Why do you need to reduce parameters for pca?..isnt one point of pca to produce principal components' and define strength (correlation) of variables to axes.....Provided data is 'cleaned', non autocorrelated and transformed appropriately. You could run a few trials.
Bioenv bv-step is better than the BEST routine for determining biotic/abiotic relationships for large datasets.
You may use PC scores to reduce variables (i.e. the correlated ones). firstly, you should do a PCA on your parameters using predetermined number of PCs (lets say N= 10 PCs). Then check to see how many PCs are needed to describe 100% cumulative %variation (for example the first 5 out of 10 PCs). In each PC (1st to 5th) choose the variable with the highest score (irrespective of its positive or negative sign) as the most important variable. Since PCs are orthogonal in the PCA, selected variables will be completely independent (non-correlated).
I have a similar situation with my dataset and I wanted to get some help. So in my case, I ran a PCA with these 7 environmental variables velocity, depth, width, slope, distance from upstream, and temperature. I am trying to relate them with the fish abundance data across many sites. My analysis results suggest
Eigenvalues
PC Eigenvalues %Variation Cum.%Variation
1 2.36 34.6 34.6
2 1.75 25.6 60.2
3 0.884 12.9 73.2
4 0.607 8.9 82.0
5 0.523 7.6 89.7
Eigenvectors
(Coefficients in the linear combinations of variables making up PC's)
Variable PC1 PC2 PC3 PC4 PC5
Velocity 0.206 -0.502 0.288 0.237 -0.626
Depth -0.461 -0.172 -0.036 0.814 0.152
Width -0.444 -0.410 -0.022 -0.451 0.154
Slope 0.389 -0.439 0.114 -0.092 -0.015
Ups distance -0.488 -0.382 0.107 -0.229 -0.019
Elevation 0.393 -0.407 -0.042 0.127 0.711
Temp 0.065 -0.215 -0.943 0.009 -0.236
In this case then should I infer that environmental variables influencing fish abundance in terms of importance are 1) upstream distance 2) velocity 3) temp 4) depth and 5) elevation? I also wonder that I haven't checked them for spatial autocorrelation, is there a way to check for this in PRIMER-E?