A Study on Spatial and Temporal Changes and Synergies/Trade-Offs of the Production-Living-Ecological Functions in Mountainous Areas Based on the Niche Width Model

Response to Reviewer 1 Comments

Dear Reviewer:

We are grateful to you for giving us this opportunity to revise our manuscript. Thank you for your comments concerning our manuscript entitled “A Study on Spatial and Temporal Changes and Synergies/Trade-Offs of the Production-Living-Ecological Functions in Mountainous Areas Based on the Niche Width Model” (ID: land-3503700). Those comments are all valuable and very insightful for revising and improving our paper, as well as the important guiding significance to our research. Our point-by-point response to the comments are given below, revised portions are marked in red in the paper. Our revised manuscript has also been re-submitted in the system.

Comments 1:

The paper applies diverse techniques for evaluation of land functions for classifying land use functional zones. My main concern with the paper is that it is focused on results description instead of describing the proposed methodology and explaining the relationships between the different techniques used. Since the final result (multifunctional zoning) derives exclusively from the k-means clustering (which is not explained in the methodology section), what is the usefulness of the results of the Spearman's index, LISA, Moran's I and dominant function analysis? How are the results of these techniques used for the study objective: “optimize the zoning and put forward optimization suggestions”?

Response 1: We sincerely appreciate the reviewer's thorough and insightful feedback, which has helped us significantly strengthen the methodological clarity and conceptual coherence of the manuscript. Response to Reviewer Comments on Methodological Logic and Technical Coherence. To address the concerns regarding the integration of methodologies, we systematically explain the coupling logic between multifunctional synergy/trade-off analysis and functional zoning through the following framework:

One、Multifunctional Synergy/Trade-off Analysis as the Theoretical Basis for Zoning

 1. Spearman's Correlation Coefficient: Quantifying Functional Relationships. Role: Identifies synergistic (positive correlation) or trade-off (negative correlation) relationships among production (PF), living (LF), and ecological (EF) functions. For example: A significant negative correlation between PF and EF (trade-off) indicates economic development at the expense of ecological integrity in certain regions. A positive correlation between PF and LF (synergy) suggests coexistence of production growth and social well-being enhancement. Implications for Zoning: Provides feature combinations for clustering. For instance, regions with strong EF-LF synergy may form an " EF -LF dual-dominant" cluster.

 2. Moran’s I and LISA: Revealing Spatial Agglomeration Patterns

Role: Global Moran’s I: Assesses spatial auto correlation (clustered/dispersed distribution) of functional scores. Local LISA: Identifies spatial anomalies (e.g., "high-high" hot pots or "low-low" cold pots). Implications for Zoning: Validates the spatial rationality of clustering results. For example, if "EF -dominant" clusters overlap with LISA-identified EF hot pots, the zoning aligns with spatial patterns.

Tow、Coupling Logic of Maxwell Triangle and k-means Clustering

 1. Role of the Maxwell Triangle: (1)Functional Contribution Mapping: Converts PF, LF, and EF scores into RGB coordinates (Equation 5) to visualize relative weights: Vertices: Single-function dominance (e.g., PF-dominant at the red vertex). Edges/Interior: Dual-function dominance (edges) or trifunction balance (interior). (2)Implications for Zoning: Guides clustering parameters (e.g., three color clusters suggest k=3); Interprets cluster characteristics (e.g., “red-green edge” = “PF -EF transitional type”).  

 2. Functional Integration Logic of k-means Clustering

 (1) Input Data: Raw functional scores (Fi, Ei, Si) are used instead of normalized coordinates (xi, yi, zi) to: Preserve absolute magnitude differences (e.g., regions with similar normalized coordinates may differ significantly in actual intensity). Capture both relative weights and absolute strengths (e.g., high-PF vs. low-PF regions with similar normalized values are differentiated).  

(2) Complementarity with Maxwell’s triangles: triangles solve the problem of “how to express the features of functional combinations”, while clustering solves the problem of “how to divide the regions of similar features”. The combination of the two achieves the dual validation of “visual exploration + quantitative classification”.

Three、How the technology chain supports “optimized zoning and recommendations”

 1. Progressive process of analysis-validation-optimization. Step 1: Identify dominant functional relationships (e.g., economic-ecological trade-offs) through Spearman's coefficient. Step 2: Locate spatial anomaly areas (e.g. ecological cold spots overlapping with economic hot spots) using LISA/Moran's I. Step 3: Determine clustering parameters based on Maxwell's triangles to observe functional combination patterns. Step 4: k-means clustering generates preliminary zoning. Step 5: Combine the above results to propose optimization recommendations (e.g., implement ecological compensation policies for economic-ecological trade-off zones).

