Biplot scores from canonical correspondence analysis

Question

I'm using the R package vegan to perform canonical correspondence analysis (CCA). As input we have two matrices, one being (sites)x(species) and the other being (sites)x(conditions).

Sample data (and source of plot) are here.

Species loadings are easily accessed with summary(cca_model)$species. What I'm trying to find is the loadings for the explanatory variables, the conditions. The only summary I can find is biplot scores. Looking through the documentation for vegan I can't find any description of how they are computed. Can I sum them across CCA components to get an idea of how much they influence the data?

This is a biplot of two CCA components. The scores are used as coordinates for the arrows.

So two questions:

What are biplot scores in the context of CCA?

and

Can biplot scores be used to determine how much of an effect conditions have on the response variables?

Answer 1

Canonical correlation analysis (CCA) not correspondence canonical analysis. Biplots are the same as in PCA: the representation in a new space of the samples and the relative position of the variables on the new space.

However, CCA seeks the values of one block that maximize the correlation with the other block. Here you don't have an independent variable that you maximize from the variables you introduced on the CCA. So the interpretation is much trickier as there isn't a direction: WaterC and FallenTwigs show the opposite effect than BarSand and CoverMoss, but there is a group of variables that explain what is the effect of water on the plants(?)