XLSTAT: Canonical Correspondence Analysis (CCA) in Excel

 

Background

Canonical Correspondence Analysis (CCA) relates species (or object) abundances to environmental (or descriptive) variables. It requires:

• A contingency table X with object frequencies across sites,

• A table Y of descriptive variables for the same sites,

• Optionally, a table Z for controlling covariates (partial CCA).

The aim is to create a map displaying objects, sites, and variables to interpret their relationships.

 

Dataset for Example

The attached data correspond to the counts of 10 species of insects on 12 different sites in a tropical region. A second table (displayed in red color) includes 3 quantitative variables that describe the 12 sites (altitude, humidity, and distance to the lake).

We will use the example to determine if the three descriptive variables can help us to explain the frequencies of the species of insects.

 

Setting up

• Open XLSTAT.

• Click on the Life Sciences/ Multiblock data analysis menu and select the Canonical Correspondence Analysis feature.

In the General tab of the dialog box:

• Select the data for species (objects) and the environmental variables (in red).

• Select the site labels.

• Ensure Column labels is checked to include headers in the analysis.

In the Options tab:

• Check the Permutation test option to assess the significance of the three variables' effect.

• Set the number of permutations to 1000.

 

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

The first results show descriptive statistics, including row and column profiles of the contingency table (insect frequencies per site). Weighted averages are the means of environmental variables, weighted by site totals.

This is followed by the permutation test results, which assess the significance of the environmental variables’ effect on species distribution.

  

The test suggests that the species data are not significantly related to the environmental variables at the 5% level (p = 0.089), but the result is borderline. It’s worth examining individual variables further.

The following table shows how inertia (variation) is divided between the constrained CCA (explained by environmental variables) and the unconstrained CCA (residual variation), helping to assess the explanatory power of the variables.

Only 40% of the inertia is explained by the constrained CCA, so deeper analysis of site-species relationships may be limited. However, for brevity, we focus on the constrained CCA results.

The eigenvector analysis shows that the first two axes capture 92.5% of the inertia, making the two-dimensional map sufficient to explore relationships among sites, species, and environmental variables.

  

The Canonical Correspondence Analysis map simultaneously displays the species, sites, and explanatory variables.

The map shows that Insect4 and Insect5 are associated with high humidity and low altitude. Insect7 is influenced by proximity to the lake, while Insect9 is linked to higher altitude or lower humidity.