Dear Dr. Vaughan,

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

Reviewer #1: Yes

Reviewer #2: Partly

Reviewer #3: No

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2. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #1: N/A

Reviewer #2: No

Reviewer #3: No

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3. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy

Reviewer #1: No

Reviewer #2: Yes

Reviewer #3: Yes

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4. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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Reviewer #1: Re #3: The author did not provide all code used in this work. Furthermore, the code is not publicly available, though I do not consider that an issue at the review stage.

Please see my attached comments for further info regarding the Major Revision decision.

Reviewer #2: This paper extends the classical Paterson worm model from 2D grids to a 3D cubic orthogonal lattice. Through exhaustive recursive simulation, the author reports 3239 unique worms and classifies their outcomes into terminating, looping, and running categories. However, several concerns limit the strength of the contribution. The reliability of the reported results is not independently verified. Some theoretical claims, such as the 13-rule upper bound, are not supported by rigorous mathematical proof. The biological motivation and application for extending the model to 3D requires further clarification.

1. The biological motivation for extending the worm foraging problem to 3D should be explained more clearly. It is unclear what real-world biological or physical process corresponds to discrete orthogonal jumps on a 3D cubic lattice. How can a worm move through 3D space without any supporting medium or substrate? Grounding the model in a concrete real-world scenario would strengthen the motivation for this research.

2. All results in this paper are based on a single fixed set of hyperparameters. For example: the population limit (53.5M steps), the loop detection thresholds (≥4 repetitions, ≥3 rules per cycle), and the manually identified mirror symmetries. A sensitivity analysis showing how the reported numbers change under different parameter choices would be important for assessing the robustness of the conclusions.

3. The purpose of the random search experiment at population limit 2,100 is unclear. Can the resulting T/L/R proportions be compared against a recursive search at the same population limit? Such a direct comparison would help clarify what this experiment contributes beyond the recursive results.

4. In Section 1.4, the author claims "It is shown with a proof that no worms in this 3D grid can use more than 13 rules." However, the argument that follows is an informal verbal explanation rather than a rigorous mathematical proof. A formal proof structure is needed to support this claim.

5. The quality of all figures in the paper is insufficient. The individual worm structures are difficult to distinguish. The figures should be reworked at higher resolution and clarity to convey the intended information.

Reviewer #3: The manuscript presents a computational study on a 3D orthogonal grid, framed as simulations of worm paths. The author extends previous 2D triangular/hexagonal grid models to 3D, enumerating 3239 unique worm configurations and classifying their outcomes.

The problem of this work which cannot be easily fixed is its narrow scope. All the experiments performed are held in very particular conditions (e.g., a reader can see a lot of arbitrary numbers as parameter values which are not justified). The author does not place his work into a broader scientific scope and fails to generalize his results. In fact, the author's work falls into the scientific area of self-avoiding walks (SAW) which is not mentioned anyhow. Based on the fact that the references list is rather short (14 papers), I assume that the author was not thorough enough when analyzing the corresponding works of other researchers.

Due to lack of quantitative justification of the results, the motivation of the study performed and lack of generalization, I cannot recommend this paper for publication. My advice to the author will be to investigate the SAW and to place adequately his work within the field, as well as add statistical methods and valid arguments of the scientific soundness of his research into the text.

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what does this mean?). If published, this will include your full peer review and any attached files.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

To ensure your figures meet our technical requirements, please review our figure guidelines: https://journals.plos.org/plosone/s/figures

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Attachments

Attachment

Submitted filename: WormsReview.docx

Mathematical model for Worm Path Simulation in 3D

PONE-D-26-12101R1

Dear Dr. Neil Vaughan,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Rui Lu

Academic Editor

PLOS One

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

Reviewer #3: (No Response)

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2. Is the manuscript technically sound, and do the data support the conclusions??>

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: No

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3. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: No

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4. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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5. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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Reviewer #1: The author has addressed my previous comments in a satisfactory manner. There is now greater clarity for readers unfamiliar with this area of research. I do still think the word codes could be explained in a way that makes their numeric representation more meaningful to readers such as myself who are not embedded in this field. That said, arriving at a first-order understanding of them is within reach of all readers. Hence, I do not consider this as disqualifying for publication.

I do really appreciate the new Figure 10. I think it adds really useful information about how these analyses evolve as the population is allowed to grow. I do think more figures like this in the future will better push the field forward. For example, proportion of worms in R as population --> inf on a log-scale.

One minor comment: there is a typo on the y-label on Figure 10. "Propostion" should be "Proportion".

Reviewer #2: (No Response)

Reviewer #3: The authors did make some cosmetic changes to the revised version of the text, however, the most worrisome issues I've mentioned in the previous review are not properly addressed. Therefore, I have to retain my previous verdict.

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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

Reviewer #3: No

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