Basic reporting

Reporting is comprehensive and most parts are relatively easy to follow even though a rather broad theoretical and empirical background literature is referred to. The background is largely discussed adequately and references are placed appropriately.

The manuscript could benefit from a more basic explanation, why multiple merger coalescents are expected to perform better than the Kingman coalescent with high-fecundity species. I agree that with high-fecundity species, the basic assumption of similar numbers of offspring between individuals is violated, however, it is not entirely clear why this should have a strong effect when empirical data sets are used, especially on a large geographic scale, as in the case of this study. After all, we would not expect samples from Greenland and Norway to share the same parents, and even on a more local scale, I would expect few if any of the sampled individuals to be siblings originating from a single high-fecundity individual. Nevertheless, the statistical comparisons do in fact support the use of multiple merger coalescents. Why is this so?

The use of the multiple merger coalescent with empirical data may most interesting for many readers, but little information is given on its practical application. The authors write that they use "analyzed site frequency sprectra using ... statistical methods developed for multiple merger Lambda coalescents (Birkner et al., 2013b)", but it is not specified whether code provided by Birkner et al. was used or whether calculations were performed with code developed by the authors. Also, if there are settings to be chosen for either code, these details would be very helpful.

The structure of the discussion could be improved. It's not entirely clear what the three possible scenarios (l. 356) to explain allelic divergence are.

I must say that I find the phrasing partially clumsy, and have highlighted the most obvious examples in the attached annotated manuscript with comments (written with Apple Preview, if these should not be readable for you, please get back to me). I would appreciate if the authors could once more go through their wording, especially for the highlighted sentences but also in other parts of the manuscript.

Supplementary S2 was not available for review, but does not seem to be crucial to assess the quality of the manuscript. Nevertheless this information should be made available to the reader.

Experimental design

The experimental design is interesting and sound. Some more details should be given regarding the application of the multiple merger coalescent (see above).

Validity of the findings

All findings are valid and discussed appropriately.