Instability of ordination results under changes in input data order: explanations and remedies

Instability of ordination results under changes in input data order: explanations and remedies Abstract. Correspondence analysis (CA) and its Detrended form (DCA) produced by the program CANOCO are unstable under reordering of the species and sites in the input data matrix. In CA, the main cause of the instability is the use of insufficiently stringent convergence criteria in the power algorithm used to estimate the eigenvalues. The use of stricter criteria gives results that are acceptably stable. The divisive classification program TWINSPAN uses CA based on a similar algorithm, but with extremely lax convergence criteria, and is thus susceptible to extreme instability. We detected an order‐dependent programming error in the non‐linear rescaling procedure that forms part of DCA. When this bug is corrected, much of the instability in DCA disappears. The stability of DCA solutions is further enhanced by the use of strict convergence criteria. In our trials, much of the instability occurred on axes 3 and 4, but one should not assume that published two‐dimensional ordinations are sufficiently accurate. Data sets which have pairs of almost equal eigenvalues among the first three axes could suffer from marked instability in the first two dimensions. We recommend that a debugged, strict version of CANOCO be released. Meanwhile, users can check the stability of their CA and DCA ordinations using the software that we have made available on the World Wide Web (http://www.helsinki.fi/jhoksane/). An accurate program for CA, a debugged, strict version of DECORANA (for DCA) and a strict version of TWINSPAN are also available at our site. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Vegetation Science Wiley

Instability of ordination results under changes in input data order: explanations and remedies

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Publisher
Wiley
Copyright
1997 IAVS ‐ the International Association of Vegetation Science
ISSN
1100-9233
eISSN
1654-1103
D.O.I.
10.2307/3237336
Publisher site
See Article on Publisher Site

Abstract

Abstract. Correspondence analysis (CA) and its Detrended form (DCA) produced by the program CANOCO are unstable under reordering of the species and sites in the input data matrix. In CA, the main cause of the instability is the use of insufficiently stringent convergence criteria in the power algorithm used to estimate the eigenvalues. The use of stricter criteria gives results that are acceptably stable. The divisive classification program TWINSPAN uses CA based on a similar algorithm, but with extremely lax convergence criteria, and is thus susceptible to extreme instability. We detected an order‐dependent programming error in the non‐linear rescaling procedure that forms part of DCA. When this bug is corrected, much of the instability in DCA disappears. The stability of DCA solutions is further enhanced by the use of strict convergence criteria. In our trials, much of the instability occurred on axes 3 and 4, but one should not assume that published two‐dimensional ordinations are sufficiently accurate. Data sets which have pairs of almost equal eigenvalues among the first three axes could suffer from marked instability in the first two dimensions. We recommend that a debugged, strict version of CANOCO be released. Meanwhile, users can check the stability of their CA and DCA ordinations using the software that we have made available on the World Wide Web (http://www.helsinki.fi/jhoksane/). An accurate program for CA, a debugged, strict version of DECORANA (for DCA) and a strict version of TWINSPAN are also available at our site.

Journal

Journal of Vegetation ScienceWiley

Published: Jun 1, 1997

References

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