Small group size promotes more egalitarian societies as modeled by the hawk-dove game

Kai-Yin Lin; Jeffrey C. Schank

doi:10.1371/journal.pone.0279545

Peer Review History

Original SubmissionAugust 22, 2022
22 Sep 2022 Decision Letter - Luo-Luo Jiang, Editor PONE-D-22-23497Small group size promotes more egalitarian societies as modeled by the hawk-dove gamePLOS ONE Dear Dr. Lin, 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 06 2022 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. 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The PLOS ONE style templates can be found at https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf 2. We note that you have stated that you will provide repository information for your data at acceptance. Should your manuscript be accepted for publication, we will hold it until you provide the relevant accession numbers or DOIs necessary to access your data. If you wish to make changes to your Data Availability statement, please describe these changes in your cover letter and we will update your Data Availability statement to reflect the information you provide. 3. Please include a caption for Figure 4. 4. Please include a copy of Table 2 which you refer to in your text on page 7. 5. Please include captions for your Supporting Information files at the end of your manuscript, and update any in-text citations to match accordingly. Please see our Supporting Information guidelines for more information: http://journals.plos.org/plosone/s/supporting-information. 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 ******** 2. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: Yes Reviewer #2: Yes ****** 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 ****** 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 ****** 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 this paper, the authors model the evolution of social organization by utilizing the hawk-dove game (HDG) and employ the evolutionary frequency of the hawk as a measure of egalitarian/despotism in society. A lower frequency of hawks implies a more egalitarian society, while a higher frequency of hawks indicates a more despotic society. In addition, the authors discuss the significance of group size for understanding and modeling primate social systems. I find that the idea is interesting, and believe their method is valid. Therefore, I can suggest publishing this paper in PLOS ONE after taking the following suggestions into account in a revision with care and love to detail. 1: Figure 1 shows the payoff matrix of the hawk-dove game, which illustrates the payoffs obtained by agents under different strategic interactions. Since it is a matrix, I suggest that it is more appropriate to represent it as an equation rather than a figure. 2: It is advisable for authors to standardize the citation format of figures in the text by using the full name “Figure” or the abbreviation “Fig”. 3: There are some grammatical mismatches and formatting mistakes in the paper. For example, line 207 on page 10 and line 261 on page 13 need to be indented as the beginning of a paragraph. I would suggest the authors proofread the paper meticulously and thoroughly. 4: The authors mention Table 2 in line 135 on page 7, but Table 2 does not appear in the text. It is difficult to give credit to research if even such elementary aspects of the work are not error-free. In addition, I recommend the author not split Table 1 into 2 pages but display it on 1 page, which would be a better layout. 5: The simulations of this paper are not sufficient, and I suggest that the authors could expand them in the following two ways. On the one hand, the authors could elaborate on each simulation in more detail. On the other hand, the authors are generating random numbers to represent the lifespan of agents by using a Gaussian distribution. How would taking other distributions (e.g., exponential distribution, gamma distribution, etc.) affect the results? 6: Many references contain errors and inconsistent formatting. Moreover, most of the authors' references are before 2017 and are too old. The references should be made error-free, and formatted in agreement with the journal guidelines, and references should cite more papers from the past five years. I suggest the authors refer to some of the related papers listed below, which are the most recent papers on games doi: 10.1016/j.physa.2022.126968; 10.1016/j.physa.2022.127297; 10.1063/5.0081954; 10.1063/5.0099444. Reviewer #2: Small group size promotes more egalitarian societies as modeled by the hawk-dove game The authors investigated the effects of group size based on Hawk-Dove games, trying to understand the organization in primate social systems. It is very interesting. However, the manuscript (MS) needs to improved in following aspects before I could recommend it to publish in Plos one. #1. Authors should explain the reason of fixed parameters in table 1. #2. In section 3.1, authors introduces Hawk-Dove game, as well as the payoff matrix in Fig. 1. However, the important parameters b and c are better to explain in detail in section 3.1 for readers to get a clear image of the game model. #3. In Fig. 3, authors should set the color bar style as follows: the lower value of in the behind and higher value in the front position. And the color bar are too small to see clearly on the whole. #4. In Fig. 4, the color bar style are obscure. Author could try to make them bold or bigger to see clearly. #5. There is too short in main text of fig.4. Are there another aspects to show the effects of group size? #6. The legends of figures are also simple. Authors may improve their current MS if the figure captions would be made more self-contained. More precisely, what panels are shown for which parameter values, one could also consider a sentence or two saying what is the central theme or message of each figure. #7. In model section, agents’ offspring either disperses to another randomly selected group in the population with probability d, which is more like the mobility of the agent. Is the parameter d is defined as natal dispersal rate? However, it is very interesting if the authors could discuss the results with the following work for Fig. 5: Li et al.; Applied Mathematics and Computation, 435 (2022) 127456; #8. Authors investigate the effects of group size theoretically. The work: Jiang et al.; Applied Mathematics and Computation 410 (2021) 126445 explored it experimentally. The section of results could be improved by discussing them. #9. The authors should check the writing and expression carefully, for example, the referee [22] should be “Nature, 428, (2004) 643–646”. There is a long blank space between line 145 and line 146. ****** 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. