Dear Giovanni,
I can see no reason why you shouldn't use path-sampling to look at the relative fit of the asymmetric and symmetric models to your data.
SPREAD can visualize both models.
The default Poisson priors on non-zero rates generated by BEAUti differ between the two models. For the symmetric model the suggested (I hesitate to say 'recommended') prior is a Poisson with mean = 0.693 (log2) and the offset = K - 1 (where K is the number of states). This has the effect of putting 50% probability on getting K-1 rates which is the minimum necessary to connect all the states.
For the asymmetric model it is a simpler Poisson with mean of K-1 (offset 0).
Andrew
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Andrew Rambaut
Institute of Evolutionary Biology University of Edinburgh
Ashworth Laboratories Edinburgh EH9 3JT
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