Dear Dr Jay,

Thank you for submitting your manuscript entitled "Modeling the stepwise extension of recombination suppression on sex chromosomes and other supergenes through deleterious mutation sheltering" for consideration as a Research Article by PLOS Biology.

Your manuscript has now been evaluated by the PLOS Biology editorial staff, as well as by an academic editor with relevant expertise, and I am writing to let you know that we would like to send your submission out for external peer review.

However, before we can send your manuscript to reviewers, we need you to complete your submission by providing the metadata that is required for full assessment. To this end, please login to Editorial Manager where you will find the paper in the 'Submissions Needing Revisions' folder on your homepage. Please click 'Revise Submission' from the Action Links and complete all additional questions in the submission questionnaire.

Once your full submission is complete, your paper will undergo a series of checks in preparation for peer review. Once your manuscript has passed the checks it will be sent out for review. To provide the metadata for your submission, please Login to Editorial Manager (https://www.editorialmanager.com/pbiology) within two working days, i.e. by Feb 20 2022 11:59PM.

If your manuscript has been previously reviewed at another journal, PLOS Biology is willing to work with those reviews in order to avoid re-starting the process. Submission of the previous reviews is entirely optional and our ability to use them effectively will depend on the willingness of the previous journal to confirm the content of the reports and share the reviewer identities. Please note that we reserve the right to invite additional reviewers if we consider that additional/independent reviewers are needed, although we aim to avoid this as far as possible. In our experience, working with previous reviews does save time.

If you would like to send previous reviewer reports to us, please email me at rhodge@plos.org to let me know, including the name of the previous journal and the manuscript ID the study was given, as well as attaching a point-by-point response to reviewers that details how you have or plan to address the reviewers' concerns.

During the process of completing your manuscript submission, you will be invited to opt-in to posting your pre-review manuscript as a bioRxiv preprint. Visit http://journals.plos.org/plosbiology/s/preprints for full details. If you consent to posting your current manuscript as a preprint, please upload a single Preprint PDF.

Given the disruptions resulting from the ongoing COVID-19 pandemic, please expect some delays in the editorial process. We apologise in advance for any inconvenience caused and will do our best to minimize impact as far as possible.

Feel free to email us at plosbiology@plos.org if you have any queries relating to your submission.

Kind regards,

Richard

Richard Hodge, PhD

Associate Editor, PLOS Biology

rhodge@plos.org

PLOS

Empowering researchers to transform science

Carlyle House, Carlyle Road, Cambridge, CB4 3DN, United Kingdom

ORCiD I plosbio.org I @PLOSBiology I Blog

California (U.S.) corporation #C2354500, based in San Francisco

Dear Dr Jay,

Thank you for submitting your manuscript "Modeling the stepwise extension of recombination suppression on sex chromosomes and other supergenes through deleterious mutation sheltering" for consideration as a Research Article at PLOS Biology. Your manuscript has been evaluated by the PLOS Biology editors, an Academic Editor with relevant expertise, and by two independent reviewers. Please note that we had also recruited a third reviewer who did not submit their review in a timely fashion. We will forward this review to you if/when we receive their comments.

The reviews are attached below. You will see that the reviewers find your manuscript interesting and of broad interest. In light of these reviews, we are pleased to offer you the opportunity to address the remaining textual concerns from the reviewers in a revised version that we anticipate should not take you very long. We will then assess your revised manuscript and your response to the reviewers' comments and we may consult the reviewers again.

*IMPORTANT* In addition, I have provided a list of data and other policy-related requests below that we need before we can accept your manuscript for publication (A-E):

(A) We would to suggest the following modification to the title, to make it more accessible for our broad readership:

"Sheltering of deleterious mutations explains the stepwise extension of recombination suppression on sex chromosomes and other supergenes"

(B) You may be aware of the PLOS Data Policy, which requires that all data be made available without restriction: http://journals.plos.org/plosbiology/s/data-availability. For more information, please also see this editorial: http://dx.doi.org/10.1371/journal.pbio.1001797

We note that the scripts used for the modelling (Figure 2) and simulations (Figure 3AB) have been deposited in GitHub. However, since the simulations will give different results each time they are run, we also need the numerical outputs of the simulations presented in the following Figures:

Fig 3C, 5AB

If there are numerical values associated with the data presented in Figure 4, we also ask that this is provided.

Note that we do not require all raw data. Rather, we ask that all individual quantitative observations that underlie the data summarized in the figures be made available in one of the following forms:

1) Supplementary files (e.g., excel). Please ensure that all data files are uploaded as 'Supporting Information' and are invariably referred to (in the manuscript, figure legends, and the Description field when uploading your files) using the following format verbatim: S1 Data, S2 Data, etc. Multiple panels of a single or even several figures can be included as multiple sheets in one excel file that is saved using exactly the following convention: S1_Data.xlsx (using an underscore).

