Correspondence site: http://www.respond2articles.com/MEE/
Testing the significance of canonical axes in redundancy analysis
Article first published online: 22 DEC 2010
© 2010 The Authors. Methods in Ecology and Evolution © 2010 British Ecological Society
Methods in Ecology and Evolution
Volume 2, Issue 3, pages 269–277, June 2011
How to Cite
Legendre, P., Oksanen, J. and ter Braak, C. J. F. (2011), Testing the significance of canonical axes in redundancy analysis. Methods in Ecology and Evolution, 2: 269–277. doi: 10.1111/j.2041-210X.2010.00078.x
- Issue published online: 2 JUN 2011
- Article first published online: 22 DEC 2010
- Received 14 May 2010; accepted 19 October 2010 Handling Editor: Emmanuel Paradis
- canonical redundancy analysis (RDA);
- numerical simulations;
- tests of significance;
- type I error
1. Tests of significance of the individual canonical axes in redundancy analysis allow researchers to determine which of the axes represent variation that can be distinguished from random. Variation along the significant axes can be mapped, used to draw biplots or interpreted through subsequent analyses, whilst the nonsignificant axes may be dropped from further consideration.
2. Three methods have been implemented in computer programs to test the significance of the canonical axes; they are compared in this paper. The simultaneous test of all individual canonical axes, which is appealing because of its simplicity, produced incorrect (highly inflated) levels of type I error for the axes following those corresponding to true relationships in the data, so it is invalid. The ‘marginal’ testing method implemented in the ‘vegan’ R package and the ‘forward’ testing method implemented in the program CANOCO were found to have correct levels of type I error and comparable power. Permutation of the residuals achieved greater power than permutation of the raw data.
3. R functions found in a Supplement to this paper provide the first formal description of the ‘marginal’ and ‘forward’ testing methods.