R CCA - Can species scores be related to CCA axis & how does the biplot arrow length relates to significance of variables?

Question

Hallo this is my first question in stackoverflow or any simliar forum, so please excuse and be kind if I missed something out ;)

I am using the vegan package in R to calculate a cca analysis. Because my study is about intraspecific variation of species traits, I do not have a "plot X species- matrix" but an "individuum X trait- matrix" representing a "physio-chemcial-niche" (so my species scores look different than they used to). So my questions are:

1. is it appropiate to do this analysis in this way?
2. Is it possible to interpret the CCA axis based on the "species scores" (which are not species scores in my case) - I would like to have informations like: CCA1 is most related to trait X.
3. How can I interpret the length of the biplot arrows in comparison to premutaion test (anova.cca) - Because I get many "long" arrows but looking at the permutation test only few of them are significant?

Here is my summary(cca)-Output:

Call:
cca(formula = mniche_g ~ cover_total * Richness + altitude +      Eastness + lan_TEMP + lan_REACT + lan_NUTRI + lan_MOIST +      Condition(glacier/transect/plot/individuum), data = mres_g_sc) 

Partitioning of scaled Chi-square:
               Inertia Proportion
Total         0.031551    1.00000
Conditioned   0.001716    0.05439
Constrained   0.006907    0.21890
Unconstrained 0.022928    0.72670

Eigenvalues, and their contribution to the scaled Chi-square 
after removing the contribution of conditiniong variables

Importance of components:
                         CCA1      CCA2      CCA3    CA1     CA2      CA3
Eigenvalue            0.00605 0.0005713 0.0002848 0.0167 0.00382 0.002413
Proportion Explained  0.20280 0.0191480 0.0095474 0.5596 0.12805 0.080863
Cumulative Proportion 0.20280 0.2219458 0.2314932 0.7911 0.91914 1.000000

Accumulated constrained eigenvalues
Importance of components:
                         CCA1      CCA2      CCA3
Eigenvalue            0.00605 0.0005713 0.0002848
Proportion Explained  0.87604 0.0827150 0.0412425
Cumulative Proportion 0.87604 0.9587575 1.0000000

Scaling 2 for species and site scores
* Species are scaled proportional to eigenvalues
* Sites are unscaled: weighted dispersion equal on all dimensions


Species scores

                  CCA1      CCA2       CCA3      CA1      CA2       CA3
SLA_range_ind  0.43964 -0.002623 -0.0286814 -0.75599 -0.04823  0.003317
SLA_mean_ind   0.01771 -0.042969  0.0246679 -0.01180  0.12732  0.053094
LNC           -0.10613 -0.064207 -0.0637272  0.07261 -0.15962  0.198612
LCC           -0.01375  0.012131 -0.0005462  0.02573 -0.01539 -0.021314
    
...

Here is my anova.cca(cca)-Output:

Permutation test for cca under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 999

Model: cca(formula = mniche_g ~ cover_total * Richness + altitude + Eastness + lan_TEMP + lan_REACT + lan_NUTRI + lan_MOIST + Condition(glacier/transect/plot/individuum), data = mres_g_sc)
                      Df ChiSquare       F Pr(>F)    
cover_total            1 0.0023710 10.4442  0.002 ** 
Richness               1 0.0006053  2.6663  0.080 .  
altitude               1 0.0022628  9.9676  0.001 ***
Eastness               1 0.0005370  2.3657  0.083 .  
lan_TEMP               1 0.0001702  0.7497  0.450    
lan_REACT              1 0.0005519  2.4313  0.094 .  
lan_NUTRI              1 0.0000883  0.3889  0.683    
lan_MOIST              1 0.0001017  0.4479  0.633    
cover_total:Richness   1 0.0002184  0.9620  0.351    
Residual             101 0.0229283                   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

and here the biplot: enter image description here

Thank you all!

Answer 1

1. I don't have sufficient information to say if it is sensible to use CCA for your data. I'm suspicious and I think it may not be sensible. The critical question is "does the sum of traits make sense?". If it does not, *CA makes no sense, because you need both row and column sums there, and if you have measured your variables in different units, their sum makes no sense. For instance, if you change the units of one "trait", say, from inches to centimetres, the results will change. It is probable wiser to use RDA/PCA with equalizing scaling of variables.

2. You can get the relationship of single variable to an axis from the analysis. It is just the ordination score of that variable. Visually you see it by projecting the point to the axis, numerically with summary or scores. However, I think you should not want to have that, but I won't stop you if you do something that I think you should not do. (Interpretation of rotated dimensions may be more meaningful – axes are just a framework of reference to draw plots.)

3. Brief answer: the arrow lengths have no relation to the so-called significances. Longer answer: The scaling of biplot arrow lengths depends on the scaling of your solution and the number of constrained axes in your solution. The biplot scores are based on the relationship with the so-called Linear Combination scores – which are completely defined by these very same variables, and the multiple correlation of the constraining variable with all constrained axes is 1. In the default scaling ("species"), all your biplot arrows have unit length in the full constrained solution, but if you show only two of several axes, the arrows appear shorter if they are long in the dimensions that you do not show, and they appear long, if the dimensions you show are the only ones that are important for these variables. With other scalings, you also add scaling by axis eigenvalues. However, these lengths have nothing to do with so-called significances of these variables. (BTW, you used sequential method in your significance tests which means that the testing order will influence the results. This is completely OK, but different from interpreting arrows which are not order-dependent.)