2) Deposition in a publicly available repository. Please also provide the accession code or a reviewer link so that we may view your data before publication.

NOTE: the numerical data provided should include all replicates AND the way in which the plotted mean and errors were derived (it should not present only the mean/average values).

(C) Please ensure that the scripts used for the study are made fully publicly available in Github at this stage. In addition, we ask that you please provide the scripts used to generate the data presented in the Supplementary Figures.

(D) Please also ensure that each of the relevant figure legends in your manuscript include information on *WHERE THE UNDERLYING DATA CAN BE FOUND*, and ensure your supplemental data file/s has a legend.

(E) Please also provide a blurb which (if accepted) will be included in our weekly and monthly Electronic Table of Contents, sent out to readers of PLOS Biology, and may be used to promote your article in social media. The blurb should be about 30-40 words long and is subject to editorial changes. It should, without exaggeration, entice people to read your manuscript. It should not be redundant with the title and should not contain acronyms or abbreviations. For examples, view our author guidelines: https://journals.plos.org/plosbiology/s/revising-your-manuscript#loc-blurb

-----------------------------------------------

As you address these items, please take this last chance to review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the cover letter that accompanies your revised manuscript.

We expect to receive your revised manuscript within 1 month.

Please email us (plosbiology@plos.org) if you have any questions or concerns, or would like to request an extension. At this stage, your manuscript remains formally under active consideration at our journal; please notify us by email if you do not intend to submit a revision so that we may end consideration of the manuscript at PLOS Biology.

**IMPORTANT - SUBMITTING YOUR REVISION**

Your revisions should address the specific points made by each reviewer. Please submit the following files along with your revised manuscript:

1. A 'Response to Reviewers' file - this should detail your responses to the editorial requests, present a point-by-point response to all of the reviewers' comments, and indicate the changes made to the manuscript.

*NOTE: In your point by point response to the reviewers, please provide the full context of each review. Do not selectively quote paragraphs or sentences to reply to. The entire set of reviewer comments should be present in full and each specific point should be responded to individually.

You should also cite any additional relevant literature that has been published since the original submission and mention any additional citations in your response.

2. In addition to a clean copy of the manuscript, please also upload a 'track-changes' version of your manuscript that specifies the edits made. This should be uploaded as a "Related" file type.

*Resubmission Checklist*

When you are ready to resubmit your revised manuscript, please refer to this resubmission checklist: https://plos.io/Biology_Checklist

To submit a revised version of your manuscript, please go to https://www.editorialmanager.com/pbiology/ and log in as an Author. Click the link labelled 'Submissions Needing Revision' where you will find your submission record.

Please make sure to read the following important policies and guidelines while preparing your revision:

*Published Peer Review*

Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out. Please see here for more details:

https://blogs.plos.org/plos/2019/05/plos-journals-now-open-for-published-peer-review/

*PLOS Data Policy*

Please note that as a condition of publication PLOS' data policy (http://journals.plos.org/plosbiology/s/data-availability) requires that you make available all data used to draw the conclusions arrived at in your manuscript. If you have not already done so, you must include any data used in your manuscript either in appropriate repositories, within the body of the manuscript, or as supporting information (N.B. this includes any numerical values that were used to generate graphs, histograms etc.). For an example see here: http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001908#s5

*Blot and Gel Data Policy*

We require the original, uncropped and minimally adjusted images supporting all blot and gel results reported in an article's figures or Supporting Information files. We will require these files before a manuscript can be accepted so please prepare them now, if you have not already uploaded them. Please carefully read our guidelines for how to prepare and upload this data: https://journals.plos.org/plosbiology/s/figures#loc-blot-and-gel-reporting-requirements

*Protocols deposition*

To enhance the reproducibility of your results, we recommend that if applicable you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols

Thank you again for your submission to our journal. We hope that our editorial process has been constructive thus far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.

Sincerely,

Richard

Richard Hodge, PhD

Associate Editor, PLOS Biology

rhodge@plos.org

*****************************************************

REVIEWS:

Reviewer #1 (Jos Käfer): Jay et al present a model for the progressive suppression of recombination on sex chromosomes and chromosomes carrying other kinds of "supergenes". Until recently, the answer to the question why recombination ceases outside the sex-determining region was thought to be sex-antagonistic selection. However, publications from the team of the authors (and others) have drawn this answer into doubt as recombination suppression also occurs in species without sex-specfific differences. The current model is both counterintuitive and convincing: counterintuitive because it's well established that recombination suppression eventually leads to the accumulation of deleterious mutations, but the authors show that less deleterious mutations cause the initial spreading of recombination suppression. The paper is convincing by combining theory (infinite populations) and simulations with more realistic assumptions, and by comparing sex chromosomes to autosomes. The modelling also nicely illustrates how the aforementioned opposing forces (i.e. the existence of fragments with less deleterious mutations and the slow accumulation of such mutations) interact. This manuscript will be of interest to many scientists working on sex chromosomes and other supergenes, and I therefore recommend acceptation in PLoS Biology.

