PCSY-D-24-00144

Connect-while-in-range: modelling the impact of spatial constraints on dynamic communication network structures

PLOS Complex Systems

Dear Dr. Kerssies,

Thank you for submitting your manuscript to PLOS Complex Systems. After careful consideration, we feel that it has merit but does not fully meet PLOS Complex Systems'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 within 60 days Feb 08 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 complexsystems@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pcsy/ 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 editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'. This file does not need to include responses to any formatting updates and technical items listed in the 'Journal Requirements' section below.

* 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, competing interests statement, or data availability statement, please make these updates within the submission form at the time of resubmission. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

We look forward to receiving your revised manuscript.

Kind regards,

Qinghua Chen, Ph.D.

Academic Editor

PLOS Complex Systems

Qinghua Chen

Academic Editor

PLOS Complex Systems

Hocine Cherifi

Editor-in-Chief

PLOS Complex Systems

Journal Requirements:

1. We ask that a manuscript source file is provided at Revision. Please upload your manuscript file as a .doc, .docx, .rtf or .tex.

Additional Editor Comments (if provided):

Thank authors for submission. After careful review by several reviewers, it has been found that the work has something innovative and meaningful. However, significant revisions are needed, especially the writing of the introduction and conclusion sections. Below are the comments from the reviewers. Please revise the paper according to the reviewers' comments. After the revision submission, the reviewers (or new reviewers) will re-evaluate whether the paper meets the publication requirements.

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Reviewer: 1

Comments to the Author(s)

This paper explores the impact of spatial constraints on network structure prediction by constructing a spatially-constrained agent-based model with Random movement and the range rule and analyzing it in comparison with the null model. The study identifies communication range and population density as key network structure influences, and is overall well-conceived, innovative, and shows sufficient effort in terms of workload. However, I have the following recommendations for this paper:

The current introduction appears to be an inadequate compendium of previous research. Although a variety of factors that may affect network structure are mentioned, it lacks an in-depth elaboration of the methodology and conclusions of previous studies. It is recommended that a review of relevant literature be added to better position the contribution of this study within the existing literature.

The presentation of data and results in the results presentation is cumbersome and lacks sufficient concluding text. This makes it difficult for the reader to quickly grasp the core findings of the study. It is recommended that a summary discussion of the main findings be added to the results section to improve readability and comprehension.

The 6 network properties mentioned in the text (average degree, clustering coefficient, average shortest path length, number of connected components, size of the largest connected component, and small-world index) fail to adequately explain their measurement significance. It is recommended to add a detailed description of these metrics and how changes in these metrics can reflect changes in network structure.

Currently the paper only shows the changes in network properties under different parameter settings, and it is recommended to further analyze how these parameters specifically affect the aggregation and small-world index of the network. Is it possible to provide some quantitative explanations to enhance the depth and persuasiveness of the study.

----------------------------

Reviewer: 2

Comments to the Author(s)

Authors conduct agent based simulations to explore the effects of cognitive biases, ind-level choices and physical proximity on the formation of communication networks in humans groups. They find spatial position constrains association when comparing to a non-spatially explicit model. They identify communication range and population density as important factors that determine structure. In particular, range limits the influence of population density on structure. In the SI, they report the results of allowing a model of CCE to run on their networks. Overall I think the paper has the potential to be a valuable contribution, and the message that spatially explicit modeling matters for understanding networks is important. The paper is framed in terms of communication networks, although the model is quite broad and could represent any social interaction, making it widely applicable for researchers studying social behavior.

Major comments

Overall, this model is quite similar to the recent study by Chimento & Farine, which authors acknowledge in the introduction. However, they do test different interaction ranges and population densities, which is a nice extension and was outside of the scope of the original model. Authors should amend L41, as Chimento & Farine did in fact measure cumulative interactions as a “static representation” of networks, in addition to instantaneous metrics.

The methods are well described, although a table summarizing parameters and their ranges tested in the sensitivity analysis, as well as output measures, would save space in sections 4.2 and 4.3.

In general, I think the results section can be made much more concise, I found myself getting lost in the text, which is verbally describing results that are easier shown than described. However, the figures need to be revised to be illustrative of the results. Specific comments for figures:

• Figure 2 is difficult to digest, there’s too many plots, and the font is far too small on the axes. I suggest choosing one parameter combination, n=40 or n=60, and simply showing those results. Everything else can be supplementary. I don’t think this figure got referenced in the text. Also, it looks like there’s some data missing in the 6th plot on Panel A (both lines), B, C (red lines)? Why don’t these lines extend to zero on the x axis

• Figure 3 needs labels, everything is described in the caption but ambiguously worded and it’s hard to make sense of it. Which are the null models? Range models?

