PCSY-D-24-00180

Inferring Leader-Follower Behavior from Presence Data in the Marine Environment: A Case Study on Reef Manta Rays

PLOS Complex Systems

Dear Dr. Fernández-Gracia,

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 Jun 09 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,

Timothy Saunders, D.Phil.

Academic Editor

PLOS Complex Systems

Hocine Cherifi

Editor-in-Chief

PLOS Complex Systems

Journal Requirements:

Additional Editor Comments (if provided):

[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: Partly

Reviewer #3: Yes

**********

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

Reviewer #1: Yes

Reviewer #2: No

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: No

Reviewer #2: Yes

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: In the context of inferring leader-follower behavior from presence data in the marine environment, the author proposed a measure for quantifying leadership from time series captured for multiple and applied the described leader-follower analysis methodology to presence data. I understand that the methods introduced in this paper are new and am happy to recommend the acceptance. The following comments could be considered for improvement.

1. On page 4, it states that "we hypothesize that the time delay between the consecutive detection of first i and then j will be longer than the reverse". Why is the following relationship determined by the length of the time delay? Please describe it in detail.

2. On page 6, the dimensions of D_{KS} and A_{KS} are different, and the notations of \lambda_2\left(t \right) or A_{KS}=-D_{KS} are not accurate.

3. Can \lambda_2\left(t \right) be expressed by a mathematical formula?

4. When \delta is negative, individual B appears, and when \deltais positive, individual B avoids. Are the conclusions the same?

5. Does such an inference of cooperative behavior also apply to the biomimetic system? For example, it can refer to “Jiawei Wu, Yongguang Yu, and Guojian Ren. Leader-following formation control for discrete-time fractional stochastic multi-agent systems by event-triggered strategy. Fractal and Fractional 8.5 (2024): 246.” and " Yuguang Yang, Foster Kevin R, Coyte Katharine Z and Aming Li. Time delays modulate the stability of complex ecosystems. Nature Ecology & Evolution 7.10 (2023): 1610-1619.".

Reviewer #2: In this manuscript the authors propose a method to infer social interactions (or in general causal relationships) from time series data, and apply it to infer and analyze a network of leadership interactions for a community of manta rays based on presence data.

Although the Introduction is well motivated and written, with clear statements on the main methodological problems studying social interactions in marine species collectives, I find there are methodological and interpretational issues that should be clarified before the paper can be accepted in PLoS Complex Systems.

Main comments:

Regarding the method to infer leader-follower relationships:

1.- Explanation of the lag distribution method to assign leader-follower interactions is somewhat confusing, especially the choice of sign for the KS distance. For instance:

- Lines 145-47: ‘If the arrow goes upwards…’ You could refer to Figure 1 on these lines, otherwise ‘upwards’ is meaningless here.

- The sentence ‘The value of the arrow is related to the excess of probability to have smaller values than τ of the cumulative distribution that lies above.’ in lines 152-153 is very convoluted and confusing. If I understood, the choice of weight as the value of KS distance indicates a stronger association of leader-follower dynamics, as a given follower will respond faster to the leader dynamics.

Lines 176-179: It would be more informative and clear if instead of using the notation t_{12} or t_{21}, since it is referring to individuals A and B, employed t_{BA} to denote the lag time between the detection of A first and then B.

In summary, the authors have to make an effort to improve the description of the methodology providing clearer and more concise explanations.

2.- Is there any advantage in using a K-S distance instead of the many other distance measurements defined to quantify similarity among distributions? Moreover, if I just want to know which of the lag time distributions (A first and then B, or B first and then A) has shorter lags, could not just simply calculate the difference between the means of both distributions along with a statistical test for significant differences between means?

3.- Lines 193-196. The description of the results for the toy model with correlated lags raises a question: how can one be sure that the dynamics inferred from the KS arrow is a follower-leader interaction (e.g. B follows A) and not an avoidance (individual A avoids B)?

4.- p-values are calculated by comparing to a null hypothesis reshuffling data, which is fine, but because they are comparing statistical significance of many pairwise distributions, the p-values should be corrected for multiple testing. In addition, since they infer the final networks by imposing a cutoff in the p-value of the interaction, the authors should provide at least a brief discussion about the specific choice of the cutoff.

Regarding the methodology of presence data acquisition:

1.- In the detection protocol for manta rays, it is not clear if detection involves only presence at a given time in a fixed location, or there is some spatial information (they could be detected on different sites or at a given spatial resolution). What does the detection radius of ~150 m mean? Does it mean that individuals are tagged as present if they are in a radius of 150 m around a given location? This seems a pretty big distance to be sure that there is any social interaction (individuals could be more than 200 m apart even if simultaneously present in the same location). Please clarify.

2.- Figure 4A: Does each raster represents a single individual? If they are so much spaced across almost three years, how is Figure 5B, with a resolution of hours, made?

