Dear Dr. Frei,

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.

The manuscript by Frei et al. presents a rich database aimed at creating a baseline specific to Denmark for the 87/86 strontium isotope ratio.

Both reviewers welcomed the manuscript but also raised some issues and topics for discussion that need to be addressed by the authors in order to make the manuscript publishable in Plos One.

In particular, reviewer 2 raised some doubts about the basis of the analysis itself. As far as I am concerned, I believe that the manuscript  should take into account the reviewers' criticisms, considering them as constructive contributions (even beyond the form). The criticisms should be integrated into the text, also showing possible alternative scenarios with a less assertive and more critical approach. Currently, the manuscript has a dual hybrid dimension, the first being a review paper (without the necessary insights), and the second one being a definition of the baseline (without an effective critical approach).

Beyond these general considerations, I must add a series of notes:

1. The database in Table S1 must also include a column indicating whether the individuals were cremated or inhumed.

2. The database contains values with four or five decimal places: where possible, it would be advisable to standardise the values as much as possible to the fifth decimal place.

3. I have carried out a quick analysis of the data in Table 6: as can be seen in the attached PDF file, 40.4% of the isotopic ratio values are present in at least two individuals, up to a maximum of six individuals, all with a value of 0.7102, and six with a value of 0.7101. Twenty-three per cent of the duplicates have isotope ratio values to four decimal places, but the remaining 77% are values to five decimal places. Although a certain percentage of duplicate data may be “reasonable” in an analysis of this type, I feel that these percentages are excessive and I invite the authors to further check Table S1. Finally, I think that this situation, if confirmed, should be discussed in the article and justified.

4. In my opinion, the use of MAD should be better justified with more literature. Furthermore, the choice to use a multiplier of 2 to define the range of “local” individuals should be better justified (also because the bibliography cited by the authors suggests a value of 2.5). I have taken the liberty of attaching a graph showing the different ranges resulting from different multiplier values. Interestingly, the value of 2.5 seems to be close to the value of Tukey's method, which is the most widely used in the literature for defining outliers.

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Luca Bondioli, PH.D.

Academic Editor

PLOS ONE

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This study was made possible through the funding to KMF provided by the Carlsberg Foundation “Semper Ardens” advance research grant CF18-0005 for which we are very grateful.

https://www.carlsbergfondet.dk/en

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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?

Reviewer #1: Yes

Reviewer #2: Partly

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

Reviewer #1: N/A

Reviewer #2: No

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

The PLOS Data policy

Reviewer #1: Yes

Reviewer #2: Yes

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

Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #1: The paper of Frei et al reviews the human Sr isotope data from Denmark and uses this dataset as a way to detect local and non-local individuals among two archaeological sites. I have only minor comments that follow.

I do believe lines from 45 to 55 should be moved at the end of the introduction.

The introduction is a bit weirdly structured: from the title and the abstract a reader expects to find a rationale behind the use of human samples to reconstruct local bioavailable Sr and then the application of this to a case study (non-elite individuals.). Overall, I think the authors should adjust the introduction following the abstract flow.

Figure 1: I think a (simplified) geological map would be important to show.

Line 128: “we compile 513 previously published strontium isotope” please indicate here from how many sites.

Table 2: please use a consistent and reasonable number of digits.

Table S1: why for some samples the 2SE is not reported?

Line 382: the result section starts from the case study and then jump to the Denmark baseline definition. I describing the baseline should come before.

Line 427: the authors used the entire dataset for the MAD approach. This means that the ‘baseline’ they calculate and refer to encompasses all of Denmark. Consequently, individuals identified as ‘non-local’ are likely those originating from outside the current boundaries of Denmark. While this approach is valid, the authors should clarify this methodological choice and provide a rationale for it. In contrast, my preferred approach would have been to calculate separate MAD values for each area or sub-region within Denmark. In addition, I think it would be important to clarify, maybe in the method section, what the authors mean by ‘non-local’.

Line 427-437: I think this part pertains the method section

Reviewer #2: General Assessment

This manuscript presents an ambitious and valuable dataset, compiling 628 human 87Sr/86Sr values from archaeological sites across Denmark. This database, in itself, is a significant contribution and will serve as an important reference for future work in the region.

However, the manuscript's central methodological premise and its primary conclusion—that a single, nationwide "baseline" (0.7089–0.7117) can be derived from this national dataset using simple statistics and then be applied to provenance individuals—is fundamentally flawed.