• Figure 4 is the same as figure 2. Most of this can be moved to the SI, I suggest choosing several illustrative comparisons to present in the main text that are most interesting.

• Figure 5 is great! More figures like figure 5. I can see everything and understand the effect on metrics as the variable of interest is manipulated. Figure 5 should be in the main text, the massive multi-panel plots can be moved to supplementary.

Finally, and most importantly, it seems like the authors performed some diffusion experiments with the model using a potion task, which is a model of cumulative cultural evolution (not communication as I was expecting). I was also confused why this is in the SI rather than the main text, as it more clearly relates the network simulation to some phenomena, even if it is not explicitly communication (more like information diffusion, which could be through communication). As it is now, the authors frame the study as relevant for communication networks, but without the explicit modeling of senders and receivers, the model is quite generic and edges can be interpreted to be about any type of social interaction. I strongly suggest shortening the existing results (verbal descriptions of the results can be made much more concise, see specific comments for ideas), and add an abridged section on the “potion task” back into the main text, with any extra details in supporting info.

Minor comments

1. Abstract – I was uncertain what was meant by “ranged networks”, since ranged could mean that agents are not constrained by spatial position (ie can connect at range), or that agents are bound by their communication range, mentioned later in the abstract. Please clarify this, I think it’s meant to be read as “spatially explicit networks”

2. L64 – each *individual* of a population… although I think this sentence could even be removed.

3. L71- citation for Moore neighborhood?

4. L75 – out-of-bounds

5. L79 – I think it’d be enough to say that agents connect to individuals where their euclidean distance <= r, rather than giving the formulas for pythagorean theorem etc.

6. 107 – rather than using the word “test”, authors should use “sensitivity analysis” to describe this procedure.

7. 139 – I wouldn’t use the words “dots”, “lines” here. networks are mathematical representations of relationships (edges) between objects or individuals (nodes).

8. L201 - “At lower values of r, the average clustering coefficient of networks increases sharply with increasing r.” this sentence doesn’t make sense to me: at lower values of r cc increases with r? I think authors are saying that CC is more sensitive to changes in r in the lower range of r. Also this should reference a figure that illustrates it

9. L211-L233 – I think this explanation can be made much shorter

10. Section 5.2 – same as previous comment, there’s a lot of redundant explanation here, and

11. Fig 6 – missing caption?

12. Fig 7,8 – the color legend should be continuous here, not discrete. The y axis of bottom plots should have fewer break points. Figure needs panel labels.

13. Potion task - Authors have missed https://royalsocietypublishing.org/doi/full/10.1098/rspb.2020.3107 which already tests the potion experiment on several types of network architectures, although using static networks. might be useful for discussion of potion task

----------------------------

Reviewer: 3

Comments to the Author(s)

This paper demonstrates a high level of innovation and depth in both theoretical and empirical analysis. Here are my review comments:

Strengths:

1. The Connect-while-in-range model you proposed provides a novel perspective and tool for studying the impact of spatial constraints on communication networks.

2. Through detailed simulation experiments, you systematically analyzed the impact of different parameters on network structure, providing a wealth of data support.

3. By comparing the spatial model with the non-spatial model, you clearly demonstrated the significant impact of spatial constraints on network structure.

4. The study not only focuses on network clustering and average shortest path length but also analyzes the number of connected components and the small-world index, providing a comprehensive perspective.

Suggestions for Improvement:

1. The study only considers a single communication range for a single-layer network, while real communication systems may use different and overlapping communication media and technologies. It is suggested to consider the impact of multiple communication media.

2. The study only compares the range model with one type of non-spatial model. It is suggested to compare with other "standard" non-spatial network generation algorithms to provide a broader picture of the impact of including spatial constraints in network generation algorithms.

3. The movement patterns in the model are random, while real individuals may exhibit more intelligent movement patterns. It is suggested to use more realistic movement patterns in future research.

[Note: HTML markup is below. Please do not edit.]

