PONE-D-25-28535A family of accessibility measures derived from spatial interaction principlesPLOS ONE

Dear Dr. Higgins,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

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We look forward to receiving your revised manuscript.

Kind regards,

Qing-Chang Lu

Academic Editor

PLOS ONE

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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?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

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

Reviewer #1: N/A

Reviewer #2: Yes

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

The PLOS Data policy requires authors to make all data 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 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—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

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

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: Thanks for the opportunity to review a paper that handles an interesting topic. I think the major contribution of the paper lies in 1) combining the concept of accessibility and spatial interaction modeling and 2) classifying the numerous accessibility measures into four categories based on the constraints. While the topic is really interesting and handles the important topic, I would like to ask the authors to revise the paper due to the following reasons.

Most importantly, the manuscript is too lengthy and verbose. I am having a hard time evaluating the manuscript since the length is about 30 pages. Given that the typical length of the paper is about 10 pages, I would like to request a summary of the key points for better deliverability.

Related to the first issue, I am not sure about the point that the authors explain the details of Newtonian’s roots and early research on human spatial interactions from Ravenstein to Stewart. Of course, I think mentioning those contents is beneficial, but it is hard to get the key point given that it is verbose.

Third, I believe the main contribution of this paper lies in classifying the accessibility measures into four groups. However, I also had a hard time finding the definition of those four groups. Given that the research articles aim to reveal previously unknown facts, the literacy level of this manuscript is relatively low. Additionally, the introduction of too many equations makes it difficult to establish connections between them. Therefore, I recommend that the authors revise and reconstruct the manuscript.

Reviewer #2: This manuscript presents a theoretically motivated and conceptually rich framework that bridges spatial interaction modeling and accessibility measures. The authors introduce a family of accessibility metrics grounded in Wilson’s spatial interaction models and argue convincingly for the reintroduction of interpretability and measurement units in accessibility analysis. The historical tracing of accessibility theory development and the synthesis of divergent literature streams are timely and valuable contributions to the field.

1. While the authors provide a detailed numerical example, the manuscript lacks any empirical case study or application to real-world accessibility data. This limits the reader’s ability to evaluate the practical utility and robustness of the proposed framework. The authors can draw inspiration from several studies such as "Factoring in temporal variations of public transit-based healthcare accessibility and equity" to better understand this concept.

2. The manuscript frequently shifts between concepts such as "potential for spatial interaction," "accessibility," and "access," especially in the discussion of the doubly constrained model. However, the terminological distinction remains conceptually blurry.

3. The historical literature review is valuable but disproportionately long. Pages are devoted to recapping classical gravitational thinking, while the more innovative contributions of the paper (e.g., balancing factor reinterpretation) are condensed. The authors should also focus on more recent publications such as "Evaluating temporal variations in access to multi-tier hospitals using personal vehicles and public transit: Implications for healthcare equity" instead of older ones.

4. The paper pays limited attention to recent methodological developments such as time-sensitive, network-based, or multi-modal accessibility models, as well as behavioral or utility-based approaches.

5. The authors argue that the constrained models restore interpretability by attaching meaningful units (e.g., number of people or opportunities). However, this is not substantiated with user- or practitioner-oriented tests.

6. Some sections suffer from repetition and overly technical language without summarizing takeaways (e.g., Table 1 is helpful, but the text before and after it repeats much of the same information).

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Reviewer #1: Yes: Jinwoo Park

Reviewer #2: No

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PONE-D-25-28535R1A family of accessibility measures derived from spatial interaction principlesPLOS ONE

Dear Dr. Higgins,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Nov 27 2025 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. 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.

We look forward to receiving your revised manuscript.

Kind regards,

Qing-Chang Lu

Academic Editor

PLOS ONE

Journal Requirements:

If the reviewer comments include a recommendation to cite specific previously published works, please review and evaluate these publications to determine whether they are relevant and should be cited. There is no requirement to cite these works unless the editor has indicated otherwise. 

Please 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.

Additional Editor Comments:

Further revisions should be addressed especially for Reviewer 4.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #2: All comments have been addressed

Reviewer #3: (No Response)

Reviewer #4: All comments have been addressed

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

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #2: Yes

Reviewer #3: Yes

Reviewer #4: Partly

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

Reviewer #2: Yes

Reviewer #3: Yes

Reviewer #4: I Don't Know

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

The PLOS Data policy requires authors to make all data 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 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—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #2: Yes

Reviewer #3: Yes

Reviewer #4: Yes

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

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #2: Yes

Reviewer #3: Yes

Reviewer #4: Yes

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6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #2: (No Response)

Reviewer #3: This is my first time seeing the paper, though I can see it has already been through a major revision. Looking at the previous comments and changes it looks like you have responded to the comments of the reviewers. The paper makes a valuable contribution in drawing together these different accessibility measures that many researchers know are somehow related but wouldn’t be able to explain how. The review of literature included also adds value and will make this a valuable paper for people working in the field to read.

I was hoping not to have to ask for any further revision because I know it can be frustrating when a new reviewer is brought in after a revision has been made. However, reading your paper reminded me of Cesario (1977) who also discussed the interpretation of balancing factors from spatial interaction models as accessibility measures. I can’t see that this is cited in the work, but given the nature of what you are doing and the historical approach taken in parts of your paper I think it should be included in the discussion.

Cesario, F. J. (1977). A new interpretation of the “normalizing” or “balancing” factors of gravity-type spatial models. Socio-Economic Planning Sciences, 11(3), 131-136.

Reviewer #4: The manuscript presents a theoretically rich and mathematically detailed framework that attempts to bridge spatial interaction modelling and accessibility analysis. While the topic is interesting and potentially valuable, I found the paper quite challenging to read due to its length and the density of the mathematical exposition. The presentation is heavy and at times difficult to follow, which limits accessibility to a broader audience.

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7. 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 #2: Yes: Yuntao Guo

Reviewer #3: No

Reviewer #4: 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.]

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. Registration is free. 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 PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

A family of accessibility measures derived from spatial interaction principles

PONE-D-25-28535R2

Dear Dr. Higgins,

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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Kind regards,

Qing-Chang Lu

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #3: All comments have been addressed

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

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #3: Yes

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

Reviewer #3: Yes

**********

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

The PLOS Data policy requires authors to make all data 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 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—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #3: Yes

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

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #3: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #3: Thank you for addressing my comment and for revising the manuscript so promptly. Congratulations on a great paper.

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7. 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 #3: No

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