Regarding data interpretation:

1.- Section 3, Results of manta ray study: the interpretation of the results is plagued by sentences like ‘stronger/weaker than expected’…’more/less than expected’. It is not clear what is ‘expected’ at this point, only after reading the caption in Figure 5 one finds out that it is ‘stronger/weaker than expected by chance..’ Please clarify in the main text. As for the deviation in average weight (y axis in Figure 5B-C) it is difficult to discern if a deviation of <0.01 in the weights, as seen for different subgroups, is significant or not.

2.- Once the network is reconstructed, the authors just analyze the number of links and link weights. Could other topological properties like degree or centrality offer some insight on ecological interactions?

3.- With respect to my previous comment regarding the spatial and temporal resolution of the presence data (and the impossibility of distinguishing avoidances from leader-follower dynamics), the authors should discuss how strong is the evidence for leader-follower dynamics given their methods and data. I am not particularly convinced that they are truly observing leader-follower dynamics or just correlated patterns in the presence data due to other reasons (foraging, different dynamics due to physiological differences between individuals, local environmental differences…)

Minor comments:

- For better reading, Figure 1 and 2 could be merged to one figure, and Figure 3 relegated to the appendix (just to show that reshuffling loss of correlations is reflected in A_{KS} measure).

- Line 127. Unfinished sentence: ‘We propose a measure for quantifying leadership from time series captured for multiple.’

- Figure 6: I think the legend for the blue line should be ‘After leader’

Reviewer #3: SPECIFIC COMMENTS:

The paper is a REALLY interesting paper looking into the quantification of the Leader-Follower Behavior from Presence Data in the Marine Environment: A Case Study on Reef Manta Rays. It is very interresting how Results revealed certain temporal patterns, including circadian rhythms and burst-like behavior with power-law distributed time gaps between presences.

It is cool the species are tracked by using acoustic telemetry and how these data are used. However, on one side I am wondering how these findings can be really applied for the impactful conservation and management of these species (?) and related to that how the information can support the management of the habitat where people live. How can we quantify the risk or ecological stress of these species?

-- Fig. 4 shows patterns of divergence and asynchronization for the male and females. I believe based on this it would be cool to see how the network in Fig. 5 changes over time; this can be useful to define the ecological stress of this community (e.g. see Li and Convertino, 2021)

-- it is not necessarily clear how you reconstructed the network of Fig. 5. Seems like you carry a lot of assumptions in the construction of that network for the directions and magnitude of interactions. What is the distance proportional to?

-- I will get into the construction of the network in my comments below. E.g. I do not believe the p-values are that meaningful and in this context cannot be used well because there is no known benchmark of what you are assessing. I also think it would be useful if you clarify what the inferred network is about, that is the likley interarrival of male-female individuals of the species considered.

How is your model unique and is that the main achievement?

Generic comments are provided below to perhaps try to find some sort of generalizabilty of results through quantification, whether possible, as well as specifics. Or to keep this as future work.

GENERAL COMMENTS:

(1) ecoNETWORKS (information-based eco-network): The ecological-environmental processes you investigate (manta rays dynamics/encouters (MRD) or ''Leader-Follower Behavior'') are largely non-linear. Non-linear models such as Convergent Cross Mapping or others (see Sugihara et al 2012, Campo-Bescós, 2013 et al., and Li and Convertino et al. 2021 for instance, that are all generic models which can be applied to any dynamics) can account for variable non-linear interactions (vs. simple correlation that does not imply causality) dependent on dynamical heterogeneity driven by divergence and asynchonicity. These models are also able to capture spatial joint variability (due to eco-environmental networks, such as ecological dependencies like corridors and flows; see Rinaldo et al. 2018) to understand spatial dependencies that are important for the variables considered (and their collective interactions, in this case of MRD). In this work you have not characterized the environment in a spatially explicit sense (e.g. water currents and quality that can affect MRD). True, however, that MRD is partially reflecting the environment but to untangle the ecology and the environment it would be necessary to include the environment. Anyway, if the MRD network is analyzed over time the potential eco-stress can be calculated based on the departure from an ideally organized network configuration (see Li and Convertino et al. 2021)

(2) INFORMATION VARIABILITY (eco-stress attribution via and systemic uncertainty decomposition): To address the model/data Uncertainty-Sensitivity coupling, global sensitivity and uncertainty analysis (GSUA, aka systemic information analysis) should be done to identify key determinants of model/data variability (including the MRD network) and universal determinants across geographies. You do not quite perform a one-factor-at-a-time sensitivity analysis, nor a non-linear sensitivity analysis to capture the variables' interactions (high-order interactions) that can be predominant in defining patterns' variability. See Pianosi et al. (2016) for an extensive discussion about this topic and how data should be used for GSUA using a simple variance-based approach. Entropy approaches of GSUA are also available when the pdfs are too complex to make the variance meaningful. The attribution of uncertainty can lead to the quantification of ecological stress attributable to different environmental causes or unknown factors.