Reviewers' Comments:

Reviewer's Responses to Questions

Comments to the Author

1. Does this manuscript meet PLOS Complex Systems’s publication criteria? Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe methodologically and ethically rigorous research with conclusions that are appropriately drawn based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

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

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

3. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception. 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: No

Reviewer #3: Yes

**********

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

PLOS Complex Systems 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

Reviewer #3: Yes

**********

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: This paper explores the impact of spatial constraints on network structure prediction by constructing a spatially-constrained agent-based model with Random movement and the range rule and analyzing it in comparison with the null model. The study identifies communication range and population density as key network structure influences, and is overall well-conceived, innovative, and shows sufficient effort in terms of workload. However, I have the following recommendations for this paper:

The current introduction appears to be an inadequate compendium of previous research. Although a variety of factors that may affect network structure are mentioned, it lacks an in-depth elaboration of the methodology and conclusions of previous studies. It is recommended that a review of relevant literature be added to better position the contribution of this study within the existing literature.

The presentation of data and results in the results presentation is cumbersome and lacks sufficient concluding text. This makes it difficult for the reader to quickly grasp the core findings of the study. It is recommended that a summary discussion of the main findings be added to the results section to improve readability and comprehension.

The 6 network properties mentioned in the text (average degree, clustering coefficient, average shortest path length, number of connected components, size of the largest connected component, and small-world index) fail to adequately explain their measurement significance. It is recommended to add a detailed description of these metrics and how changes in these metrics can reflect changes in network structure.

Currently the paper only shows the changes in network properties under different parameter settings, and it is recommended to further analyze how these parameters specifically affect the aggregation and small-world index of the network. Is it possible to provide some quantitative explanations to enhance the depth and persuasiveness of the study.

To summarize, we suggest the authors to make a major revision of the paper.

Reviewer #2: Authors conduct agent based simulations to explore the effects of cognitive biases, ind-level choices and physical proximity on the formation of communication networks in humans groups.

They find spatial position constrains association when comparing to a non-spatially explicit model. They identify communication range and population density as important factors that determine structure. In particular, range limits the influence of population density on structure. In the SI, they report the results of allowing a model of CCE to run on their networks. Overall I think the paper has the potential to be a valuable contribution, and the message that spatially explicit modeling matters for understanding networks is important. The paper is framed in terms of communication networks, although the model is quite broad and could represent any social interaction, making it widely applicable for researchers studying social behavior.

Major comments

Overall, this model is quite similar to the recent study by Chimento & Farine, which authors acknowledge in the introduction. However, they do test different interaction ranges and population densities, which is a nice extension and was outside of the scope of the original model. Authors should amend L41, as Chimento & Farine did in fact measure cumulative interactions as a “static representation” of networks, in addition to instantaneous metrics.

The methods are well described, although a table summarizing parameters and their ranges tested in the sensitivity analysis, as well as output measures, would save space in sections 4.2 and 4.3.

In general, I think the results section can be made much more concise, I found myself getting lost in the text, which is verbally describing results that are easier shown than described. However, the figures need to be revised to be illustrative of the results. Specific comments for figures:

• Figure 2 is difficult to digest, there’s too many plots, and the font is far too small on the axes. I suggest choosing one parameter combination, n=40 or n=60, and simply showing those results. Everything else can be supplementary. I don’t think this figure got referenced in the text. Also, it looks like there’s some data missing in the 6th plot on Panel A (both lines), B, C (red lines)? Why don’t these lines extend to zero on the x axis

• Figure 3 needs labels, everything is described in the caption but ambiguously worded and it’s hard to make sense of it. Which are the null models? Range models?

• Figure 4 is the same as figure 2. Most of this can be moved to the SI, I suggest choosing several illustrative comparisons to present in the main text that are most interesting.

• Figure 5 is great! More figures like figure 5. I can see everything and understand the effect on metrics as the variable of interest is manipulated. Figure 5 should be in the main text, the massive multi-panel plots can be moved to supplementary.

Finally, and most importantly, it seems like the authors performed some diffusion experiments with the model using a potion task, which is a model of cumulative cultural evolution (not communication as I was expecting). I was also confused why this is in the SI rather than the main text, as it more clearly relates the network simulation to some phenomena, even if it is not explicitly communication (more like information diffusion, which could be through communication). As it is now, the authors frame the study as relevant for communication networks, but without the explicit modeling of senders and receivers, the model is quite generic and edges can be interpreted to be about any type of social interaction. I strongly suggest shortening the existing results (verbal descriptions of the results can be made much more concise, see specific comments for ideas), and add an abridged section on the “potion task” back into the main text, with any extra details in supporting info.