The model raises many questions, as any new model would, and some are briefly discussed, maybe too briefly. E.g., indeed, large non-recombining regions seem to be less common in plants than in animals, but important differences exist among plants which are unlikely to be caused by the strength of haploid selection alone (lines 516-519). Mutation rate doesn't seem to vary a lot among plants, and all plants with sex chromosomes are dioecious, and thus have the same mating system. So what could explain the differences? Also, large non-recombining regions are only known for sex chromosomes, not for supergenes of self-incompatibility, what could be the cause for that difference? If the authors develop these points a bit more based on their knowledge of the model, it might become easier to figure out how to test it. Because as it stands, the manuscript doesn't seem to point at signs one could look for in genomic data to test whether the processes that are modelled are actually occurring.

I agree with the authors that the model could potentially apply to a large number of cases, as it is based on processes that occur in nearly all genomes and it just needs fixed heterozygosity (such as in sex determining systems) to change from a regime in which inversions are counterselected (autosomes) to a regime that favours their fixation (sex chromosomes). However, although the majority of mutations are probably deleterious, I wonder what the effect of positive selection or sex-antagonistic selection might be. As the non-recombining region of the Y never recombines, the effect of a beneficial mutation (in the classic sense, i.e. a mutation yielding an increase in fitness, and not merely a less-loaded piece of DNA) that will become fixed might completely dominate the effect the authors model. I imagine it doesn't change the main outcome of the model, because I guess beneficial mutations arise with equal probability on the inversion or on the non-inverted DNA, but it would be helpful if the authors discuss this point (or better, model it explicitly).

Some minor remarks/suggestions:

- line 104: "recombination suppressor": would it need to be "suppression" or "suppressors"?

- line 267: P_t is written with a capital "P" while there is a lower-case "p" in the equation line 266.

- line 292: u=1e^{-08}, would that need to be 10^{-8} or e^{-8} ? In scientific notation, "e" often stands for the power of 10, not the mathematical constant e. This should be checked and to avoid confusion, the human readable $\\times 10^{n}$ should be used instead of "e+/-n" which is used for convenience in plain text.

- Figure 3: the X axis labels of the left and right graphs of panels a and b overlap. Also, in panel c, the Y axis scales for the upper and lower graphs should be the same to allow direct comparison.

Reviewer #2: There is an idea out there that sexual antagonism is the reason for strata on the sex chromosomes. Several observations (e.g., the lack of strata on all sex chromosomes, the presence of strata on mating-type chromosomes in the absence of true sexes) have called that idea into question. Here the authors test a different hypothesis for the existence of strata—the avoidance of deleterious recessives. The authors show several things. First, they find that most inversions are fitter than average when heterozygous (ignoring any costs that may owe to crossing over within the inversion). These inversions are predicted to therefore rise in frequency. Their fate differs for autosomal vs. sex chromosomal linkage, though. Autosomal inversions are limited in their rise because as they become common, their homozygosity increases, and they are thus selected against. However, Inversions on permanent heterozygotes don't run into this trouble and can instead fix. So, as an example, Y chromosomes can come to be fixed for an inverted arrangement. Next, they also look at mutation accumulation as an inversion rises in frequency and find that things differ depending on population size. In small populations you may see fixation of the inversion because it fixes faster than mutations can accumulate, but in larger and in infinite populations you find the opposite. This result can be seen as striking a balance between the speed of fixation of an inversion and the speed of Muller's ratchet. Finally, if one allows inversions to reverse, then you might see the loss of an inversion as Muller's ratchet turns. This possibility is rare, though, unless inversion breakpoints are few.

Overall, I found the paper clear and compelling, and I am sure that it will spark much further thought and work. My comments are few and mostly minor.

General comments

A style suggestion. I would recommend better signposting in the Results and Discussion. It felt like there were three main results (as outlined above): first, that inversions spread easier on Y chromosomes; second, that population size matters; third, that reversions are possible. The Results section could be broken up into three subsections with boldface headers above each.

All of the natural selection in this paper occurs on diploids, if I'm not mistaken, and the main result depends on the recessivity of deleterious mutations. In species with haplontic life cycles (i.e., in which selection may occur more strongly, or at least in addition, during the haploid phase), do you arrive at the same predictions? Aren't the recessives exposed in the haploid phase, and wouldn't this change things? I didn't see this addressed explicitly in the paper, but I did see mention of strata on mating-type loci, which occur in species with an independent haploid phase.

