I have four datasets: morphological measurements for a set of species (M1),
ecological measurements for the same set of species (E1), morphological
measurements for a second set of species (M2), and ecological measurements
for this second set of species (E2).

I am interested in finding the linear combinations of variables between M1
and E1, and between M2 and E2. That is, I'd like to know what combinations
of morphological measurements are associated with what combination of
ecological measurements--for each set of species separately. This seems
like a good use of CCA (two separate CCAs).

But here's where things get tricky for me. I'd like to see whether the same
linear combinations from one set of species do a good job of explaining the
variation in the second set of matrices. And I'd like to see how they
differ, if possible...e.g. yes the canonical function from the first CCA
does explain some of the variation in the second, but a different function
could do a lot better.

Is this making any sense? I could see simply running these as two separate
CCAs, then comparing the results qualitatively. But that doesn't seem very
rigorous. Should I be considering some other approach entirely?

Thanks for any input!

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