Vegetation analysis and order invariant gradient models
 I. C. Prentice
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An ideal ordination method would have known properties with respect to an explicit, order invariant ecological response model defined in more than one dimension. The CurtisMcIntosh model (each species weakly unimodal) is a good generalpurpose model of a single gradient, but not current method is guaranteed to dispose samples from such a gradient along a straight line. There is some theoretical justification for using reciprocal averaging (RA), or local nonmetric multidimensional scaling (NMDS) with Kendall's simple similarity coefficient, but the former tends to produce arches rather than straight lines and the latter can produce erratic curves (as illustrated here by applying the method to simulated coenocline data). The nonmetric method is nevertheless shown to perform well (a) with high betadiversity plant distribution data and (b) with simulated coenoplane data, where its performance is better than that of RA. Results with coenoclines and coenoplanes concur with those of Fasham (1977) who tested NMDS with a different coefficient. Local scaling is shown to be preferable to global, and primary tie treatment to secondary, in tests on coenocline and coenoplane data. A possible alternative nonmetric approach is mentioned.
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 Title
 Vegetation analysis and order invariant gradient models
 Journal

Vegetatio
Volume 42, Issue 13 , pp 2734
 Cover Date
 19801001
 DOI
 10.1007/BF00048867
 Print ISSN
 00423106
 Online ISSN
 15735052
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Authors

 I. C. Prentice ^{(1)}
 Author Affiliations

 1. Department of Plant Biology, The University, NE1 7RU, Newcastle upon Tyne, United Kingdom