Question about interpreting 'Final Likelihood (-lnL)' and when to use --poisson in CAFE5 #255

Dear Hahnlab CAFE team,
Thank you for developing and maintaining CAFE5 — it has been very helpful.
I am running CAFE5 on a small dataset (6 taxa) and I am a bit confused about how to interpret and compare the model outputs, especially the “Final Likelihood (-lnL)” value and the use of the root frequency option.

I ran the base model with the same input matrix and timetree, changing only whether I include the Poisson root frequency option:

1. Without --poisson:
   cafe5 -i filtered.cafe.input.tsv -t timetree_6species.nwk -o base

Model Base Final Likelihood (-lnL): 161736
Lambda: 0.0018652515272477
Maximum possible lambda for this topology: 0.0134469
55 values were attempted (0% rejected)

2. With --poisson (estimated):
   cafe5 -i filtered.cafe.input.tsv -t timetree_6species.nwk --poisson -o base_p

Model Base Final Likelihood (-lnL): 74282.9
Lambda: 0.001952787471529
Maximum possible lambda for this topology: 0.0134469
55 values were attempted (0% rejected)

My questions:

1. Is “Final Likelihood (-lnL)” the negative log-likelihood, so that a smaller value indicates a better fit (equivalently, a larger lnL)? If so, is it valid to compare these two runs directly since they differ only in the root frequency assumption (uniform vs Poisson)?
2. In typical analyses, do you recommend always trying --poisson (estimated) in addition to the default, and then selecting the one with better likelihood? Or are there scenarios where you would prefer the default uniform root frequency?
3. I have seen references to a “gamma model” in some discussions/tutorials. In CAFE5, is there a recommended situation where I should also try a gamma-based option/model (and if so, which specific option in CAFE5 corresponds to that)? If “gamma model” is not applicable to CAFE5, please ignore this question — I may be mixing this up with another framework.

Thank you very much for your time and guidance.

Best regards,
WangWang