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy. Reviewer #1: No Reviewer #2: No ******** [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. Attachments Attachment Submitted filename: small.docx https://doi.org/10.1371/journal.pone.0279545.r001
Revision 1
6 Nov 2022 Author Response Reviewer #1: In this paper, the authors model the evolution of social organization by utilizing the hawk-dove game (HDG) and employ the evolutionary frequency of the hawk as a measure of egalitarian/despotism in society. A lower frequency of hawks implies a more egalitarian society, while a higher frequency of hawks indicates a more despotic society. In addition, the authors discuss the significance of group size for understanding and modeling primate social systems. I find that the idea is interesting, and believe their method is valid. Therefore, I can suggest publishing this paper in PLOS ONE after taking the following suggestions into account in a revision with care and love to detail. 1: Figure 1 shows the payoff matrix of the hawk-dove game, which illustrates the payoffs obtained by agents under different strategic interactions. Since it is a matrix, I suggest that it is more appropriate to represent it as an equation rather than a figure. We changed fig 1 to equation 1 and changed them in the text. 2: It is advisable for authors to standardize the citation format of figures in the text by using the full name “Figure” or the abbreviation “Fig”. According to the PLOS ONE formatting guideline, we have named Fig both in the text and in the figure title. 3: There are some grammatical mismatches and formatting mistakes in the paper. For example, line 207 on page 10 and line 261 on page 13 need to be indented as the beginning of a paragraph. I would suggest the authors proofread the paper meticulously and thoroughly. They were both figure titles, so they should not be indented. We also proofread the paper carefully. 4: The authors mention Table 2 in line 135 on page 7, but Table 2 does not appear in the text. It is difficult to give credit to research if even such elementary aspects of the work are not error-free. In addition, I recommend the author not split Table 1 into 2 pages but display it on 1 page, which would be a better layout. We followed the reviewer’s suggestion to correct the table reference in the text. There should be only one table in this manuscript, so we changed all table 2 to table 1. We have arranged for table 1 to display on 1 page. Please see the changes on page 9. 5: The simulations of this paper are not sufficient, and I suggest that the authors could expand them in the following two ways. On the one hand, the authors could elaborate on each simulation in more detail. On the other hand, the authors are generating random numbers to represent the lifespan of agents by using a Gaussian distribution. How would taking other distributions (e.g., exponential distribution, gamma distribution, etc.) affect the results? We elaborated on the simulations in more detail: (1) In section 3.1, we elaborate the HDG in more detail. Please see lines 156-163 on page 8. (2) In section 3.3, we explain why we choose Gaussian distribution for the lifespan simulation. Please see lines 178-187 on page 10. (3) In the simulation section, we elaborate three different sets of simulations in more detail. Please see lines 196-211 on page 11-12. We also explained why we use the Gaussian lifespan distribution. Please see lines 181-187 on page 10. In short, the main reason is that the overall population size in the model can be stable without fluctuations. 6: Many references contain errors and inconsistent formatting. Moreover, most of the authors' references are before 2017 and are too old. The references should be made error-free, and formatted in agreement with the journal guidelines, and references should cite more papers from the past five years. I suggest the authors refer to some of the related papers listed below, which are the most recent papers on games doi: 10.1016/j.physa.2022.126968; 10.1016/j.physa.2022.127297; 10.1063/5.0081954; 10.1063/5.0099444. We have checked and followed journal instructions on formatting references. Reviewer #2: Small group size promotes more egalitarian societies as modeled by the hawk-dove game The authors investigated the effects of group size based on Hawk-Dove games, trying to understand the organization in primate social systems. It is very interesting. However, the manuscript (MS) needs to improve in following aspects before I could recommend it to publish in Plos one. #1. Authors should explain the reason of fixed parameters in table 1. The reasons for fixed parameters were stated in the table 1 caption. More details were explained in section 3.1, 3.2, and 3.3. #2. In section 3.1, authors introduce Hawk-Dove game, as well as the payoff matrix in Fig. 1. However, the important parameters b and c are better to explain in detail in section 3.1 for readers to get a clear image of the game model. We also explain the game process in