In summary: Spearman's coefficient and spatial autocorrelation analyses are not directly used in clustering algorithms, but rather provide a scientific basis and validation of effectiveness for functional partitioning. For example, we found that PF and EF showed a significant negative correlation (Spearman ρ=-0.442, p<0.01), which explains why k-means clustering separates the two categories of “economy-dominated” and “ecology-dominated” regions. Combined with the LISA analysis, it was found that these categories showed significant high - high spatial clustering, indicating that the partitioning results conformed to the law of spatial dependence. Ultimately, combined with the distribution characteristics of functional weights in Maxwell's triangle, we are able to design differentiated land use policies for different zoning types.

Comments 2:

You say the abstract lacks methodology description. However, the description of results is
too long. Some of the supposed conclusions are descriptionss of results.

Response 2: Thank you for pointing this out. We apologize for the lack of a description of the method and the lack of clarity in the description of the results. In the revised manuscript, our abstract has been well illustrated and the results section has been revised, and I think it may be the word conclusions that is confusing the reviewers, so we have also revised it here.
The revised content is as follows: Abstract: As a typical ecologically fragile mountainous area, Liangshan Yi Autonomous Prefecture in Sichuan Province faces the problems of irrational allocation of land resources and uncoordinated development in the process of urbanization. Based on the ecological niche width model, this paper uses the correlation coefficient method and spatial autocorrelation analysis to explore the spatiotemporal characteristics and synergy/trade-off relationship of the "production-life-ecology" functions (PLEFs) in 2010-2020, and divides the land-use functional zones to put forward optimization suggestions. The findings showed that: (1) Production function (PF) and living function (LF) exhibit a "core-periphery" spatial pattern (high-value clusters in the south, low-value contiguous areas in the north), while ecological function (EF) displays a "high-low-high" ring-shaped pattern (high values in the northwest and southeast, declining in the central region due to development pressure); (2) Synergies and trade-offs coexist among PLEFs: the synergistic effect between PF and EF strengthens significantly, the trade-off relationship between PF and LF weakens slightly, and the trade-off between LF and EF remains prominent (HL/LH conflict zones exceed 55%); (3) Based on synergy/trade-off relationships, the study area is divided into six functional zones (e.g., economic priority zones, ecological protection zones), with proposed optimization strategies such as "intensive valley development, eco-cultural tourism in border areas, and urban-rural coordination in central regions," providing scientific support for sustainable territorial spatial utilization in mountainous areas.

Comments 3: Lines 103-112 are a summary of methodology that should not be in the introduction.

Response 3: Thank you for your careful feedback. According to the reviewers' comments, we put the specific methods in the methods section, and the introduction section mainly summarizes the research objectives. Reviewers can see the relevant methods in the Methods section. (Line 98-112)

Comments 4:

Lines 231-247. Are the factors the indicators of the previous section? It is confusing.

Response 4: Thank you for your careful feedback. We fully understand the reviewers' concerns and explain the questions raised by the reviewers as follows: Yes, the factors in this section of the calculation come from the indicator factors above. We standardized and weighted the 22 indicator factors, and the calculation of the ecological niche width of the PLEFs was done based on the indicator factors in the previous section. Specific explanation: firstly, "state" is understood as the closeness between the real value and the ideal value, and the maximum value after standardization of each factor is chosen as the ideal value, which is calculated by Eq. (1); "potential" is expressed as the strength of convergence of the real ecological niche to the most suitable ecological niche The "potential" is the strength of the convergence effect of the real ecological niche on the most suitable ecological niche, which is calculated by equation (2); finally, considering the changes of the "state" and "potential" of the ecological niche, the corresponding factor ecological niches for each function and each factor of each evaluation unit are derived. Finally, according to Shefold's law of limitation and taking into account the different importance of each factor, the integrated ecological niche of each of the three functions was calculated (Eq. 3).(Line 223-243)

Comments 5:

Section 4.3. LISA is not explained in the methodology.

Response 5: Thank you very much for your careful inspection. We have made corrections based on the comments made by the reviewers, and we describe the LISA values and methods in Section 3.3 on spatial correlation. Reviewers can see the revised manuscript on lines 253-261.

Comments 6:

Sections 3.4 and 4.4.1 refer to the same technique with different names.

