Exploring Methane Emission Dynamics Using Bayesian Networks and Machine Learning Analysis of Nutritional and Production Traits in Dairy Cattle

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

General Comments

The manuscript has a clear objective and employs advanced statistical tools (Bayesian networks, machine learning) to model CH₄ emissions in dairy production systems. However, the language is often unclear, sentences are overly long, and terminology is inconsistent. Additionally, the work contains numerous technical and grammatical errors that detract from its overall quality. The structure is solid, but the methodology and results sections deserve clearer presentation and deeper interpretation.

Specific comments

Abstract

Line 27: Please change “ME has correlations ranged...” into “ME showed correlations ranging from...”

Introduction

Line 50: Please change “approximate 11%” into “approximately 11%”

Lines 56–66: This part is repetitive (methane from manure is mentioned multiple times). Consider shortening and simplifying.

Line 76: Please change “3-nitroxpropanol” into„3-nitrooxypropanol (3-NOP)“.

Materials and Methods

Lines 93-94: “research work” is redundant – leave only “225 peer-reviewed papers.”

Line 98: Please change „Additionally, the dataset includes 97 production-related variables, included body weight (BW)...“ into „Additionally, the dataset consists of 97 production-related variables, such as body weight (BW)...“

Line 104: Please correct “how it can impact on production traits” to the following form “how it can impact production traits” (remove on).

Lines 156–165 (machine learning models): sentences here should be simplified and broken up for better readability.

Discussion

More in-depth interpretation of the findings is needed – avoid simply restating the results.

Lines 416–417: “Higher levels of NDF and ADF exhibited a strong positive association...” – please connect this with fermentability and hydrogen production.

Please discuss the limitations of the study (e.g., variability among studies, etc.).

Conclusion

Please add the practical implications related to potential utility in precision feeding strategies.

Author Response

Dear Editor

We would like to sincerely thank you and the reviewers for the time and effort dedicated to evaluating our manuscript entitled “Exploring methane emission dynamics using Bayesian networks and machine learning analysis of nutritional and production traits in dairy cattle.”  We greatly appreciate the constructive feedback provided, which has helped us strengthen and clarify the manuscript. In response to the reviewers’ comments, we have carefully revised the manuscript to address all suggestions and concerns. Key revisions include:

Corresponding Author

 

 

Reviewer #1

General Comments

The manuscript has a clear objective and employs advanced statistical tools (Bayesian networks, machine learning) to model CH₄ emissions in dairy production systems. However, the language is often unclear, sentences are overly long, and terminology is inconsistent. Additionally, the work contains numerous technical and grammatical errors that detract from its overall quality. The structure is solid, but the methodology and results sections deserve clearer presentation and deeper interpretation.

Specific comments

Abstract

Line 27: Please change “ME has correlations ranged...” into “ME showed correlations ranging from...”

Authors: The correction has been made.

Introduction

Line 50: Please change “approximate 11%” into “approximately 11%”

Authors: The correction has been made.

Lines 56–66: This part is repetitive (methane from manure is mentioned multiple times). Consider shortening and simplifying.

Authors: The correction has been made.

Line 76: Please change “3-nitroxpropanol” into„3-nitrooxypropanol (3-NOP)“.

Authors: The correction has been made.

Materials and Methods

Lines 93-94: “research work” is redundant – leave only “225 peer-reviewed papers.”

Line 98: Please change „Additionally, the dataset includes 97 production-related variables, included body weight (BW)...“ into „Additionally, the dataset consists of 97 production-related variables, such as body weight (BW)...“

Authors: The correction has been made.

Line 104: Please correct “how it can impact on production traits” to the following form “how it can impact production traits” (remove on).

Authors: The correction has been made.

Lines 156–165 (machine learning models): sentences here should be simplified and broken up for better readability.

Authors: We listed the machine learning models in two main categories: linear and nonlinear. Each category includes four models, which are numbered for clarity.

Discussion

More in-depth interpretation of the findings is needed – avoid simply restating the results.

Authors: The correction has been made.

Lines 416–417: “Higher levels of NDF and ADF exhibited a strong positive association...” – please connect this with fermentability and hydrogen production.

Authors: The correction has been made.

Please discuss the limitations of the study (e.g., variability among studies, etc.).

Authors: Thanks for your suggestion we discussed and added a paragraph between lines 531-536.

Conclusion

Please add the practical implications related to potential utility in precision feeding strategies.

Authors: Thanks for your suggestion and we revised it.

Authors: We revised the writing and discussed it in more details. 