Minor comments

1. Abstract – I was uncertain what was meant by “ranged networks”, since ranged could mean that agents are not constrained by spatial position (ie can connect at range), or that agents are bound by their communication range, mentioned later in the abstract. Please clarify this, I think it’s meant to be read as “spatially explicit networks”

2. L64 – each *individual* of a population… although I think this sentence could even be removed.

3. L71- citation for Moore neighborhood?

4. L75 – out-of-bounds

5. L79 – I think it’d be enough to say that agents connect to individuals where their euclidean distance <= r, rather than giving the formulas for pythagorean theorem etc.

6. 107 – rather than using the word “test”, authors should use “sensitivity analysis” to describe this procedure.

7. 139 – I wouldn’t use the words “dots”, “lines” here. networks are mathematical representations of relationships (edges) between objects or individuals (nodes).

8. L201 - “At lower values of r, the average clustering coefficient of networks increases sharply with increasing r.” this sentence doesn’t make sense to me: at lower values of r cc increases with r? I think authors are saying that CC is more sensitive to changes in r in the lower range of r. Also this should reference a figure that illustrates it

9. L211-L233 – I think this explanation can be made much shorter

10. Section 5.2 – same as previous comment, there’s a lot of redundant explanation here, and

11. Fig 6 – missing caption?

12. Fig 7,8 – the color legend should be continuous here, not discrete. The y axis of bottom plots should have fewer break points. Figure needs panel labels.

13. Potion task - Authors have missed https://royalsocietypublishing.org/doi/full/10.1098/rspb.2020.3107 which already tests the potion experiment on several types of network architectures, although using static networks. might be useful for discussion of potion task

Reviewer #3: Dear Authors,

Thank you for submitting your paper on the impact of spatial constraints on dynamic communication network structures. This paper demonstrates a high level of innovation and depth in both theoretical and empirical analysis. Here are my review comments:

Strengths:

1. The Connect-while-in-range model you proposed provides a novel perspective and tool for studying the impact of spatial constraints on communication networks.

2. Through detailed simulation experiments, you systematically analyzed the impact of different parameters on network structure, providing a wealth of data support.

3. By comparing the spatial model with the non-spatial model, you clearly demonstrated the significant impact of spatial constraints on network structure.

4. The study not only focuses on network clustering and average shortest path length but also analyzes the number of connected components and the small-world index, providing a comprehensive perspective.

Suggestions for Improvement:

1. The study only considers a single communication range for a single-layer network, while real communication systems may use different and overlapping communication media and technologies. It is suggested to consider the impact of multiple communication media.

2. The study only compares the range model with one type of non-spatial model. It is suggested to compare with other "standard" non-spatial network generation algorithms to provide a broader picture of the impact of including spatial constraints in network generation algorithms.

3. The movement patterns in the model are random, while real individuals may exhibit more intelligent movement patterns. It is suggested to use more realistic movement patterns in future research.

Overall, this paper provides significant contributions and value in understanding and simulating communication network structures. I look forward to seeing you address these limitations in future research and further develop the theory and applications in this field.

Best wishes,

Reviewer

**********

6. 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.

Do you want your identity to be public for this peer review? If you choose “no”, your identity will remain anonymous but your review may still be made public.

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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Figure resubmission:

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. If there are other versions of figure files still present in your submission file inventory at resubmission, please replace them with the PACE-processed versions.

Reproducibility:

To enhance the reproducibility of your results, we recommend that authors of applicable studies deposit 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

PCSY-D-24-00144R1

Connect-while-in-range: modelling the impact of spatial constraints on dynamic network structures

PLOS Complex Systems

Dear Dr. Kerssies,

Thank you for submitting your manuscript to PLOS Complex Systems. After careful consideration, we feel that it has merit but does not fully meet PLOS Complex Systems'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 within 30 days Apr 25 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 complexsystems@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pcsy/ 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 editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'. This file does not need to include responses to any formatting updates and technical items listed in the 'Journal Requirements' section below.

* 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, competing interests statement, or data availability statement, please make these updates within the submission form at the time of resubmission. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

We look forward to receiving your revised manuscript.

Kind regards,

Qinghua Chen, Ph.D.