Response 6: Thanks to the reviewers for their careful review. In order to make the explanation of the methodology, the logic clearer, and to facilitate the understanding of the following analysis, we have made changes in the manuscript: We divided Section 3.4 into 3.4.1 and 3.4.2, which are Maxwell's triangle and K-means clustering, respectively. The dominant functional analysis in section 4.4.1 corresponds exactly to Maxwell's triangle in 3.4.1. (Line 264-294).

Comments 7: What is the usefulness of the results reflected in figure 7?

Response 7: We fully understand the reviewer's concerns, as was the question of the first comment raised earlier by the reviewer, the paper applies diverse techniques for evaluation of land functions for classifying land use functional zones, So the method and the result, and the relationship between the method and the method are particularly important. Figure 7 shows the multifunctional spatial distribution of land based on Maxwell's triangle. The results obtained have the following significance: to provide prior knowledge for k-means clustering: to judge the rationality of the number of clusters k by color distribution (e.g., if there are three color clusters in the triangle, then k=3); Auxiliary interpretation of clustering results (e.g., a cluster corresponds to the "red-green edge zone" in the triangle, which can be named "production-ecological transition"). Based on Maxwell's triangle observation function combination pattern, the clustering parameters are determined to provide a basis for subsequent functional partitioning.

Comments 8: Section 4.4.2. K-means clustering is based on "the main land use function values". Which are the land use function values? The ecological niche widths?
Response 8: Thanks to the reviewers for pointing out this issue in the manuscript. The main land-use function values represent the values of different dominant functions calculated under Maxwell's triangle method, although these values are calculated according to the niche width model. This is because the niche width model in this paper is a way to calculate the functional values. The different dominant functions provide ancillary analyses (e.g., determination of clustering parameters) for subsequent k-means clustering. There are some deficiencies in the explanation here, and I have made relevant changes in the methods section of the original article to make the logic clearer. Reviewers can see the changes in section 3.4.2 of the manuscript and hopefully answer your question.

Comments 9:
Discussion. The first paragraph of discussion is not related to the results of the techniques
applied in the paper.
Response 9: We would like to thank you for your valuable comments on the discussion and conclusions! Your suggestions have helped us significantly improve the logical rigor and academic value of our paper. In response to the issues you pointed out, we have made the following changes to the relevant sections, and focused on optimizing the relevance and structure of the discussion and conclusions in the revised draft: Revision of the discussion section (the first paragraph of the original discussion did not closely integrate the analysis techniques with the research results)
Measures to modify: The analytical method is used as a framework to connect the results with the theory. The new first paragraph ensures that the discussion always revolves around the technical approach of the paper, which reflects the rationality of the niche theory and is also in line with the topic of the article (45, 46, 47, 48 for the new literature); The theoretical dialogue was strengthened, and the general discussion was deleted: the macro discussion that was not related to the analysis method in the original first paragraph was removed, and the multi-functional synergy mechanism was explained by combining the relevant analysis results with the natural, socio-economic and other aspects. Then, the research results were further discussed in combination with the current situation of the country and the study area, the significance of the research was expounded, and finally the research was insufficient. You can see the relevant revisions in lines 526-623 of the manuscript. We believe that the above revisions have effectively addressed the questions raised by you, and have made the discussion part both theoretical and practical. Thank you again for your professional review and constructive comments! Looking forward to your further guidance

Comments 10:
Conclusions. The two first paragraphs of the conclusions are descriptions of results or discussion, but not conclusions.
Response 10: Thank you sincerely for your valuable comments on the conclusion section! Your criticism helps us to realize that the first two paragraphs of the original conclusion. To this end, we have carried out a systematic reconstruction of the conclusion section, highlighting the core contribution and policy enlightenment of the research. The specific modifications are as follows:
1. Conclusion reconstruction: shift from "descriptive results" to "value refinement"
(1) Core contributions:
Delete the detailed description of the spatial and temporal differentiation characteristics of the "ecological niche" function (such as niche width value change, functional relationship dynamics, etc.) in the original conclusion, and instead emphasize the innovation and practical significance of the methodology: By integrating the framework of "niche width model-spatial autocorrelation analysis-cluster partition", this study reveals the dynamic mechanism of PLEFs synergy / trade-off in mountainous fragile areas, providing a new perspective of "quantitative drive of functional interaction relationship" for traditional functional partition studies.
(2) Policy association in the second section: avoid repeating the specific analysis of the discussion part, and directly refine the practical value of functional zoning and optimization strategy: The six functional areas (Figure 8) designated based on the coordination / balance relationship define the differentiated path of "strict protection of ecological priority areas, green transformation of valley economic belt, and ecological compensation of marginal areas" in Liangshan Prefecture.
2. Delete the redundant descriptions and strengthen the conclusion hierarchy
Representation of the removal results: In the original conclusion, "the relationship between PF and LF has gradually shifted from trade-off to synergy" and "LF-EF contradiction intensifies" have been moved to the discussion part, and the current conclusion only retains the summary of key mechanisms and policy implications.
We believe that the above revision has effectively solved the problem of "the first two paragraphs of the conclusion of the results", making the conclusion part really become the concise and sublimation of the full text. Thank you again for your rigorous review and constructive comments! You can check the specific changes in lines 626-673 of the manuscript.

