how to interpret cca vegan output

How much variation is explained by X?

In a CCA, variance isn't variance in the normal sense. We express it as the "mean squared contingency coefficient", or "inertia". All the info you need to ascertain how much "variation" in Y is explained by X is contained in the section of the output that I reproduce below:

Partitioning of mean squared contingency coefficient:
              Inertia Proportion
Total           4.151     1.0000
Constrained     1.705     0.4109
Unconstrained   2.445     0.5891

In this example there is total inertia 4.151 and your X variables (these are "Constraints") explain a total of 1.705 bits of inertia, which is about 41%, leaving about 59% unexplained.

The next section referring to eigenvalues allows you to see both in terms of inertia explained and proportion explained which axes contribute significantly to the explanatory "power" of the CCA (the Constrained part of the table above) and the unexplained "variance" (the Unconstrained part of the table above.

The next section contains the ordination scores. Think of these as the coordinates of the points in the triplot. For some reason you show the site scores in the output above, but they would normally be there. Note that these have been scaled - by default this is using scaling = 2 - so site points are at their weighted average of the species scores IIRC etc.

The "Biplot" scores are the locations of the arrow heads or the labels on the arrows - I forget exactly how the plot is drawn now.

Which of all these numbers are important to my analysis?

All of them are important - if you think the triplot is important an interpretable, it is based entirely on the information reported by summary(). If you have specific questions to ask of the data, then perhaps only certain sections will be of paramount importance to you.

However, StackOverflow is not the place to ask such questions of a statistical nature.

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