Dear Miss Pettersson,

Thank you very much for submitting your manuscript "Spatial heterogeneity enhance robustness of large multi-species ecosystems" for consideration at PLOS Computational Biology.

As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. In light of the reviews (below this email), we would like to invite the resubmission of a significantly-revised version that takes into account the reviewers' comments.

Thank-you for your submission and apologies for the delay in providing a recommendation.

Both reviewers see the question of how spatial mechanisms influence both stability and robustness as an extremely important area of investigation. However, both reviewers also question whether there is a sufficient amount of novel insight (relative to existing literature) in the current manuscript to merit publication. Reviewer 1 highlights specific recent papers combining pairwise species interactions and spatial processes---I agree with the reviewer that it is important to highlight what precisely are the differences and novel findings here so that readers will understand what is being added to our understanding. Reviewer 2 raises more general concerns about the broader context of diversity-stability relationships. Like the reviewer, I am not sure that the goals here are identical to those papers (and perhaps they speak more to the question of robustness in the current ms than to local stability) but it is fair to say that readers may find this context extremely helpful.

In seeing these concerns, I believe that revisions may be difficult. I do think that it would be possible to send the paper out to review again if the authors were to choose to resubmit to PLOS Comp Biol, but the authors would need to highlight more clearly the comparison with existing results and broader concepts.

We cannot make any decision about publication until we have seen the revised manuscript and your response to the reviewers' comments. Your revised manuscript is also likely to be sent to reviewers for further evaluation.

When you are ready to resubmit, please upload the following:

[1] A letter containing a detailed list of your responses to the review comments and a description of the changes you have made in the manuscript. 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.

[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).

Important additional instructions are given below your reviewer comments.

Please prepare and submit your revised manuscript within 60 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email. Please note that revised manuscripts received after the 60-day due date may require evaluation and peer review similar to newly submitted manuscripts.

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

Sincerely,

Natalia L. Komarova

Deputy Editor

PLOS Computational Biology

Natalia Komarova

Deputy Editor

PLOS Computational Biology

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Thank-you for your submission and apologies for the delay in providing a recommendation.

Both reviewers see the question of how spatial mechanisms influence both stability and robustness as an extremely important area of investigation. However, both reviewers also question whether there is a sufficient amount of novel insight (relative to existing literature) in the current manuscript to merit publication. Reviewer 1 highlights specific recent papers combining pairwise species interactions and spatial processes---I agree with the reviewer that it is important to highlight what precisely are the differences and novel findings here so that readers will understand what is being added to our understanding. Reviewer 2 raises more general concerns about the broader context of diversity-stability relationships. Like the reviewer, I am not sure that the goals here are identical to those papers (and perhaps they speak more to the question of robustness in the current ms than to local stability) but it is fair to say that readers may find this context extremely helpful.

In seeing these concerns, I am suggesting a rejection. I do think that it would be possible to send the paper out to review again if the authors were to choose to resubmit to PLOS Comp Biol, but the authors would need to highlight more clearly the comparison with existing results and broader concepts.

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: The authors look at dynamics of interacting species (via the GLV equations), and add connected space to the system. The species interact in each location and are able to migrate between the different locations. They find that stability limits on GLV system when considered without space, are no longer restrictive due to the possibility of spatial heterogeneity, and the related appearance of unsynchronized oscillations of the abundances.

The manuscript looks well-written and draws clear and potentially interesting conclusions. But at the moment it is hard for me to judge the novelty of the work because it seems, as far as I can see, very closely related to the following publications:

* Roy, Felix, Matthieu Barbier, Giulio Biroli, and Guy Bunin. “Complex Interactions Can Create Persistent Fluctuations in High-Diversity Ecosystems.” PLOS Computational Biology 16, no. 5 (2020): e1007827.

* Pearce, Michael T., Atish Agarwala, and Daniel S. Fisher. “Stabilization of Extensive Fine-Scale Diversity by Ecologically Driven Spatiotemporal Chaos.” Proceedings of the National Academy of Sciences 117, no. 25 (2020): 14572–83.

In both these references, different locations in space with GLV (or replicator equations) are coupled via migration. Dynamics of the abundances appear and are argued to allow for stability bounds to be crossed. The theme of de-synchronization plays a role in these references as well, as does the non-trivial dependence on migration rates.

One difference between the present manuscript and these references, is that the locations in space are here placed on a grid versus all-to-all connections. But in the present manuscript the topology of the connections is claimed not to be very important to the qualitative results (when using 1d versus 2d or 3d grid).