the details to make the game model clear. Please see the simulation section at line 156-163 on page 10. #3. In Fig. 3, authors should set the color bar style as follows: the lower value of in the behind and higher value in the front position. And the color bar are too small to see clearly on the whole. Now Fig 3 becomes Fig 2, and we followed the suggestion to re-arrange the legend. The color bars are lengthened and re-ordered as suggested. Please see the file fig2.tif. #4. In Fig. 4, the color bar style are obscure. Author could try to make them bold or bigger to see clearly. Now Fig 4 becomes Fig3 because we change Fig 1 to an equation. We have enlarged the whole legend and made the color bars longer to see clearly. #5. There is too short in main text of fig.4. Are there another aspects to show the effects of group size? The main idea in this manuscript is that different group sizes would lead to deviations of the hawk frequencies (i.e., evolutionary stable states) beyond the theoretical b/c. #6. The legends of figures are also simple. Authors may improve their current MS if the figure captions would be made more self-contained. More precisely, what panels are shown for which parameter values, one could also consider a sentence or two saying what is the central theme or message of each figure. We have added the central idea for each figure. Also, the parameters were described in the captions as well. Fig. 1 at line 143-146 on page 7 Fig. 2 at line 222-226 on page 12 Fig. 3 at line 241-243 on page 13 Fig. 4 at line 254-256 on page 14 #7. In model section, agents’ offspring either disperses to another randomly selected group in the population with probability d, which is more like the mobility of the agent. Is the parameter d is defined as natal dispersal rate? However, it is very interesting if the authors could discuss the results with the following work for Fig. 5: Li et al.; Applied Mathematics and Computation, 435 (2022) 127456; In this model, the dispersal rate is defined as the natal dispersal rate, representing a newborn dispersing to another group away from the natal groups. We have discussed the natal dispersal and wide-range mobility effects on cooperative behaviors. In short, both results showed a negative impact on cooperation. The local movement / small group size promotes cooperation, while the wide-range movement/dispersal decreases the cooperation level. Our results align with the suggested paper. We have discussed and cited this article in the discussion section, lines 259-270 on page 14. #8. Authors investigate the effects of group size theoretically. The work: Jiang et al.; Applied Mathematics and Computation 410 (2021) 126445 explored it experimentally. The section of results could be improved by discussing them. We cited this paper on page, line 113 in the context of other work on threshold public goods games and group size. #9. The authors should check the writing and expression carefully, for example, the referee [22] should be “Nature, 428, (2004) 643–646”. There is a long blank space between line 145 and line 146. All the reference formats have been checked. Journal Requirements: When submitting your revision, we need you to address these additional requirements. 1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf 2. We note that you have stated that you will provide repository information for your data at acceptance. Should your manuscript be accepted for publication, we will hold it until you provide the relevant accession numbers or DOIs necessary to access your data. If you wish to make changes to your Data Availability statement, please describe these changes in your cover letter and we will update your Data Availability statement to reflect the information you provide. The repository information can be assessed on git hub, and the link is below: https://github.com/kaiyinlin/spatialESS_groupSize 3. Please include a caption for Figure 4. Now Fig 4 becomes Fig3 because we change Fig 1 to an equation. A caption has been added at line241-243 on page 13. 4. Please include a copy of Table 2 which you refer to in your text on page 7. There is no Table 2 in this manuscript. We have corrected the typo in the main text. 5. Please include captions for your Supporting Information files at the end of your manuscript, and update any in-text citations to match accordingly. Please see our Supporting Information guidelines for more information: http://journals.plos.org/plosone/s/supporting-information. We don’t have supporting information files in this version. The repository information has been uploaded on git hub and we have provided the link above (and in the submission system). Attachments Attachment Submitted filename: Response to Reviewers.docx https://doi.org/10.1371/journal.pone.0279545.r002
12 Dec 2022 Decision Letter - Luo-Luo Jiang, Editor Small group size promotes more egalitarian societies as modeled by the hawk-dove game PONE-D-22-23497R1 Dear Dr. Lin, 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 http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org. If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org. Kind regards, Luo-Luo Jiang, Ph.D. Academic Editor PLOS ONE https://doi.org/10.1371/journal.pone.0279545.r003
Formally Accepted
15 Dec 2022 Acceptance Letter - Luo-Luo Jiang, Editor PONE-D-22-23497R1 Small group size promotes more egalitarian societies as modeled by the hawk-dove game Dear Dr. Lin: I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department. If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org. If we can help with anything else, please email us at plosone@plos.org. Thank you for submitting your work to PLOS ONE and supporting open access. Kind regards, PLOS ONE Editorial Office Staff on behalf of Dr. Luo-Luo Jiang Academic Editor PLOS ONE https://doi.org/10.1371/journal.pone.0279545.r004

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