Testing the significance of canonical axes in redundancy analysis

P. Legendre, J. Oksanen, C.J.F. ter Braak

Research output: Contribution to journalArticleAcademicpeer-review

258 Citations (Scopus)


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
Original languageEnglish
Pages (from-to)269-277
JournalMethods in Ecology and Evolution
Issue number3
Publication statusPublished - 2011


  • ecological data
  • bimultivariate redundancy
  • environment relationships
  • neighbor matrices
  • monte-carlo
  • regression

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