Academic Editor

PLOS Complex Systems

Qinghua Chen

Academic Editor

PLOS Complex Systems

Hocine Cherifi

Editor-in-Chief

PLOS Complex Systems

Additional Editor Comments (if provided):

We are pleased to see that the authors have revised the manuscript based on the previous round of review comments, resulting in significant improvements to the quality of the paper. However, as there remain some obvious issues identified in this round of review, we kindly request the authors to carefully address these points through proper modifications or detailed responses.

[Note: HTML markup is below. Please do not edit.]

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 #1: All comments have been addressed

Reviewer #2: All comments have been addressed

Reviewer #3: All comments have been addressed

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2. Does this manuscript meet PLOS Complex Systems's publication criteria? Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe methodologically and ethically rigorous research with conclusions that are appropriately drawn based on the data presented.

Reviewer #1: Partly

Reviewer #2: Yes

Reviewer #3: Yes

**********

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

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception. 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

Reviewer #3: Yes

**********

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

PLOS Complex Systems 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

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 #1: I have reviewed the paper based on the uploaded document. The manuscript focuses on agent-based simulations to investigate how spatial constraints, specifically communication range, influence the formation and dynamics of communication networks. Below are my detailed comments and suggestions:

1. Clarification of "Ranged Networks": The term "ranged networks" could be confusing, as you rightly point out. Instead, refer to "spatially explicit networks" or "range-constrained networks" consistently throughout the manuscript to avoid ambiguity.

2. Ensure consistency in terminology (e.g., using "nodes" and "agents" interchangeably could confuse readers).

3. Address minor phrasing issues and ensure that all figures have properly formatted captions and labels. The feedback on specific lines (such as L64 and L201) should be incorporated for greater precision.

4. The addition of the potion task as part of the diffusion experiments is an interesting choice, but its inclusion in the supplemental materials may detract from its relevance to the main text. Consider moving this section to the main body of the manuscript, with necessary details in the supporting information.

5. The authors mention excluding data points where the small-world index was undefined (due to division by zero). While this is addressed in the response letter, it should be explicitly stated in the main text (e.g., in the Methods or Results section) to ensure readers understand the rationale for missing data in figures like Figure 2.

6. The revised "Output Measures" section now includes motivations for each metric, but these explanations could be better integrated into the Results section. For instance, when discussing clustering or small-world index, briefly reiterate their significance in the context of the findings to improve readability for non-specialists.

7.While the Discussion acknowledges limitations (e.g., random movement, empty environments), it could delve deeper into how these assumptions might limit the model’s applicability. For example, human movement is rarely purely random; future work could incorporate Lévy flights or goal-directed motion. Emphasizing these points would strengthen the paper’s critical perspective.

8. Figures 2 and 4 remain complex despite simplifications. Consider adding insets or annotations to highlight key trends (e.g., the transition point at r/g=0.2) or using color gradients instead of discrete colors for continuous parameters (as suggested by Reviewer 2).

9. The term "ranged networks" in the abstract was removed to avoid ambiguity, but phrases like "range-constrained networks" appear elsewhere. Ensure consistent terminology (e.g., "spatially constrained networks") throughout the manuscript.

10. The authors note the model’s generalizability to non-human systems (e.g., animal groups, robot swarms). This is a strength but could be expanded in the Discussion to highlight interdisciplinary implications, such as applications in swarm robotics or urban planning.

11. he potion task and diffusion results in the supplement are critical for contextualizing network impacts. Consider briefly summarizing key supplemental findings (e.g., crossover event rates) in the main Results or Discussion to reinforce the practical relevance of spatial constraints.

The revisions significantly improve the manuscript’s rigor and clarity. With minor adjustments to enhance accessibility of figures, deepen discussion of limitations, and consolidate terminology, this paper provides a valuable contribution to understanding spatial constraints in dynamic networks. Accept after minor revisions.

Reviewer #2: The authors did a good job of addressing my concerns, and the manuscript is greatly improved. I only have a few minor comments

1. L262 latex rendering error “Fig. ??”

2. L264 section heading should read “many more” rather than “much more”

3. L396 upside down questionmark, I think is meant to be a greater than sign? This is found quite a bit throughout the paper

4. L418 latex rendering error in citations

5. L445 latex rendering error, upside down exclamation point

5. L575 latex rendering error

6. L618 rendering error in citations

Reviewer #3: The authors have addressed all the comments. And I recommend to accept and publish the manuscript.

**********

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.

Do you want your identity to be public for this peer review? If you choose “no”, your identity will remain anonymous but your review may still be made public.

For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

Reviewer #3: None

**********

[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.]