It may very well be that the present manuscript contains novel results beyond these publications, but in order to make a judgement, I'd first like to see a comparison by the authors, between their work and the above references.

Reviewer #2: Please find my comments attached

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Have all data underlying the figures and results presented in the manuscript been provided?

Large-scale datasets should be made available via a public repository as described in the PLOS Computational Biology data availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.

Reviewer #1: Yes

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Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

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Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #2: No: I see no working links to data or code repositories

Figure Files:

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org.

Data Requirements:

Please note that, as a condition of publication, PLOS' data policy requires that you make available all data used to draw the conclusions outlined in your manuscript. Data must be deposited in an appropriate repository, included within the body of the manuscript, or uploaded as supporting information. This includes all numerical values that were used to generate graphs, histograms etc.. For an example in PLOS Biology see here: http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001908#s5.

Reproducibility:

To enhance the reproducibility of your results, we recommend that 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 to publish peer-reviewed clinical study protocols. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols

Attachments

Attachment

Submitted filename: Reply to Spatial heterogeneity enhance robustness of large multi-species ecosystems.odt

Dear Miss Pettersson,

Thank you very much for submitting your manuscript "Spatial heterogeneity enhance robustness of large multi-species ecosystems" for consideration at PLOS Computational Biology. As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. The reviewers appreciated the attention to an important topic. Based on the reviews, we are likely to accept this manuscript for publication, providing that you modify the manuscript according to the review recommendations.

Thanks for your work on addressing the reviewer comments. I would be happy to consider a revised manuscript that addresses the remaining (relatively minor) comments of reviewer 2

Please prepare and submit your revised manuscript within 30 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email.

When you are ready to resubmit, please upload the following:

[1] A letter containing a detailed list of your responses to all review comments, and a description of the changes you have made in the manuscript. 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

[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).

Important additional instructions are given below your reviewer comments.

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

Sincerely,

James O'Dwyer

Deputy Editor

PLOS Computational Biology

Natalia Komarova

Deputy Editor

PLOS Computational Biology

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

A link appears below if there are any accompanying review attachments. If you believe any reviews to be missing, please contact ploscompbiol@plos.org immediately:

[LINK]

Thanks for your work on addressing the reviewer comments. I would be happy to consider a revised manuscript that addresses the remaining (relatively minor) comments of reviewer 2

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: The authors have taken the comments of both myself and the other reviewer into account. The new version of the manuscript better connects with the existing literature on spatial effects, and in particular metacommunities.

The manuscript contains a number of interesting observations, specifically on the conditions under which space can stabilize communities at higher species richness, and the dynamics which allow this to happen.

Reviewer #2: Review uploaded as attachment

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Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data and code should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: None

Reviewer #2: Yes

**********

PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: Yes: Jacob O'Sullivan

Figure Files:

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org.

Data Requirements:

Please note that, as a condition of publication, PLOS' data policy requires that you make available all data used to draw the conclusions outlined in your manuscript. Data must be deposited in an appropriate repository, included within the body of the manuscript, or uploaded as supporting information. This includes all numerical values that were used to generate graphs, histograms etc.. For an example in PLOS Biology see here: http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001908#s5.

Reproducibility:

To enhance the reproducibility of your results, we recommend that 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 to publish peer-reviewed clinical study protocols. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols

References:

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 rebuttal letter that accompanies your revised manuscript.

If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

Attachments

Attachment

Submitted filename: Reply to Spatial heterogeneity enhance robustness of large multi-species ecosystems resubmission.odt

Dear Miss Pettersson,

We are pleased to inform you that your manuscript 'Spatial heterogeneity enhance robustness of large multi-species ecosystems' has been provisionally accepted for publication in PLOS Computational Biology.

Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow up email. A member of our team will be in touch with a set of requests.

Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.

IMPORTANT: The editorial review process is now complete. PLOS will only permit corrections to spelling, formatting or significant scientific errors from this point onwards. Requests for major changes, or any which affect the scientific understanding of your work, will cause delays to the publication date of your manuscript.

Should you, your institution's press office or the journal office choose to press release your paper, you will automatically be opted out of early publication. We ask that you notify us now if you or your institution is planning to press release the article. All press must be co-ordinated with PLOS.

Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Computational Biology. 

Best regards,

James O'Dwyer

Deputy Editor

PLOS Computational Biology

Natalia Komarova

Deputy Editor

PLOS Computational Biology

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