Comments 11: Lines 618-619 state that multifunctional zones depend on the synergy and trade-offs of functions, but how are the synergy and trade-offs used for the functional zoning?
Response 11: Thank you very much for this question. I'm sorry I didn't make this clear in the
article and confused the reviewers. Specifically, the multi-functional synergy/trade-off analysis can be used as a theoretical basis for zoning, and after we preliminarily obtain the zoning results, we can clarify the priority of zoning through the synergistic/trade-off relationship. For example, if it is a strong trade-off area between PF and EF in the south, it should be considered as an "economic transition zone" to limit high pollution, while a functional complementary PF and EF area, such as Muli County, can be prioritized as an " ecologically livable area". The trade-off and synergy analysis of land use functions can provide a scientific basis for functional zoning by revealing the functional interaction mechanism, locating conflicts and potential areas, so as to achieve optimal allocation of resources, contradiction alleviation and sustainable development. The practice of Liangshan Prefecture shows that the zoning strategy based on trade-off/synergy can effectively coordinate the ecological protection and economic development of vulnerable mountainous areas, and provide a reference paradigm for similar areas. Implications for Zoning:Provides feature combinations for clustering. For instance, regions with strong EF-LF synergy may form an "EF-LF dual-dominant" cluster. The trade-off and synergy analysis of land use functions can provide a scientific basis for functional zoning by revealing the functional interaction mechanism, locating conflicts and potential areas, so as to achieve optimal allocation of resources, contradiction alleviation and sustainable development. The practice of Liangshan Prefecture shows that the zoning strategy based on trade-off/synergy can effectively coordinate the ecological protection and economic development of vulnerable mountainous areas, and provide a reference paradigm for similar areas.

Comments 12: Table 2. Lines to divide different functions are required
Response 12: Thanks to the reviewers for reviewing the manuscript carefully, we have made relevant changes in Table 2.

Comments 13: There are numerous punctuation errors throughout the paper.
Response 13: Many thanks to the reviewers for pointing out the errors, which I have made in the manuscript. Apologies for such an oversight.

Comments 14: Line 474. Figure 7 is figure 8.
Response 14: Thank you very much to the reviewers for their careful review, and we have made changes in the corresponding positions in the article.

Point 1: Comments on the Quality of English Language English needs review
Response 1: We sincerely appreciate the reviewer's constructive feedback on the language quality. We have thoroughly revised the manuscript to improve English expression, including:
1. Professional proofreading to refine grammar, vocabulary, and sentence structure;
2. Restructuring complex sentences and enhancing logical coherence;
3. Standardizing terminology (e.g., " 生态位宽度" as "niche width") and correcting punctuation/formatting.

The revised manuscript has been checked via Grammarly and Turnitin to ensure linguistic
accuracy and originality. We believe these revisions have significantly enhanced the
readability and academic rigor of the paper. Thank you for your valuable suggestions!
We would like to express our sincere gratitude for your thoughtful and constructive comments.
In response to the suggestions provided, we have re-edited the manuscript to the best of our
ability. We believe these changes do not affect the overall content and structure of the paper.
We deeply appreciate the editors" and reviewers” efforts, and we hope that the revisions will
meet with their approval. Once again, we would like to thank you for your valuable comments
and suggestions.

