PONE-D-21-00751

A Behavioural Model of Minority Language Shift: Theory and Empirical Evidence

PLOS ONE

Dear Dr. Uriarte,

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

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We look forward to receiving your revised manuscript.

Kind regards,

Boyu Zhang, Ph.D

Academic Editor

PLOS ONE

Additional Editor Comments:

Both reviewers agree that this paper studied an interesting and important question. However, they feel that the mathematical model is too complicated and difficult to understand. Since target readers are linguists, the author may provide some detailed explainations for background knowledge, e.g., evolutionary game method, and discuss why this method is better than other existing methods. Furthermore, since the model has several parameters, the author should provide intuitions for why these parameters are necessary and how they work.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

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

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

Reviewer #1: Yes

Reviewer #2: Yes

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

Reviewer #1: Yes

Reviewer #2: I Don't Know

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

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

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

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

Reviewer #1: No

Reviewer #2: Yes

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5. Review Comments to the Author

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

Reviewer #1: This paper proposes language use game and uses Nash equilibrium theory and evolutionary stable solution to estimate the outcome of language shift in a community with a monolingual A and bilingual A & B. The authors briefly described the method and math behind and conducted experiments using theoretical setting and a setting supported by real data.

My general feeling is that the adoption of equilibrium based math in language shift modeling is a great innovation, though it requires deep math knowledge to understand, which may drive away linguists who are interested in the topic of language shift. To better understand the relevant concepts, it would be great that the authors provide some simple examples of ESS and background knowledge, before jumping directly to the complex math model. Keep in mind that the readers of your paper may not come from physics or math, but historical/contact linguistics, who may not have sufficient knowledge to understand your current writing, no understanding, no use.

In addition, why using such math, whether it is because it has some advantages that other approaches cannot provide, or this method can avoid some parameters that are hard to estimate from real data. The authors mentioned something similar only in the conclusion section (why other models cannot address the issues you raised), it would be great to move that part early in the introduction, and also, additional justification is needed.

Finally, given the parameters in the model, is it possible to conduct an analysis on the effect of major parameters, like alpha or alpha star, i found the current values are set pretty arbitrary.

minor issues:

line 23, delete ","

line 40, 'european'--> 'European'

the 2nd paragraph in introduction is too long, and incorporate many points, better to separate each point into one paragraph.

line 126: why street use of Basque is short for KE?

line 151: "could is it" -> 'is it'

line 470: citefortEtal2012 must be changed to reference

Reviewer #2: In my opinion this is an important attempt to understand linguistic behaviour of people in bilingual societies and may add to policy makers' decisions (and to the awareness of speakers of language B) when trying to save endangered languages.

My knowledge of game theory and statistics is not sufficient to judge the corresponding equations, but I feel they are O.K.

Some details:

Why not show data points of recorded observations in the figures in the main text?

Fig.2: I think the axis should read "fraction", not "%", same in figures in supp.info.

Alpha, not alpa.

Line 470: Fort and Perez-Losada

Supp.info:

p.2, Ireland: delete "As for 1996 this distinction is not at all clear we skipped this wave in the revised version of our paper."

p.9: "..where ??? and Nij(t)=Ni represents the share of bilinguals of locality i playing pure strategy j at t (j = R; H)."

p.12: (***)

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Reviewer #1: No

Reviewer #2: No

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PONE-D-21-00751R1

A Behavioural Model of Minority Language Shift: Theory and Empirical Evidence

PLOS ONE

Dear Dr. Uriarte,

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 Jun 13 2021 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

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

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

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Boyu Zhang, Ph.D

Academic Editor

PLOS ONE

Additional Editor Comments (if provided):

Reviewer 1 is generally satisfied with the revision. However, reviewer 2 has some questions that need to be addressed. Please explain these questions in detail.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

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

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

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

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

Reviewer #1: Yes

Reviewer #2: Yes

**********

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

Reviewer #1: Yes

Reviewer #2: Yes

**********

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

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

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

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

Reviewer #1: Yes

Reviewer #2: 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: some minor points to clarify. Zhang & Gong's work can also handle imperfect cases, like the ones with missing data or ongoing competition, your replies are not accurate. You may clarify this in the revised version.