Figure resubmission:

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. If there are other versions of figure files still present in your submission file inventory at resubmission, please replace them with the PACE-processed versions.

Reproducibility:

To enhance the reproducibility of your results, we recommend that authors of applicable studies deposit 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

Connect-while-in-range: modelling the impact of spatial constraints on dynamic network structures

PCSY-D-24-00144R2

Dear Mr. Kerssies,

We are pleased to inform you that your manuscript 'Connect-while-in-range: modelling the impact of spatial constraints on dynamic network structures' has been provisionally accepted for publication in PLOS Complex Systems.

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

Best regards,

Luca Maria Aiello

Section Editor

PLOS Complex Systems

Hocine Cherifi

Editor-in-Chief

PLOS Complex Systems

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I am pleased to recommend accepting the paper for publication. In response to the reviewers' comments, the authors have carefully revised the manuscript and made substantial improvements in terminology consistency, clarity of figures/captions, and methodological transparency. At this stage, there only are a few minor revisions suggested, and the authors may consider addressing them before publication.

Reviewer Comments (if any, and for reference):

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 #1: All comments have been addressed

Reviewer #2: All comments have been addressed

Reviewer #3: All comments have been addressed

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2. Does this manuscript meet PLOS Complex Systems's publication criteria? Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe methodologically and ethically rigorous research with conclusions that are appropriately drawn based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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4. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception. 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

Reviewer #3: Yes

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

PLOS Complex Systems 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

Reviewer #3: 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 #1: The authors have diligently addressed the reviewers' comments, resulting in a more robust and coherent manuscript.Revise the following issues prior to publication. Below are my observations and recommendations:

1. Terminology Consistency

Improvement: The shift from "ranged networks" to "range model networks" enhances clarity. Instances like "range-constrained dynamic networks" in the abstract (Page 47) and "ranged model" in the Discussion (Page 67) should be standardized to "range model networks" for full consistency.

Suggestion: Perform a global search for terms like "ranged" or "range-constrained" and ensure alignment with the chosen terminology.

2. Figure and Caption Clarity

Improvement: Figures 2 and 4 now include detailed captions. However, the caption for Figure 3 (Page 60) redundantly states, "In order to make visual comparison easier..." after already explaining this in the main text.

Suggestion: Remove repetitive phrases in Figure 3’s caption. Use annotations (e.g., arrows, labels) in Figures 2 and 4 to highlight critical trends (e.g., the transition at r/g=0.2).

3. Methodological Transparency

Improvement: The exclusion of undefined small-world indices (due to division by zero) is now explicitly mentioned in the Methods (Page 17). This is critical for reproducibility.

Suggestion: In the Results (Page 19), briefly reiterate this exclusion when discussing Figure 2’s lower-right panel to aid reader interpretation.

4. Interdisciplinary Applications

Improvement: The expanded discussion of swarm robotics and animal populations (Page 12) strengthens the model’s broader relevance.

Suggestion: Integrate a concise example (e.g., how swarm robots might use range-based communication) to ground these applications concretely.

5. Limitations and Future Work

Improvement: The discussion of movement assumptions (e.g., Lévy flights) and environmental complexity (Page 28–29) is thoughtful.

Suggestion: Consider adding a subsection in the Discussion titled "Limitations and Future Directions" to organize these points thematically, enhancing readability.

6. Minor Revisions

Page 51 (Introduction): The phrase "correlate with differences in outcomes of collective processes in human groups such as..." is redundant. Remove "in human groups."

Page 67 (Discussion): The citation [44, 48, 49]? includes an errant question mark. Correct to [33, 44, 48, 49].

Page 73 (Supporting Information): The URL in Section 7.1 lacks hyperlink formatting. Ensure all links are clickable in the final version.

7. Strengths

The model’s simplicity and generalizability to non-human systems are major strengths.

The integration of diffusion processes (e.g., potion task) effectively bridges network structure and functional outcomes.

The comparison to both random and small-world networks contextualizes the findings within existing literature.

The manuscript is significantly improved and suitable for publication pending minor revisions. The authors have thoughtfully addressed reviewer concerns, and the revisions enhance the paper’s rigor and clarity. A final proofread to catch formatting inconsistencies and typographical errors (e.g., "publically" → "publicly" on Page 70) is recommended.

Reviewer #2: The authors have addressed all of my minor comments from the previous round of revisions.

Reviewer #3: My comments have been solved. I don't have further questions.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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