Multivariate techniques that discriminate community composition based on environmental variables between two a priori defined groups?

Question

I have a methodological question that I have not been able to get an answer of. Basically, I am investigating the impacts of invasive species on soil microbial communities. I have a study design where I have a couple of sites each with paired invaded and uninvaded areas, and within each area I have collected a couple of soil replicates (for example n = 5 sites x 2 treatment groups x 6 replicates = 60). The data I have consists of a community data table (abundance data, species x samples ) for bacterial communities, and a set of environmental variables (soil variables, e.g. N, C etc).

So, I want to find out which environmental variables discriminate between the two a priori defined treatment groups, in other words are there variables that are significantly altered by invasion and which are linked to changes in community composition, or rather: which environmental variables are responsible for changes in community composition under invasion. However, none of the methods seem to offer me this. Linear discriminant analysis seems close, but the response is just the groups (which would be invaded vs uninvaded for me), and then environmental variables, but no place for a community table. Same which other methods like CCA or RDA, which constrain environmental variables to community composition, but I want to specifically constrain them to the two a priori groups (invaded vs. uninvaded). Also, CCA and RDA are significance tests, no? In my mind I can envisage a formula looking something like this: (Community ~ environmental variables, groups=Invasion treatment), the groups argument would be the a priori specified groups between which to constrain the analysis.

Hope this makes sense......

Answer 1

Why not using one multivariate technique (e.g. RDA or CCA as you said, BIOENV procedure based on similarity matrix might work as well) for each treatment (invaded VS uninvaded) then comparing the results between treatments?

Model like Y ~ environmental variables X Treatment + 1|Site can also be useful if you want to manipulate community metrics (e.g. Number of species, Total abundance, Shannon Index, etc.) in a univariate framework.