Specific comments

Line 163. What precisely is n? Is it the number of sites that are polymorphic? Or is it the number of sites that may affect fitness?

Line 174. A question/comment about notation. Is n*q the same as nq? I think so. But for a brief instant I was looking around for the definition of n*, as though that was some special value of n.

Line 187 I see r defined, but it's missing from the equation.

Line 192. Is the assumption that WII, WIN, and WNN remain fixed values a good one? Is the idea that, sure, some of those non-inverted haplotypes are fitter than others, which will see them spread to higher frequency, but then mutations will arise again and bring things back to mutation-selection balance, which is where we started?

Line 365. "…only deleterious or nearly neutral mutations…" Should this be stated as "only weakly deleterious mutations"? Because nearly neutral alleles can include mildly beneficial alleles, right? And this paper concerns itself only with deleterious alleles.

Line 446. From my armchair it seems like the direction of the result would be unaffected by including this assumption, though it might raise the threshold for some inversions to spread and/or fix. And would including this assumption in one of the simpler models be so difficult? Can't you just add a fixed heterozygous cost of inversions as a function of the size of the inversion?

Line 459. Is part of the reason for the discrepancy between your model, which makes it seem like evolving inversions should be easy, and the data, which make it seem like inversions don't have such an easy time, perhaps due to the assumption that inversions have no heterozygous costs?

Another kind of permanent heterozygote can be found in some drive systems. There are some large meiotic drivers (e.g., the t haplotype in mouse; the SD system in Drosophila) that gain a transmission advantage through male meiosis but that can't fix owing to the presence of recessive lethals. These haplotypes have accrued inversions owing, we think, to the presence of interacting genes within the inversion, and muller's ratchet has led them to a situation in which they then posses recessive lethals. Could subsequent inversions be favored owing to the mechanism described here in this paper? Some drivers become very, very big indeed, with two involving basically the entire X chromosome (e.g. Dyer, K. A., Charlesworth, B., & Jaenike, J. (2007). Chromosome-wide linkage disequilibrium as a consequence of meiotic drive. Proceedings of the National Academy of Sciences, 104(5), 1587-1592. & Reinhardt, J. A., Brand, C. L., Paczolt, K. A., Johns, P. M., Baker, R. H., & Wilkinson, G. S. (2014). Meiotic drive impacts expression and evolution of X-linked genes in stalk-eyed flies. PLoS Genetics, 10(5), e1004362.)

Dear Paul,

Thank you for the submission of your revised Research Article "Sheltering of deleterious mutations explains the stepwise extension of recombination suppression on sex chromosomes and other supergenes" for publication in PLOS Biology. On behalf of my colleagues and the Academic Editor, Laurence Hurst, I am pleased to say that we can accept your manuscript for publication, provided you address any remaining formatting and reporting issues. These will be detailed in an email you should receive within 2-3 business days from our colleagues in the journal operations team; no action is required from you until then. Please note that we will not be able to formally accept your manuscript and schedule it for publication until you have completed any requested changes.

Please take a minute to log into Editorial Manager at http://www.editorialmanager.com/pbiology/, click the "Update My Information" link at the top of the page, and update your user information to ensure an efficient production process.

PRESS

We frequently collaborate with press offices. If your institution or institutions have a press office, please notify them about your upcoming paper at this point, to enable them to help maximise its impact. If the press office is planning to promote your findings, we would be grateful if they could coordinate with biologypress@plos.org. If you have previously opted in to the early version process, we ask that you notify us immediately of any press plans so that we may opt out on your behalf.

We also ask that you take this opportunity to read our Embargo Policy regarding the discussion, promotion and media coverage of work that is yet to be published by PLOS. As your manuscript is not yet published, it is bound by the conditions of our Embargo Policy. Please be aware that this policy is in place both to ensure that any press coverage of your article is fully substantiated and to provide a direct link between such coverage and the published work. For full details of our Embargo Policy, please visit http://www.plos.org/about/media-inquiries/embargo-policy/.

Thank you again for choosing PLOS Biology for publication and supporting Open Access publishing. We look forward to publishing your study. 

Sincerely, 

Richard

Richard Hodge, PhD

Associate Editor, PLOS Biology

rhodge@plos.org

PLOS

Empowering researchers to transform science

Carlyle House, Carlyle Road, Cambridge, CB4 3DN, United Kingdom

ORCiD I plosbio.org I @PLOSBiology I Blog

California (U.S.) corporation #C2354500, based in San Francisco