Dear Dr. Raphael,

Thank you very much for submitting your manuscript "A zero-agnostic model for copy number evolution in cancer" 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 very likely to accept this manuscript for publication, providing that you modify the manuscript according to the reviewers' minor recommendations.

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,

Philipp M Altrock, Ph.D.

Guest Editor

PLOS Computational Biology

Zhaolei Zhang

Section 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:

Reviewer's Responses to Questions

Comments to the Authors:

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

Reviewer #1: Upon reviewing the updated manuscript, I find significant improvements in both its readability and accessibility. The changes introduced have made the content more comprehensible and are likely to appeal to a broader audience. I also appreciate that the authors have convincingly addressed all the concerns raised in the initial feedback.

Reviewer #2: The paper aims to solve an important problem of inferring tumor phylogenies from copy number profiles due to its inherited special property of dependent loci changes. A widely used model for copy number evolution is the CNT model, yet little work has been done to develop methods on CNT model using maximum parsimony. The author introduced a relaxation of the CNT model and provided an efficient approximation algorithm Lazac for the small parsimony, combined with heuristic searching to solve for the large parsimony.

The author tested on the simulation data and showed that the relaxed ZCNT has even the highest accuracy in inferring the copy number phylogenetic tree. The authors also validated the method thoroughly on a real breast cancer single cell dataset and demonstrated that Lazac can output more resolved, biologically meaningful, and consistent results with the original clustering labels, as well as smaller ZCNT score than an existing tool Sitka in the majority of the cases, which also showed a better supports with SNV evidence. The qualitative analysis on sample SA1292 most straightforwardly demonstrated the more reliable result.

The paper is well-written, with clear definitions and comprehensive mathematical proofs for the relaxed version of CNT. Also the parts of comparison with other methods for solving the original CNT as well as the approximation error analysis justifies that the relaxed version has reasonable theoretical foundation as well as little negative influence with regard to actual application.

Since it was previously submitted to RECOMB-CCB, the authors’ solved the previous comments comprehensively and made corresponding edits to the paper.

Comments:

The author used p for both copy number profiles and delta profiles in various definitions and theorems. It might make it more clear if different variable names are used.

Is there any plausible reason for ZCNT performing better than CNT? Could it be some bias in the simulation because it seems a little bit odd to me that ZCNT almost is superior in all the settings.

The paper addresses a critical challenge: inferring tumor phylogenies from copy number profiles, complicated by the inherent property of dependent loci changes. While the CNT model is widely used for copy number evolution, there has been limited development of maximum parsimony methods for it. The author introduces a relaxation of the CNT model and presents the efficient approximation algorithm, Lazac, for small parsimony, complemented by heuristic searching for large parsimony.

The study includes rigorous testing on simulation data, showing that the relaxed ZCNT model consistently exhibits the highest accuracy in inferring copy number phylogenetic trees. Furthermore, the authors conduct a thorough validation on a real breast cancer single-cell dataset, showcasing Lazac's capacity to generate more refined, biologically meaningful, and consistent results, aligned with original clustering labels. Additionally, Lazac consistently produces smaller ZCNT scores compared to the existing tool, Sitka, in most cases, further supported by its better alignment with single-nucleotide variant (SNV) evidence. The qualitative analysis, particularly on sample SA1292, offers a clear demonstration of the method's enhanced reliability.

The paper is well-crafted, with lucid definitions and comprehensive mathematical proofs for the relaxed version of the CNT model. The sections comparing the relaxed version with other methods for solving the original CNT model and analyzing approximation errors provide strong justifications for the theoretical foundation and practical applicability of the approach.

Notably, the authors have diligently addressed previous comments following the paper's earlier submission to RECOMB-CCB, making corresponding edits and enhancing the paper's quality.

Minor comments:

The author used "p" for both copy number profiles and delta profiles in different parts of the paper. It might help make things clearer if they used different variable names.

As for ZCNT with MP performing better than CNT with NJ in all scenarios, is there a plausible explanation for that? Could it be just caused by specific simulation strategy?

**********

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: Yes

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: No

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.

Dear Dr. Raphael,

We are pleased to inform you that your manuscript 'A zero-agnostic model for copy number evolution in cancer' 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,

Philipp M Altrock, Ph.D.

Guest Editor

PLOS Computational Biology

Zhaolei Zhang

Section Editor

PLOS Computational Biology

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