Response to Reviewer 3 Comments

Dear Reviewer:

We are grateful to you for giving us this opportunity to revise our manuscript. Thank you for your comments concerning our manuscript entitled "A Study on Spatial and Temporal Changes and Synergies/Trade-Offs of the Production-Living-Ecological Functions in Mountainous Areas Based on the Niche Width Model" (ID: land-3503700). Thank you for your careful review of this article and your valuable comments! We sincerely thank you for your recognition of the research, including the compatibility of the topic selection with the scope of the journal, the scientific nature of the methodology, the clarity of the presentation of the results, and the rationality of the conclusions. Our point-by-point response to the comments is given below, revised portions are marked in red in the paper. Our revised manuscript has also been re-submitted in the system. Thank you again for your professional advice that provided important guidance for the further improvement of the paper!  

Suggestion 1: You say "In line 113 to 118 is presented the aim of research. This text should be a particular paragraph for presenting the aim of research,as the last paragraph of the chapter of Introduction!"

Response 1: Thank you for pointing this out and I agree with this comment. Therefore, I read it carefully and added a more detailed explanation of the purpose of the study and put it in the last paragraph of the introduction section. It reads as follows:

In view of this, this paper takes Liangshan Yi Autonomous Prefecture (hereinafter referred to as "Liangshan Prefecture") as the research object, and analyses the types of synergistic/trade-off relationships and spatial and temporal changes of the PLEF terms of quantity and spatial distribution based on the grid scale (2000m×2000m). The aim is to comprehensively reveal the spatial and temporal variability of the synergies and trade-offs among the PLEFs in Liangshan Prefecture and their dynamic interaction mechanisms. On this basis, a functional zoning optimization framework that takes into account ecological protection and socioeconomic development is proposed, and spatially differentiated management strategies and policy recommendations that suit the characteristics of mountainous regions are suggested. The research results are expected to provide a theoretical basis for the synergistic development of land space in ecologically fragile mountainous areas, in particular, implementable solutions for the coordination of poverty alleviation needs and ecological protection needs in national autonomous regions. It will provide theoretical support and scientific reference for promoting sustainable development and optimal adjustment of land use in mountainous areas. (This passage is located in lines 98-112 of the manuscript)

We would like to express our sincere gratitude for your thoughtful and constructive comments. In response to the suggestions provided, we have re-edited the manuscript to the best of our ability. We believe these changes do not affect the overall content and structure of the paper. The manuscript was also scrutinized, and some other typos and grammatical errors were corrected. We deeply appreciate the editors" and reviewers" efforts, and we hope that the revisions will meet with their approval. Once again, we would like to thank you for your valuable comments and suggestions. 

Best regards,

Yours sincerely,

Corresponding author: Ping Ren

E-mail: renping@sicnu.edu.cn

Response to Reviewer 1 Comments

Dear Reviewer:

Thank you again for giving us the opportunity to revise the manuscript. Thank you for your comments concerning our manuscript entitled “A Study on Spatial and Temporal Changes and Synergies/Trade-Offs of the Production-Living-Ecological Functions in Mountainous Areas Based on the Niche Width Model” (ID: land-3503700). Those comments are all valuable and very insightful for revising and improving our paper, as well as the important guiding significance to our researches. Our point-by-point response to the comments are given below, revised portion are marked in red in the paper. Our revised manuscript has also been re-submitted in the system.

Comments 1:

“Implications for Zoning: Provides feature combinations for clustering. For instance, regions with strong EF-LF synergy may form an " EF -LF dual-dominant" cluster.”

Lines 297-301 provides a general description of the k-means clustering but does not specify how are the results of PLEFs synergy/trade-off analysis used as input data or the method is configurated. More detailed explanations on the specific application of this method are required.

Response 1: We are very grateful for the valuable advice of the reviewers. We think it is important to clarify the methodology, and first of all, we apologize for the lack of accuracy in the previous responses and thus confusing the reviewers. Firstly, the function combination model based on Maxwell's triangle can directly reflect the trade-offs or synergies between multiple objectives in each county, and its functional values are input into K-maens, and the K-means clustering method optimizes the clustering center through repeated iterations, and finally obtains the optimal clustering partition results, following the "functional synergy-spatial cluster-policy adaptation" The principle gives suggestions for functional optimization, which can also be understood in conjunction with reply 8 and reply 11. Of course, issues such as data entry and partitioning are covered in the Methods section and the Results section. Specifically, in Sections 3.4.2 (lines 291-308), 3.4.2 (lines 310-328) and 4.4.2 (lines 513-519).