 

Reviewer 2 Report

Comments and Suggestions for Authors

This article employs Bayesian networks and machine learning techniques to analyze the relationships among dietary chemical components, methane emissions (ME), and production traits in dairy cattle. The research holds significant academic and practical value.
Several aspects of the manuscript require further refinement to enhance clarity and scientific rigor:
1. The abstract should include a brief description of the sample information used in the analysis (1–2 sentences), as this is essential for assessing the reliability of the findings.
2. Although the Materials and Methods section outlines the sample details, it lacks specific information regarding sample size, which is crucial for evaluating the validity of the results. It is strongly recommended that the authors provide the dataset in the form of an supplementary table.
3. The two conclusions presented in lines 227–229 are particularly insightful and should be summarized and incorporated into the abstract to highlight the key findings of the study.
4. The spelling of "smal" on the X-axis of Figure 2 should be corrected to "small". Additionally, it is recommended to indicate the sample size for each data group in the figure caption and to annotate the specific average values directly on the figure.
5. Line 286 incorrectly refers to Figure 2; this should be corrected to refer to Figure 3.
6. In Table 1, the first footnote marker is not formatted using a superscript; this should be adjusted to conform to standard academic formatting conventions.
7. The font sizes in lines 307–318 and 341–353 appear inconsistent with the rest of the document. Please verify and ensure typographical uniformity throughout the manuscript.
8. The citation format used in line 428 does not conform to standard academic practices and should be corrected. Furthermore, the Discussion section contains extensive descriptive language but lacks sufficient supporting references, which deviates from the conventional scholarly writing style. Additional citations should be included to strengthen the academic foundation of the discussion.

Author Response

Dear Editor

We would like to sincerely thank you and the reviewers for the time and effort dedicated to evaluating our manuscript entitled “Exploring methane emission dynamics using Bayesian networks and machine learning analysis of nutritional and production traits in dairy cattle.”  We greatly appreciate the constructive feedback provided, which has helped us strengthen and clarify the manuscript. In response to the reviewers’ comments, we have carefully revised the manuscript to address all suggestions and concerns. Key revisions include:

Corresponding Author

Reviewer # 2

This article employs Bayesian networks and machine learning techniques to analyze the relationships among dietary chemical components, methane emissions (ME), and production traits in dairy cattle. The research holds significant academic and practical value.
Several aspects of the manuscript require further refinement to enhance clarity and scientific rigor:
1. The abstract should include a brief description of the sample information used in the analysis (1–2 sentences), as this is essential for assessing the reliability of the findings.

Authors: We added more information and revised the abstract. This meta-analysis included 303 observations across multiple studies, with sample sizes per trait ranging from 83 records for NDF intake to 301 for methane measurements. This broad coverage ensures robust statistical power for evaluating dietary effects on methane emissions and related traits.

2. 
   Although the Materials and Methods section outlines the sample details, it lacks specific information regarding sample size, which is crucial for evaluating the validity of the results. It is strongly recommended that the authors provide the dataset in the form of asupplementary table.
   Authors: We added sample size per trait and measurement in lines 134-146.
3. 
   The two conclusions presented in lines 227–229 are particularly insightful and should be summarized and incorporated into the abstract to highlight the key findings of the study.

Answer: We thank the reviewer for the constructive suggestion. As recommended, we have incorporated the key findings from lines 227–229 into the abstract. Specifically, we now highlight that methane intensity decreases with increasing milk yield, regardless of body size, and that larger cows emit more methane in total but are generally more efficient when producing more milk. We believe this addition strengthens the abstract by emphasizing the practical implications of our results.

4. 
   The spelling of "smal" on the X-axis of Figure 2 should be corrected to "small". Additionally, it is recommended to indicate the sample size for each data group in the figure caption and to annotate the specific average values directly on the figure.

Authors: The spelling error on the X-axis of Figure 2 has been corrected and sample size added.

5. 
   Line 286 incorrectly refers to Figure 2; this should be corrected to refer to Figure 3.

Authors: Corrected the reference on line 286 to Figure 3.

6. 
   In Table 1, the first footnote marker is not formatted using a superscript; this should be adjusted to conform to standard academic formatting conventions.

Authors: It has been corrected to superscript format.

7. 
   The font sizes in lines 307–318 and 341–353 appear inconsistent with the rest of the document. Please verify and ensure typographical uniformity throughout the manuscript.

Authors: The font sizes have been corrected for consistency.

8. 
   The citation format used in line 428 does not conform to standard academic practices and should be corrected. Furthermore, the Discussion section contains extensive descriptive language but lacks sufficient supporting references, which deviates from the conventional scholarly writing style. Additional citations should be included to strengthen the academic foundation of the discussion.

Authors: Thanks for the note. We corrected the citations format accordingly.

 

 

Reviewer 3 Report

Comments and Suggestions for Authors

Dear authors, respectfully, I believe this manuscript addresses a valuable topic and demonstrates potential. However, several issues currently affect the overall quality and clarity of the work. Some suggestions below:

 

Abstract: The abstract presents relevant information; however, I suggest improving the writing style to make it more informative and precise. Consider including numerical data and additional details such as the number of studies selected, models used, and other methodological highlights.

 

Keywords: I recommend using keywords that differ from the title and reviewing the journal’s author guidelines for proper keyword selection.

