I am not an expert in these models, only a user of the software for analyzing data. But the HyPhy developers recommend their newer method MEME (rather than FEL or REL) for identifying sites under selection. The main advantage is that MEME is sensitive to finding sites under selection in only some lineages or at only some times in the history of the gene tree. Unless you have a hypothesis to test about which sites are expected to be under selection (like a binding site or a catalysis site) it might be better to treat the sites under selection as a random effect (REL) or a mixed effect (MEME).

Hi Giulia 

For fitting a nucleotide model or amino acid model to your data you can simply work with the free available MEGA software (http://www.megasoftware.net/). Once you downloaded and installed the software, simply check the "model selection" tab.

To detect positive selection you can use variety of methods and approaches.  Take a look here:

http://www.cathdb.info/wiki/doku/?id=tutorials:eccb_t2_studer

I highly recommend using CODEML program within the PAML suite so you need to work with codon models. It might be time-consuming in the beginning but it is worth the try as you would be able to do variety of analyses. Take a look here :

http://www.molecularevolution.org/resources/activities/paml_activity

http://people.inf.ethz.ch/anmaria/papers/Chapter%202.pdf

Do the following systematic analysis:

1) First do a M0 analysis to estimate branch lengths. 

2) Do a M1, M2, M7, M8 analysis and record the log-likelihood values.

3) Perform likelihood ratio test (M1 vs. M2 or M7 vs. M8) to see whether you see any site under positive selection. [If the M7 vs. M8 model was significant, you need to do another test which is called M8fixed. This is simply M8 model by setting dN/dS=1].

In M2 or M8 models you might get variety of different sites under positive selection.

Remember that all the model comparisons assume that evolution rate is the same in different branches of your phylogeny and is only variable across different residues of your protein. However, this is not biologically valid as we may observe periods of rapid evolution across branches. To make sure that evolution rate is variable across branches or not you should compare M0 model with a model called "Free ratio model" where each branch has a different rate. If this comparison was significant then you need to focus on each branch of your phylogeny using "branch-site test for positive selection". Take a look here:

http://www.ch.embnet.org/CoursEMBnet/PagesPHYL07/Exercises/day2/day2.html

Also, if you are interested in selection on amino acid properties you might like to take a look at TreeSAAP approach:

http://dna.cs.byu.edu/treesaap/

Thank you very much. I already did all the analyses under PAML (which is based on the REL approach) but than when the same analysis was performed in HyPhy using the FEL approach, I got completely different results. Maybe 7 sites out of the 30 identified by PAML were shared among the two analyses, and since on the HyPhy manual it was said that the outputs ought to be similar, I was wondering why..