Comments 2:

 Moran’s I and LISA: Revealing Spatial Agglomeration Patterns. Role: Global Moran’s I: Assesses spatial auto correlation (clustered/dispersed distribution) of functional scores. Local LISA: Identifies spatial anomalies (e.g., "high-high" hot pots or "low-low" cold pots). Implications for Zoning: Validates the spatial rationality of clustering results. For example, if "EF -dominant" clusters overlap with LISA-identified EF hot pots, the zoning aligns with spatial patterns.”

The paper does not explain how LISA is used to validate the spatial rationality of clustering. What are the results of Moran’s I used for?

Response 2: Many thanks to the reviewers for pointing out this issue, these comments are very valuable and helpful. We are sorry that the previous reply was not accurate enough to confuse the reviewers, and we will explain and revise it further. First of all, section 3.3 of the method is the correlation analysis, including spearman correlation analysis and bivariate local spatial autocorrelation analysis, which is to effectively reveal the interrelationship and dynamic change trend of the land in the study area from the quantity and space respectively, so as to realize the analysis of the synergy / trade-off relationship between functions. The local spatial autocorrelation calculates the Moran index through geoda software, and the Lisa distribution map is used to realize the functional synergy / trade-off relationship. We modified section 3.3 in the text to make the method more clear. The synergy / trade-off relationship provides quantitative basis and theoretical support for the later partition, and the above examples is to illustrate this point. Modification at lines 265-279. This part can also be understood in combination with the following reply 11 and 8.

Comments 3:

“Progressive process of analysis-validation-optimization. Step 1: Identify dominant functional relationships (e.g., economic-ecological trade-offs) through Spearman's coefficient. Step 2: Locate spatial anomaly areas (e.g. ecological cold spots overlapping with economic hot spots) using LISA/Moran's I. Step 3: Determine clustering parameters based on Maxwell's triangles to observe functional combination patterns. Step 4: k-means clustering generates preliminary zoning. Step 5: Combine the above results to propose optimization recommendations (e.g., implement ecological compensation policies for economic-ecological trade-off zones).

In summary: Spearman's coefficient and spatial autocorrelation analyses are not directly used in clustering algorithms, but rather provide a scientific basis and validation of effectiveness for functional partitioning. For example, we found that PF and EF showed a significant negative correlation (Spearman ρ=-0.442, p<0.01), which explains why k-means clustering separates the two categories of “economy-dominated” and “ecology-dominated” regions. Combined with the LISA analysis, it was found that these categories showed significant high - high spatial clustering, indicating that the partitioning results conformed to the law of spatial dependence. Ultimately, combined with the distribution characteristics of functional weights in Maxwell's triangle, we are able to design differentiated land use policies for different zoning types.”

This is not explained in the text neither in the methodology nor in the discussion. Combination of LISA analysis and clustering results are not used in the discussion.

Response 3: Thanks for the suggestion of the reviewer, we are very sorry for the above negligence. The statement in the reply here may not accurately convey our meaning, so you are confused. First, based on the suggestions of the reviewer, our description of the method has been perfected in sections 3.3 and 3.4, respectively, including spatial autocorrelation analysis LISA graph, Maxwell triangle, and K-means clustering method. We also read through the full text many times to ensure logical coherence. The above response is to answer the logical questions raised by the reviewer, so it is not reflected in the text, but is now perfected to answer the reviewer's comments. For the discussion part, the following explanations are given according to our understanding of the reviewers' comments: In the second paragraph of the discussion, we focused on the current situation of the research area under the functional synergy / trade-off relationship, and analyzed the relevant reasons. In addition, we discussed the rationality of the post-clustering partition results in combination with the policy and natural-socio-economic factors. For example, lines 624-632 of the article, combined with the partition results (Figure 8), illustrate the rationality of the partition results. It is hoped that the above answer can answer the reviewer's question.

Comments 4:

Abstract. Methodology description is still too short compared to explanation of results. Meaning of HL/LH is not explained in the abstract.

Response 4: Thanks again to the reviewers for their valuable comments, we have made relevant revisions to the abstract according to the reviewers' suggestions, strengthened the description of the methodology, explained the relevant meanings, enhanced the structure and logical level, paid attention to the application of professional terms, and ended by emphasizing the contribution of research theory and practice, echoing the reviewers' concerns about scientific significance. Hopefully, it can meet the requirements of the reviewers. The modifications are made as follows:

Abstract: As a typical ecologically fragile mountainous area, Liangshan Yi Autonomous Prefecture in Sichuan Province faces challenges of irrational land resource allocation and uncoordinated urbanization. This study employs an ecological niche width model to quantify the functional status of "production-living-ecological" functions (PLEFs) across 2010–2020. Methodologically, we integrated spatial autocorrelation analysis and Spearman’s correlation coefficients to systematically evaluate spatiotemporal synergies and trade-offs among PLEFs. Based on this, Spatial clustering patterns were further analyzed using Maxwell’s triangle and K-means algorithms to delineate functional zones. Key findings include: The findings showed that: The findings showed that: (1) Production function (PF) and living function (LF) exhibit a "core-periphery" spatial pattern (high-value clusters in the south, low-value contiguous areas in the north), while ecological function (EF) displays a "high-low-high" ring-shaped pattern (high values in the northwest and southeast, declining in the central region due to development pressure); (2) Synergy and trade-off relationships coexist in the study area. Synergies and trade-offs coexist among PLEFs: the synergistic effect between PF and EF strengthens significantly, the trade-off relationship between PF and LF weakens slightly, and the trade-off between LF and EF remains prominent, High-Low (HL) clusters and Low-High (LH) clusters exceed 55%; (3) Based on synergy/trade-off relationships, the study area is divided into six functional zones (e.g., economic priority zones, ecological protection zones), with proposed optimization strategies such as "intensive valley development, eco-cultural tourism in border areas, and urban-rural coordination in central regions," providing scientific support for sustainable territorial spatial utilization in mountainous areas.

Comments 5:

If factors and indicators are the same, these should be clarified in the text.

Response 5: Thank you very much for your careful review, which we have revised in lines 230-236 based on your comments. It has not been stated separately before because the calculation of the index factor of PLEFs is to calculate the niche width value of each function. In Section 3.2 of the paper, it also says that the calculation of the niche width is the key index to measure the advantages of production, life and ecology, that is, corresponding to the three functions. We show in the paper that the calculation of the niche width value is derived from the indicator factor.

Comments 6:

 In spite of the inclusion of lines 253-261 refered to LISA values, neither a bibliographic reference to this method nor an explanation of this acronym is included in the text. Response 6: Thank you very much for the reviewer's suggestion and we apologize for the oversight. There was no specific explanation of LISA before, because it is a common tool in Geoda software, and the resulting graph is called the LISA distribution map. The full name of the LISA is the Local Indicators of Spatial Association. According to the recommendations of the reviewer, we made relevant modifications and added the relevant literature reference [43] in line 265-729 of the text.

Comments 7: 

The usefulness of Maxwell’s triangle is explained in this response, but this explanation has not been included in the manuscript.

Response 7: Thanks to the reviewers for their suggestions, we have elaborated on the methods in section 3.4.1 of the manuscript to demonstrate the validity of the above methods. In conjunction with Section 3.4.2 below, the usefulness of the method can be clearly stated. Specifically in lines 281-328 of the text.

Comments 8:

The text does not explain clearly which are the dominant functional values. The response indicates: “The main land-use function values represent the values of different dominant functions calculated under Maxwell's triangle method, although these values are calculated according to the niche width model”. This is also unclear. Please, explain clearly and precisely what are the input values for the clustering analysis.

Response 8: Thank you for the reviewers‘ valuable suggestions, first of all, in response to the reviewers’ suggestions, we have the following explanations to answer the reviewers' questions: First of all, we are sorry that the problem we expressed may have made the reviewers feel ambiguous, the value of the main land use function here is the value of the dominant function, which means the value obtained by applying Maxwell's Triangle, and it is the value calculated in section 3.4.1:、和. On top of this, the visualization is further used to represent the combined contribution of the three main functions. The expression "main land use function value" has been removed from the revised text. Because this part of the problem is due to Section 4.4.2, we have made the following changes in the first paragraph of Section 4.4.2: Using the K-means clustering method, the dominant function values of all counties were analyzed, resulting in the identification of the following multifunctional areas (fig. 8), with relevant optimization suggestions for each zone provided. The term "dominant function value" is used here, which corresponds to the dominant function analysis in 4.4.1. A description has been added in section 3.4.1 for ease of understanding. "Main land use function values" has been removed from the revised text. Since this part of the problem is due to problems caused by Section 4.4.2, we amended the first paragraph in Section 4.4.2 to answer the reviewers.

Interpretation of the input values of clustering analysis: Maxwell's triangles reveal the spatial patterns of functional relationships and guide the selection of clustering features. Maxwell's triangle provides a standardized input and partition basis for k-means clustering, and the value obtained by Maxwell's triangle can be understood as the normalized functional proportion, in which the normalized value is input to calculate the Euclidean distance from each region to the center of the cluster, and the functional proportion of the center of the cluster reflects the type of partitioning. The specific methods and procedures are supplemented and modified in section 3.4.2 of the text. We hope that these notes and changes will answer the reviewers' questions.