Other than this, the other comments seem well addressed in the revised version.

Reviewer #2: Thank you for answers to my questions/comments and for the appealing example.

I still think that this is a highly interesting new approach to language shift touching on psychology and sociology, and that it certainly deserves publication. The way it is presented, however, is a real challenge to possible readers not familiar with game theory, and that could be the overwhelming majority.

Being until now not familiar with game theory I tried to learn the concepts and to check whether the conclusions of the paper appear plausible. I have to confess that still I can not follow all steps.

• On page 8 you write: “The replicators are the pure strategies R and H.” For non-specialists (e.g. me) at least a little surprising. How can…? But certainly correct (for game theorists), could you explain in detail?

I think that in particular Theorem 1 (page 9) could be presented in a way which permits better access to non-specialists.

Some ideas:

• Realize that the terminology might be repulsive for linguists et al. Could you try not to shock non-specialists with terminology like: “standard replicator dynamics”, “replicator dynamics equation” in other place just called “replicator equation”, “evolutionary stable state strategy ESS”, “Nash equilibrium”, “global attractor”, most of which presented in just 3 lines on page 9? Of course, by searching in Wikipedia also non-specialists can learn what all that means, but will they do so? And I doubt that you really need all of this terminology: it could be mentioned in footnotes for specialists who otherwise might be frustrated to miss it.

• Structure the explanation of the most important Theorem 1, i.e. in particular allow more space for deriving the replicator equation for the derivative of p_i. Possibly without making extensive use of game-theory terminology.

I believe equ. (1) is correct, but have to confess that I was not able to convince myself.

Typing errors and alike:

p.5 “…understand how is it possible a decay…”

Fig.2: I still believe that the labelling of both axes must be “proportion” (or fraction) and not %. Also Fig. 2 of SI.

SI p.8: perceive, not perceived.

SI p.13, line 7 from bottom: please replace g prime by g dot (twice).

SI p. 15: S1-S3 Tables, S1-S3 Figs. should read Tables S1-S3 and Figs. S1-S3, resp.

Terminology

Please define “private information”.

Is there a difference between “payoff” and “benefit”? On SI p.13 you even sometimes change from benefit to profit, that appears confusing. And how about “utility”, e.g. “perceptible utility gain” (SI p.7, third line from bottom) - what is difference from payoff or benefit? My confusion continues on SI p.8 where new term “preference intensity” appears.

SI 9: new term: “one-population replicator dynamics”. Why “one-population”?

SI p.10: “Hawk-Dove Game”�delete! If you love that term, please put into footnote.

SI p.11: why p_i^* ɛ(0, 0.293)?

SI p.12-13: what is difference E(KE) – P(KE), E(DU) – P(DU), resp.? Is “predicted” not the same as “expected”?

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Reviewer #1: Yes: Tao Gong

Reviewer #2: No

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A Behavioural Model of Minority Language Shift: Theory and Empirical Evidence

PONE-D-21-00751R2

Dear Dr. Uriarte,

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,

Boyu Zhang, Ph.D

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Congratulations! All revewers' comments have been addressed properly and they are satisfied with the current version.

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

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

Reviewer #2: All comments have been addressed

**********

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

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

Reviewer #2: Yes

**********

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

Reviewer #2: Yes

**********

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

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #2: Yes

**********

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

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

Reviewer #2: Yes

**********

6. Review Comments to the Author

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

Reviewer #2: Thanks für answering my questions, resp. misunderstandings, and explaining derivation which I had not understood before.

I hope that non-specialists will be able to follow the short presentation of theorem 1 (which now is "explained" by ONE more sentence).

Wish many interested followers!

Thank you indeed for your lectures on game theory and "eco-socio-psycho" issues.

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7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

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Reviewer #2: No