" I have two competing hypothesis of sub-species arrangements and both produce significative results."

Did you consider the case that your seemingly competing sub-species concepts are not actually in conflict with each other? Perhaps your sample includes not only 2 but 3 or 4 sub-species that are equally well supported by your data.

I suppose that, if both hypothesis are equally supported, than the anova test between linear models would indicate that both are not significantly different from each other. If might be the case that they are equally valid, and they are only different because one hypothesis have more groups than the other (9x12).

In either way, that would be a good result, but I want to know if that this is the case.

I could calculate likelihood values for each hypothesis and calculate the AIC (or BIC, or whatever) based on that, but I'm not sure if that is correct for multivariate datasets. I think I can calculate likelihoods using the mvtnorm package, but I was wondering if there were any easier alternatives.

I think there is still another problem: If you got a (morphometrics-based) multivariate dataset that includes different subspecies (for example A, B, C, D) you can get two (or more) different hypotheses of sub-species arrangements (lets'say A+B vs. C+D and A+C vs. B+D) and in both cases the differences between these groupings may be significant according to various tests.

If so, one hypothesis might not actually be better than the other or have a greater explanatory power because both types of sub-species arrangements might have totally different causes e.g. one type of grouping (A+B vs. C+D) is the consequence of similar ecology whereas the other type of grouping (A+C vs. B+D) is the consequence of closer phylogenetic relationship (are you looking for that?).

Perhaps it is not a good idea to search for a "better" hypothesis in the first place (at least not with this kind of data) but to endorse both (if they both pass significance tests).

My issue with this is that both hypothesis are not fully independent: both are more or less geographical and overlap greatly. They are not completely nested, but there is a great part of it that is. In other words, I just want to know if the morphometric data suports a more detailed taxonomic arrangement.

And yes, we are evaluating phylogenetic affinities and our hypothesis is based on that and hypotheses of geographical barriers. The different kind of data are non-overlapping: we do not have genetic data for all individuals, nor populations, but they do allow us to infer some biogeographical hypothesis of isolation and test it for the morphometric data.

I guess it would suffice to just test our hypothesis and call it the day, but it seems... not completely justified to just test against a null hypothesis of no arrangement at all.

A nice and straightforward procedure for comparing phylogenetic hypotheses (could be based on geographic barriers, molecular dara or else) by means of morphometric data was employed by Klingenberg & Gidaszewski (2010).

You might give it a shot, even though the authors concluded for the particular example they had studied (Drosophila) that geometric morphometrics was no good.

http://sysbio.oxfordjournals.org/content/59/3/245.full.pdf+html

To compare multivariate model you have to come up with conceptual model, hypothesis belong to one dimensional statistic, you are moving in field of human activities some name as statistical learning. Best

If they are fit to the same data you can compute your own AIC as -2*LL + 2k (k is the number of parameters in the model), R has the function logLik() for getting the Log-Likelihood. Then compare, the lower the better. Look at the book (or articles) from Anderson and Burnham on model selection and multimodel inference.

Stumbled on this late, but +2k or +2(k + 1) is INCORRECT for a penalty term in AIC for multivariate data. The real penalty term is 2(kp +0.5p(p+1)). The first part, kp, is the number of coefficients for parameters in the model; the second part is the number of unique cells in the error covariance matrix. If p, the number of variables, is 1 for univariate data, then the equation simplifies to 2(k + 1), which is what most people know to be the formula. It is really easy to make a mistake here!