Comments 9:

New lines 551-569 should be in the introduction not in the discussion, since these statements are not derived from this work.

Response 9: Thank you very much for your careful examination, we consider deleting this paragraph, because the introduction is sufficient for the purpose of the study, and we do not need to repeat the narrative here.

Comments 10:

Conclusions are related exclusively to the study area. I miss conclusions about the proposed methodology, which are the most interesting aspects for international readers.

Response 10: We have carefully considered the suggestions given by the reviewers, and are very much for the constructive comments, and believe that the revision will make the article more meaningful. Regarding the method, since the article is based on the functional synergy / trade-off relationship under the niche width model, we mainly discuss the niche width model in the discussion section. However, we are sorry for the description of the lost method in the conclusion section, so according to the opinions of the reviewer, we added the conclusion about the method in the last paragraph, hoping to improve the depth of the conclusion theory and the international dialogue ability through the structured description. Specific modifications are given in article lines 726-748. The Supplementary contents are as follows:

In general, this study systematically reveals the spatial and temporal evolution rules and interaction mechanism of PLEFs in ecologically fragile areas. While providing localized spatial optimization scheme, the method and theoretical framework constructed in this paper has universal value for the sustainable spatial governance of the similar areas worldwide.The niche width model, by introducing the "state” and “potential" theory, achieves a quantitative evaluation of multifunctional land-use dynamics, effectively bridging ecological principles with socio-economic metrics. This methodology demonstrates strong generalizability for application in other regions confronting land-use competition conflicts; Combining local spatial autocorrelation and Spearman correlation analysis, exploring quantitative and spatial synergy / trade-off relationships, breaking the limitations of traditional one-scale analysis, deepening the research paradigm of "pattern-process-mechanism" in geography. The partition optimization study using Maxwell triangle and k-means clustering method provides a spatial tool for the interpretation of multidimensional interaction relationships. Its core value lies in transforming complex human-person interaction into operational management unit through spatial expression and clustering optimization of synergy/ trade-off relationship, providing methodological innovation for global sustainable spatial governance. The empirical application of Liangshan Prefecture verifies the effectiveness of this framework, and the interdisciplinary and cross-scale research is of scientific significance to explore the relationship between human and land in ecologically fragile areas. Its core value lies in the implementation of differentiated management through the spatial expression and clustering optimization of synergy/ trade-off relationship.

Comments 11:

“Specifically, the multi-functional synergy/trade-off analysis can be used as a theoretical basis for zoning, and after we preliminarily obtain the zoning results, we can clarify the priority of zoning through the synergistic/trade-off relationship. For example, if it is a strong trade-off area between PF and EF in the south, it should be considered as an "economic transition zone" to limit high pollution, while a functional complementary PF and EF area, such as Muli County, can be prioritized as an " ecologically livable area"

I cannot understand this explanation. Anyway, this is not explained in the manuscript. An example is not the correct way to explain a methodological process… It should be clarified how the synergy/trade-off analysis is used to improve/modify/prioritize zoning.

Response 11: I understand the questions raised by the reviewers and thank again to the reviewers for spending their valuable time making constructive suggestions. The reviewers wanted the logic to be clearer, so we add relevant explanations in sections 3.4.1,3.4.2 and 4.4.2 of the text, explaining how the synergy / trade-off relationship of function acts to the partition, which can be understood in combination with replies 1,2 and 8. However, I still want to explain some points: synergy / trade-off research is to provide quantitative basis and theoretical support for functional partition by revealing the spatial law of functional interaction, so as to provide dynamic adjustment of partition strategy. Partition always follows the principle of "functional collaboration-spatial clustering-policy adaptation". For example, time series analysis (2010-2020) shows that the negative correlation between PF and EF has weakened, reflecting the effect of ecological restoration policies. Therefore, on the basis of the existing functional zoning, optimization suggestions can be put forward that "economic priority zone" can gradually introduce green industries and transition to "green transformation zone". What I want to express is that it is more of a theoretical framework than a method, which is actually reflected in the specific partition part. Of course, the example cannot explain the methodology, which is not the original intention of this part. I sincerely thank the reviewers for their serious comments, and we apologize for the inconvenience caused to the reviewers.