The authors correctly criticize the limitations of environmental isoscapes (e.g., those based on modern water or soil), but they fail to demonstrate that their proposed alternative is a more suitable or accurate tool for provenancing. In fact, the proposed method ignores the single most important factor in strontium-based mobility studies: spatial variability.

Major Points for Revision

1. The Methodological Fallacy of a Single National Baseline

The core flaw of this paper is the assumption that a single 87Sr/86Sr range can represent "local" for the entire nation of Denmark. The authors' own sources and the wider literature (e.g., Frei & Frei, 2011) show that bioavailable strontium is spatially variable across Denmark due to its complex glacial geology.

The authors' approach conflates two different concepts: "local" (an individual originating from the specific geological catchment of the burial site) and "Danish" (an individual originating from anywhere within the modern political borders of Denmark).

By "flattening" all of Denmark's diverse geological signatures into a single statistical range, the authors' baseline becomes (a) too broad to detect inter-regional mobility and (b) too narrow to correctly identify locals from high- or low-Sr regions of Denmark. For example, an individual moving from a high-Sr region (e.g., 0.7115) to a low-Sr region (e.g., 0.7090) would be classified as "local" in both places, rendering the baseline ineffective for tracking mobility within Denmark.

2. Misapplication of Statistical Methods

The statistical method chosen (Median Absolute Deviation, or MAD, to clean the data, followed by 2 sigma to define the range) is a valid approach for defining a local baseline at a single site, where it is reasonable to assume the majority of individuals are local to that site's specific geology.

However, applying this method to a composite national dataset drawn from hundreds of different sites with different geological backgrounds is statistically inappropriate. The resulting range (0.7089–0.7117) is not a "baseline" for mobility studies; it is merely a statistical summary of the central 95% of all bioavailable Sr values in Denmark.

This method statistically defines individuals from the highest- and lowest-Sr regions of Denmark as "non-local," which is a critical error. This has direct implications for the case study: the six "non-local" individuals from Sølager may not be from outside Denmark; they may simply be from a part of Denmark with a naturally high-Sr signature that was statistically trimmed from the "local" range by the MAD analysis.

3. Failure to Demonstrate Suitability (A Path Forward)

The authors criticize environmental isoscapes but fail to provide any evidence that their method is superior. To validate their claims, they must directly compare their "simple baseline" against a spatially-explicit model.

Given that the 628 data points in the database are geolocated (as implied by Figure 1), the authors are in a prime position to do this. The critical revision required for this manuscript is as follows:

• The authors must use their 628 human data points to generate a human-derived 87Sr/86Sr isoscape for Denmark using appropriate spatial statistics (e.g., kriging).

• They must then compare the predictive power of this new isoscape against their "simple baseline."

• This re-analysis would allow them to re-evaluate the Sølager and Kalvehavegård individuals against a spatially-relevant local value (as predicted by their new human isoscape), rather than an arbitrary national average.

Without this spatial analysis, the paper's central argument is unsubstantiated, and its conclusions regarding non-elite mobility are unreliable.

Conclusion

The dataset presented is of great value to the archaeological community. However, the methodology used to interpret this data is flawed and ignores the foundational principles of strontium provenance. The "simple baseline" approach is inappropriate for a nationwide study.

I recommend Major Revisions. The paper cannot be accepted until the authors address this fundamental methodological flaw, preferably by conducting the spatial analysis suggested above and re-evaluating their conclusions accordingly.

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Reviewer #1: No

Reviewer #2: No

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Attachments

Attachment

Submitted filename: Frei at all editorial supplement.pdf

Bronze Age non-elite mobility in Denmark examined through a new human-based bioavailable strontium isotope range

PONE-D-25-53013R1

Dear Dr. Frei,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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Kind regards,

Luca Bondioli, PH.D.

Academic Editor

PLOS One

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

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??>

Reviewer #1: Yes

Reviewer #2: Yes

**********

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

Reviewer #1: N/A

Reviewer #2: Yes

**********

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

The PLOS Data policy

Reviewer #1: Yes

Reviewer #2: Yes

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

Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #1: (No Response)

Reviewer #2: The authors have adequately addressed the comments. The transition from calling the data a "baseline" to a "range" is a critical improvement. It correctly frames the findings as a statistical summary of typical Danish signatures rather than a spatially explicit environmental model. The revised manuscript is technically sound and provides a valuable new resource for the archaeological community.

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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

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