GIlles, although this doesn't answer your question, just for your information, SIMPER and ANOSIM have serious issues since it is very difficult to determine whether differences are attributed to within-group or between-group variation, which may provide misleading results. You may want to look Warton et al. 2012. Distance-based multivariate analyses confound location and dispersion effects. Methods in Ecology and Evolution, 3, 89--101.

PCA or End member analysis may be what you are looking for. If you are looking at relative proportions, you may also need to think of doing composition analysis to transform the data before hand as the variables will not be truly independent of one another. This is easy to do in R.

https://cran.r-project.org/web/packages/compositions/compositions.pdf

To test for differences among groups, I suggest you use a PERMANOVA (main and pairwise tests). It is robust enough do deal with assumptions that other analyses have. Besides, this technique is applied to a distance matrix, regardless of its nature (distance).

To identify the variables responsible for the main differences, there are two approaches in my opinion.

1) Use an ordination (PCoA or NMS) on the distance matrix. Then correlate your variables with the ordination axes, and identify those that are more responsible for each gradient.

2) Apply an IndVal analysis controlling your groups, and see the values for each variable that are responsible for the most important differences.

Hey Matheus,

I am relatively new at multivariate analysis. How do you perform the correlation between variables and ordination axes ? Can you provide an example in R?

Thanks,

Ayush