DOI: 10.2307/2258138
Stable URL: http://www.jstor.org/stable/2258138
Page Count: 11
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The Problem of Non-Linearity in Ordination: Experiments with Two-Gradient Models
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Abstract

Models have been constructed representing an environmental space with two factors to which species are assumed to have a bell-shaped response curve. Ordination of vegetation stands taken from this model, using principal component analysis and the weighted similarity coefficient, does not recover the original distribution of the stands. Various forms of the basic model were examined and two types of distortion were distinguished: involution, where extreme stands occur closer to the centre of the environmental plane than less extreme stands, and spurious axes which appear in the ordination although they do not represent independent environmental gradients. Several standardizations were applied to the data; some reduced the distortion but these improvements were not consistent for any single standardization over the range of variations studied. It was concluded that all present ordination techniques with the exception of the original continuum analysis of Curtis & McIntosh (1951) are subject to this form of distortion due to the incompatibility of the linear mathematical model and the non-linear ecological model of species response to environment.

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