I realise that this question is now three years old! But for all of you who are still googling the same question and happen to land here, a colleague of mine showed me this useful script which answers this question:

https://github.com/kdyson/R_Scripts

Cheers, Mark

Well This is a very good question. The documentation for Vegan was posted exactly 2 days ago. It is a lengthy document which I have attached. I see no reference to AIC, BIC, etc.  Are you sure this does variable selection.? If you can't find anything about AIC in this document and given that it is so new, I would suggest contacting the maintainer. Sorry I couldn't be of help. Good luck and Best wishes.  

Dear Maru,

you cannot use extractAIC() with adonis, because the object resulting from adonis() simply do not have any AIC. adonis() perform multivariate ANOVA and test the significance of the explanatory variables by permutation (therefore PERMANOVA). You can theoretically compare different models built with adonis() by their R2 (which is included in the standard adonis() output), but this of course depends on the number of explanatory variables etc.

I do not know any R package, which can calculate PERMANOVA based on AIC, and I really doubt that it exists (also the original fortran code for PERMANOVA from M.J. Anderson did not use AIC).

HTH.

martin

Hi Maru: Though adonis doesn't calculate AIC, I don't see why you couldn't calculate it by hand (or write a script to do so). There's more than one formula; one estimation for AIC (w/o using maximum likelihood) is

AIC=2k+n[Ln(2(pi) RSS/n)+1], 

where k is the number of model parameters and RSS is the Residual Sum of Squares. This is not my field, though, so I'd vet this approach with a real statistician.

In any case, I'd be interested in hearing what you come up with. adonis() seems like a great tool for PERMANOVA and it'd be helpful I suspect for many others if there were a way to do some model selection.

Cheers, Pete 

I realise that this question is now three years old! But for all of you who are still googling the same question and happen to land here, a colleague of mine showed me this useful script which answers this question:

https://github.com/kdyson/R_Scripts

Cheers, Mark

and if you are interested in calculating the null model here is a modified version script from kdyson:

AICc.NULL = 1))

stop("object not output of adonis {vegan} ")

# Ok, now extract appropriate terms from the adonis model

# Calculating AICc using residual sum of squares (RSS) since I don't think that adonis returns something I can use as a likelihood function...

RSS