Dear Prof. Xu,

Thank you very much for submitting your manuscript "Estimating Genetic Variance Contributed by a Quantitative Trait Locus: A Random Model Approach" 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.

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:

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[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).

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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,

Mingyao Li

Associate Editor

PLOS Computational Biology

Jian Ma

Deputy Editor

PLOS Computational Biology

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Reviewer's Responses to Questions

Comments to the Authors:

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

Reviewer #1: This manuscript proposes a random-effect model approach to estimating the QTL variance.

The method reformulates the QTL model by treating the QTL effect as random and directly estimate the QTL variance (as a variance component) or adjust the bias by taking into account the error of the estimated QTL effect. A moment method of estimation has been proposed to correct the bias. The method has been validated via Monte Carlo simulation studies. The method has been applied to QTL mapping for the 10-week-body-weight trait from an F2 mouse population. The manuscript was well written, and developed a novel method that can be applied to many real data sets. I evaluate the work as a useful contribution and can be published. I have two comments.

1. The manuscript includes too many equations and derivations, some of which are easily derived and standard. I recommend simplify the mathematical presentation and thus improve readable.

2. The proposed random-effect assumes that the QTL effects follow a normal prior. What is the prior on the prior variance? You use an uniform prior. However, it results in a estimation towards zero. Gelman et al. Bayesian Data Analysis (Chapter 5) suggests weakly informative prior, which can solve the problem.

Reviewer #2: This manuscript presents an old but important question in QTL mapping and GWAS; i.e., how to correct biased genetic variance explained by a single QTL. The manuscript was well written and results are scientifically sound. I only have a minor comment.

In this reviewer's opinion, mapping and estimating a single QTL is not meaningful in practical breeding schemes. As claimed by the authors, a small-effect but statistically significant QTL is not useful in practice. Yet, such QTLs are very commonly detected in plant, animal and human genetic studies. According to a recent study, an insignificant locus by statistical testing is not necessarily insignificant on its merit, rather its effect is compromised by negative regulators (Wang et al. 2021). I believe that an in-depth discussion on this issue is crucial for strengthening this manuscript's quality and impact.

Wang HJ, et al. (2021) Modeling genome-wide by environment interactions through omnigenic interactome networks. Cell Reports 35: 109114.

Reviewer #3: The paper tries to address bias in h2 estimate due to non Beavis effect theoretically and empirically. However, their results suggest that such bias is negligible as long as n is not too small. Given that Beavis effects over dominant non Beavis ones, practically, it is thus important to simultaneously correct both for studies with very small n, which should be properly addressed. Otherwise, this research has very limited practical usages. Some other concerns

1. Not agree with the comments made between lines 277-282. The variance in (10) is a conditional variance of y given X and Z. The conditional variance of y given X only will depend on Z, so does the marginal variance of y.

2. Equations (16)-(18) are very confusing. So are equations (18) and (19), and it is not clear what is the difference between the two hat estimates of alpha in these two equations.

3. Section 2 is very wordy and can be significantly shortened. The authors should only present the models and derive the biases concisely without lengthy explanations.

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

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Reviewer #1: None

Reviewer #2: Yes

Reviewer #3: Yes

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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Attachments

Attachment

Submitted filename: review for PCOMPBIOL.docx

Dear Prof. Xu,

We are pleased to inform you that your manuscript 'Estimating Genetic Variance Contributed by a Quantitative Trait Locus: A Random Model Approach' 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,

Mingyao Li

Associate Editor

PLOS Computational Biology

Jian Ma

Deputy Editor

PLOS Computational Biology

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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 nicely addressed my previous comments. The revised manuscript has been improved. I have no further concerns.

Reviewer #2: The authors have satisfactorily addressed my concern.

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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: None

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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