(3) SYSTEMIC STABILITY and eco-STATES CONTROL: How indicators/predicted variables (i.e. MRD network indicators or values) change over space and/or time, conditional to optimal or desired outcomes (e.g. related to MRD optimal ranges... what are those and what is the expected optimal network?), is critical for mapping site-/time-specific and universal patterns and shifts, and more importantly environment-ecological controls. The stability of ecological patterns over predictors' gradients and their critical change, should be quantified because that can define potential stable states over which the predictands (causal factors) are relatively stable or approaching a transition. These calculation can be done by doing MonteCarlo filtering over the pdfs of MRD.

RECOMMENDATION:

I suggest accepting the paper after Moderate Revisions. The paper is very interesting but I think the findings are quite dependent on the area considered and uniqueness, limitations, and uncertainty should be stated or addressed more explictily. I also recommend to highly justify and be precise about what the network means and how that can be used for species investigation and management.

REFERENCES:

Jie Li,Matteo Convertino (2021)

Temperature increase drives critical slowing down of fish ecosystems

https://doi.org/10.1371/journal.pone.0246222

Campo-Bescós MA, Muñoz-Carpena R, Kaplan DA, Southworth J, Zhu L, Waylen PR (2013) Beyond Precipitation: Physiographic Gradients Dictate the Relative Importance of Environmental Drivers on Savanna Vegetation. PLoS ONE 8(8): e72348. https://doi.org/10.1371/journal.pone.0072348

Rinaldo at el al (2018)

River networks as ecological corridors: A coherent ecohydrological

perspective, Adv in Water res

https://water.usask.ca/documents/dls-2021/dls-discussion_rinaldo.pdf

Pianosi et al. (2016)

Sensitivity analysis of environmental models: A systematic review with practical workflow

Environmental Modelling & Software

Volume 79, May 2016, Pages 214-232

Packages for GSUA

- https://www.safetoolbox.info/info-and-documentation/

Sugihara G et al (2012)

Detecting Causality in Complex Ecosystems

https://www.science.org/doi/10.1126/science.1227079

**********

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

**********

[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

PCSY-D-24-00180R1

Inferring Leader-Follower Behavior from Presence Data in the Marine Environment: A Case Study on Reef Manta Rays

PLOS Complex Systems

Dear Dr. Fernández-Gracia,

Thank you for submitting your manuscript to PLOS Complex Systems. The referees have assessed your revised submission. There is one particular point raised by Referee 3, regarding "distinguish between leader-follower and avoidance dynamics". The suggestion from the referee would improve the approachability of the manuscript and I hope you can meet the suggestion.

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 Sep 03 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,

Timothy Saunders, D.Phil.

Academic Editor

PLOS Complex Systems

Timothy Saunders

Academic Editor

PLOS Complex Systems

Hocine Cherifi

Editor-in-Chief

PLOS Complex Systems

[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

**********

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

**********

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: (No Response)

Reviewer #2: The authors have clarified the interpretation and some methodological issues I raised in my previous comments. They have also appropriately discussed the shortcomings of their method and the limitation of the experimental data to interpret leader-follower dynamics given the low spatial resolution. I think the manuscript is now suitable for publication in PLoS Complex Systems. Just two minor comments:

- Regarding my previous question to distinguish between leader-follower and avoidance dynamics, the authors have convincingly argued how can one differentiate these scenarios. In particular, they state:

‘Using the artificial presence model, we found that for avoidance behavior, the individual exhibiting avoidance shows a lower appearance rate before $\tau$ compared to the other, while for times greater than $\tau$ both rates become similar. In contrast, for leader-follower behavior, both appearance rates are similar before $\tau$, but after $\tau$ the following individual exhibits a higher appearance rate.’

I think these results are important to clarify interpretation, but I don’t see them in the paper (I would expect a figure showing the described behavior). This should be shown at least in the supplementary information and referenced accordingly in the main text.

- Regarding their response to my comment 6 on Figure 4A, it is quite clarifying and I think it would help to explicitly state in the Figure caption that what one actually sees in panel 4A are detection bursts with long waiting times between them.

Reviewer #3: The manuscript has been largely modified and it is ready for publication. I look forward to further continuations of the study

**********

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: No

**********

[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

Inferring Leader-Follower Behavior from Presence Data in the Marine Environment: A Case Study on Reef Manta Rays

PCSY-D-24-00180R2

Dear Dr. Fernández-Gracia,

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.

An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at https://www.editorialmanager.com/pcsy/ click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. For questions related to billing, please contact billing support at https://plos.my.site.com/s/.

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 complexsystems@plos.org.

Kind regards,

Timothy Saunders, D.Phil.

Academic Editor

PLOS Complex Systems

Additional Editor Comments (optional):

Reviewers' comments: