Canonical Ordinations: Redundancy Analysis (RDA) and Canonical Correspondence Analysis (CCA)

This Eco-Tool implements two forms of canonical ordination: Redundancy Analysis (RDA) and Canonical Correspondence Analysis (CCA). The main input consists of a matrix where rows represent sites and columns contain either dependent variables (typically observations of species abundances) or candidate predictor variables (measurements of some environmental quality at each site). A second input is the number of predictor variables; this is used to divide the input matrix into its two components. A third input is the number of randomizations used to test the significance of the dependent variables in determining the observations. Optional inputs are row and column labels.

An example of an input matrix is given below. This is the made-up tropical reef dataset used in Numerical Analysis (Legendre and Legendre 1998, p590).

1 2 3 4 5 6 Depth Coral Sand Other
1 1 0 0 0 0 0 1 0 1 0
2 0 0 0 0 0 0 2 0 1 0
3 0 1 0 0 0 0 3 0 1 0
4 11 4 0 0 8 1 4 0 0 1
5 11 5 17 7 0 0 5 1 0 0
6 9 6 0 0 6 2 6 0 0 1
7 9 7 13 10 0 0 7 1 0 0
8 7 8 0 0 4 3 8 0 0 1
9 7 9 10 13 0 0 9 1 0 0
10 5 10 0 0 2 4 10 0 0 1

There are ten sites, six species, and four predictor variables. Note that all predictors except Depth are numerical codings for a single qualitative variable one might call Substrate Type. Because these categories are exhaustive (meaning that every site must be in one of the categories), then using all three of the columns in the analysis is redundant (and will lead to numerical problems in the calculations). One option is to simply remove one of the columns, but this has the disadvantage that it is no longer possible to calculate the correlation of that environmental variable with any of the ordination axes. So, in this Eco-Tool we implement the option to keep redundant variables in the data, and simply specify which columns they are.

Input

Input file should be a tab-delimited text file, with contents organized as described above. The file may include column or row headings or not; choose the appropriate option below. Note that headings should not contain spaces or commas, so instead of using “Veg Ht”, use something like “Veg_Ht”. Also, note that long headings may make the plots in the output difficult to read.

Use my data:

Use artificial dataset of fish abundances at six sites along a tropical reef transect (data from table above). Used as example data for RDA in Numerical Analysis.

Use artificial dataset of fish abundances at ten sites along a tropical reef transect. Used as example data for CCA in Numerical Analysis.

Number of predictor columns:  

Ordination type:     

Number of randomizations  

Options

Column headers?     

Row headers?     

Redundant predictors?  

If there are redundant predictor variables in your data, the input box above should contain a list of column numbers, separated by commas. The numbers are relative to the start of the predictor columns. For example, to classify the Other column from the example dataset as redundant, one would enter “4” in the box.