For nucleotide models: Is the score that GARLI reports at the end of a run equivalent to what PAUP* would calculate after fully optimizing model parameters and branch lengths on the final topology?

It depends. The model implementations in GARLI are intentionally identical to those in PAUP, so in general the scores should be quite close, although PAUP* does more intensive optimization. If you’ve run GARLI for sufficiently long and not played with the optimization settings, the score will probably be within a few tenths of a log-likelihood unit from the score one would get optimizing in PAUP*.

On very large trees it may be somewhat more. In some very rare conditions the score given by GARLI is better than that given by PAUP* after optimization, which appears to be due to PAUP* getting trapped in local branch-length optima. This should not be cause for concern.

If you want to be absolutely sure of the lnL score of a tree inferred by GARLI, optimize it in PAUP*. More.

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