Redundancy Analysis (RDA)

Redundancy Analysis (Legendre & Legendre 1998) takes as input a site/data matrix where each site has given values for one or more environmental/explanatory variables as well as a number of response (dependent) variables. The ordination axes are linear combinations of the explanatory (independent) variables. RDA can be thought of as a canonical version of PCA, i.e. with axes constrained by explanatory variables.

Each site should occupy one row in the spreadsheet. The explanatory variables should enter in the first columns, followed by the response data (the program will ask for the number of explanatory variables).

The implementation in PAST follows Legendre & Legendre (1998). The ordinations can be shown as site scores or fitted site scores. Explanatory variables are plotted as correlations with site scores. Both scalings (type 1 and 2) of Legendre & Legendre (1998) are available. The scores can be manually scaled with the “Amplitude” controls for a clearer plot (these factors should be reported together with the plot).

Missing values are supported by column average substitution.

Mystery rows: Rows can contain missing values (‘?’) for all explanatory variables. These rows, which must be placed at the bottom of the data matrix, are not included in the RDA analysis itself, but their site scores are estimated using the RDA vectors and included in the biplot. This could be used, for example, when explanatory variables are only known for a modern data set but not for “fossil” (downcore) samples. Mystery rows are only reported for unfitted site scores.


Legendre, P. & L. Legendre. 1998. Numerical Ecology, 2nd English ed. Elsevier, 853 pp.

Published Aug. 31, 2020 9:31 PM - Last modified Aug. 31, 2020 9:31 PM