Program RdaCca

Pierre Legendre
April 1998
Département de Sciences Biologiques
Université de Montréal
Note: please see the Polynomial RdaCca for another approach to the RdaCca problem. This program performs two forms of canonical analysis, i.e. redundancy analysis (Rao, 1964) and canonical correspondence analysis (ter Braak, 1986, 1987), using multiple regression followed by direct eigenanalysis. The method of calculation is described in Chapter 11 of Legendre & Legendre (1998). This program is a pedagogical tool. Its objective is to demonstrate that the calculations can indeed be carried out in this way, and to provide users with a simple program allowing one to obtain all the eigenvectors and ordination axes from PCA or CA ordination, or from canonical analysis (RDA or CCA). It is not meant to replace advanced programs for canonical ordination, such as CANOCO. In particular, this program does not do forward selection of explanatory variables, nor does it carry out permutation tests of significance. Eigenanalysis is carried out using either a Householder procedure or singular value decomposition (SVD). The subroutines used are from Numerical Recipes (Press et al., 1986). References:
Legendre, P. & Legendre, L. 1998. Numerical Ecology, 2nd English edition. Elsevier Science BV, Amsterdam. xv + 853 pages. Press, W. H., B. P. Flanery, S. A. Teukolsky & W. T. Vetterling. 1986. Numerical Recipes - The art of scientific computing. Cambridge Univ. Press, Cambridge. xx + 818 p. Rao, C. R. 1964. The use and interpretation of principal component analysis in applied research. Sankhya A 26: 329-358. ter Braak, C. J. F. 1986. Canonical correspondence analysis: a new eigenvector technique for multivariate direct gradient analysis. Ecology 67: 1167-1179. ter Braak, C. J. F. 1987. The analysis of vegetation-environment relationships by canonical correspondence analysis. Vegetatio 69: 69-77.