Testing the significance of canonical axes in redundancy analysis

Methods in Ecology and Evolution - Tập 2 Số 3 - Trang 269-277 - 2011
Pierre Legendre1, Jari Oksanen2, Cajo J. F. ter Braak3
1Département de sciences biologiques, Université de Montréal, C.P. 6128, succursale Centre-ville, Montréal, QC H3C 3J7, Canada
2Department of Biology, University of Oulu, P.O. Box 3000, FIN-90014 Oulu, Finland
3Biometris, Wageningen University and Research Centre, Box 100, 6700 AC Wageningen, The Netherlands

Tóm tắt

Summary

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.

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Methods in Ecology and Evolution

Tập 2 Số 3

269-277

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