Reviewer 2's Review

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In this manuscript, the authors examine the performance of two methods for the reconstruction of ancestral nucleotide sequences (a parsimony method and a likelihood-based method) with respect to codon bias. They use a simulation approach (with parameters roughly based on D. melanogaster and its close relatives) to examine the effects of several factors, including tree length, changes in mutation bias, and changes in selection intensity, on the accuracy of both methods. The likelihood-based method performs better than the parsimony approach under most scenarios, although changes in population size and lineage-specific departures from stationarity are problematic for both methods. This paper is generally well thought out and executed, and should have a significant impact given broad current interest in codon bias and synonymous site evolution.

The data are well presented, and the authors present their main conclusions fairly and in a convincing manner. However, I have two methodological concerns that I would like to see addressed before publication:
(1) Model choice: Really two concerns here, one regarding the "parsimony" inference and one regarding the choice of ML model.
(a) Parsimony: The authors use a Jukes-Cantor model with a short tree to emulate MP, justifying this choice as follows: "Comparisons of this procedure to an iterative method of parsimony inference gave almost identical results". Under what scenarios was this comparison performed? Are they the same under the various non-stationary scenarios investigated in this paper? And if so, why not present results from the actual parsimony analysis? At the very least, please present the comparison between the JC inference and the iterative parsimony inference as a supplement.
(b) ML: The authors perform the ML inference under the HKY85 model, presumably because this is the simplest commonly used likelihood model that allows for differences in equilibrium base composition. However, as the authors themselves point out (p. 15), this is not an entirely appropriate model, given the differences between the GCpref model and HKY85 (or between real codon-biased data and HKY85). Wouldn't a more complicated model, e.g. GTR, be more appropriate? Please explain the choice of HKY85.
(2) Quantification of error: The authors compare the ML and MP inference methods under various evolutionary scenarios, often concluding that the ML method is less biased than MP. It is difficult to gauge the strength of these claims, however, in the absence of statistical comparisons. Given the authors' use of a simple ML model as a proxy for MP, some form of likelihood ratio test or AIC comparison might be in order. Even more convincing would be the use of a statistic (RMSE?) to evaluate the extent to which each method is biased.


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N.B. These are the general comments made by the reviewer when reviewing this paper in light of which the manuscript was revised. Specific points addressed during revision of the paper are not shown.