Overview of results
This study seeks to reveal the population genetic processes that influence microbial evolution within and between hosts.  Specifically, they find novel ways to use shotgun metagenomic data to look at the interplay between ecological and evolutionary processes in the human gut. This ambitious paper set out to describe two timescales of microbiome evolution across many bacterial species: evolution shaping the species-level diversity among hosts, and that governing changes that occur within hosts over the course of months. They focus on individual single nucleotide variation, gene gain and loss events and shifts in strain composition. The first describe how new hosts are colonized frequently by several strains of a particular bacterial species (oligo-colonization). However, they find that other hosts have a single prevailing strain, and they concentrate their analysis on these strains within these hosts. Examining the dominant strains of a given species across a panel of human hosts, they observe evidence that purifying selection is important. Within hosts, they find that purifying selection is weaker, but positive selection is apparent, acting largely on variation introduced by genetic exchange between bacteria as opposed to SNVs. They also introduce the puzzle of an intermediate timescale of evolution, by which bacteria from diverse hosts and locations appear anomalously similar.
What we found most significant  
The ideas are novel, the reasoning is sound, the analysis is very comprehensive, and the amount of work that went into this paper is admirable. The introduction especially was very well written and informative.
A major selling point of this paper is the novelty of the method used to examine evolutionary processes. The authors use a statistical analysis to ‘quasi-phase’ alleles in the dominant haplotype for samples carrying just one major strain of a given species. To our knowledge, this is one of the few times microbiome-wide shotgun metagenomic data has been used to infer the adaptive dynamics of individual strains, both in terms of ecological (relative abundance), and genome-wide evolutionary (gene gain/loss, SNP allele frequencies) trajectories, across >30 common bacterial species. Carefully-chosen statistical tests and comparison to null models were supplied for every analysis presented.
While not specifically hypothesis driven, this paper is a fascinating exploration of the dynamics of microbiome evolution, and suggests a number of questions to be examined further in more targeted studies. For example, the proposed oligo-colonization hypothesis lacks a mechanistic explanation and may be well-suited for an experimental approach. More fundamentally, if evolution is driven mainly by introgression and at the rates described here, this would prompt a true paradigm shift in our assessment of the extent of microbiome dynamics hidden from standard taxon-focused microbiome data (such as 16S sequencing) and could greatly inform the timescale of sampling in future studies. To us, the findings further warrant a careful exploration of the host-phenotypic consequences of bacterial evolution.
Suggestions for improvement
The main drawback we found was that this paper is dense. It is very descriptive and thorough, but still can be hard to distill the main points.  A few suggestions for clarifying the text follow:
  1. It would be helpful to give more intuition about what we might expect to see in individual plots if different scenarios were true.
  2. Picking who your target audience is, and then using words/phrases that are intuitive to that community will make this more accessible.
  3. Clearing the main text to focus on the main points, and then putting all the validation, null models, etc in the supp would help a lot.
  4. The figures often try to cover too much ground at once.  Some reorganizing may be useful so that each figure has one main take-home point, and the panels are different ways to support that point.
  5. It would be helpful to have figure captions and section titles that state the “bottom-line” / take-home point, rather than a description of what the analysis was
  6. While the title may have intentionally have been kept vague, we would advocate for a title that more succinctly relays the main finding - for example: “Quasi phasing identifies introgression as the primary mode of evolution in the microbiome”
Additionally, we were intrigued by the hypothesis that recombination between bacterial strains was a driving source of genetic variation acted upon by positive selection. However, wouldn’t it also be possible that low frequency variants (below the quasi-phasing threshold) could have been selected to higher frequency over the course of the sampling, and the patterns observed in Figure 5 were compositional shifts among strains with variation as opposed to introgressed regions spreading in new strains? It would be useful to address this alternative hypothesis.