 

Introduction: The introduction contains important information, but I suggest using more specific descriptions rather than general statements. This will enhance the reader's understanding of the study's context and implicitly highlight its necessity.

 

Also, note that “ME” is a common abbreviation for “Metabolizable Energy.” I recommend choosing a different abbreviation to avoid confusion.

 

Line 48: Ensure the citation is properly formatted and that the corresponding reference is included in the reference list.

 

Line 53: Clarify what "rate" refers to and provide the corresponding value.

 

Lines 53–54: Specify the comparison – compared with which data?

 

Lines 61–64: Quantify the production mentioned. How much is produced?

 

Lines 66–67: Justify the statement. Why does this issue require considerable attention? What is happening specifically?

 

Materials and Methods: The description of all models used in the study needs to be improved. Please include the specific parameters and statistical criteria used to evaluate model performance (e.g., R², RMSE, AIC, BIC, CCC, etc.), and clearly explain how each model was applied. It is important to justify which model(s) provided the best fit and why. This will enhance the transparency and scientific rigor of your methodology.

 

Line 209: The abbreviation “MY (MY)” appears to be repeated. Please correct it.

 

Results

 

Lines 267–272: This passage resembles a discussion. I recommend moving it to the discussion section and removing it from the results. Apply the same suggestion to any similar content throughout the results section.

 

Line 324: “Unit” is too generic. Indicate the exact unit of measurement (e.g., %, kg, g/day, etc.).

Discussion: Since the results are presented using subheadings, consider using subheadings in the discussion section as well to improve clarity and organization.

 

The discussion should aim to explain how the results were obtained. To do this effectively, incorporate relevant theories, biological or physiological mechanisms, and environmental or methodological justifications. Currently, the discussion provides a good general review, describes the results (which should be avoided to prevent repetition), and compares findings with those of other authors. However, it lacks a deeper analysis of the mechanisms behind the results.

 

Lines 398–399: Ensure correct citation and that the reference appears in the reference list.

 

Lines 408–427: This section is too general and lacks depth. Consider rewriting or removing it.

 

Lines 445–446: This is a comparative statement between current findings and literature data. Rewrite it to reflect a deeper analysis as part of the discussion.

 

Conclusion: The conclusion should be more objective and concise, emphasizing the main findings of the study. After this, you may include implications, limitations, and potential future research directions.

Author Response

Dear Editor

We would like to sincerely thank you and the reviewers for the time and effort dedicated to evaluating our manuscript entitled “Exploring methane emission dynamics using Bayesian networks and machine learning analysis of nutritional and production traits in dairy cattle.”  We greatly appreciate the constructive feedback provided, which has helped us strengthen and clarify the manuscript. In response to the reviewers’ comments, we have carefully revised the manuscript to address all suggestions and concerns. Key revisions include:

Corresponding Author

 

Reviewer # 3

Dear authors, respectfully, I believe this manuscript addresses a valuable topic and demonstrates potential. However, several issues currently affect the overall quality and clarity of the work. Some suggestions below:

 

Abstract: The abstract presents relevant information; however, I suggest improving the writing style to make it more informative and precise. Consider including numerical data and additional details such as the number of studies selected, models used, and other methodological highlights.

Authors: Thank you for your helpful suggestion. In response, we have revised the abstract to include key methodological details: the study analyzed a meta-dataset derived from 225 peer-reviewed publications and applied Bayesian networks along with eight machine learning models both linear and nonlinear to assess the influence of diet and production traits on methane emissions.

Keywords: I recommend using keywords that differ from the title and reviewing the journal’s author guidelines for proper keyword selection.

 Authors: Thanks for the suggestion. Keywords have been revised as recommended.

 

Introduction: The introduction contains important information, but I suggest using more specific descriptions rather than general statements. This will enhance the reader's understanding of the study's context and implicitly highlight its necessity.

 Authors: Thank you for the valuable suggestion. I’ve added specific scientific details to enhance clarity and better highlight the study’s context, as recommended.

Also, note that “ME” is a common abbreviation for “Metabolizable Energy.” I recommend choosing a different abbreviation to avoid confusion.

 Authors: Thank you for the thoughtful suggestion. We've updated the abbreviation to avoid any confusion with Metabolizable Energy.

 

Line 48: Ensure the citation is properly formatted and that the corresponding reference is included in the reference list.

 Authors: Thank you for the reminder. I've reviewed the citations and ensured they are properly formatted and included in the reference list.

 

Line 53: Clarify what "rate" refers to and provide the corresponding value.

 Authors: we revised the text and added:
CH₄ concentrations have been increasing at an unprecedented annual growth rate of ~17–18 ppb/year in recent years (compared to ~5–8 ppb/year in the early 2000s), and since 2014, they have been nearing the highest GHG emission scenarios

 

Lines 53–54: Specify the comparison – compared with which data?

 Authors: The correction has been made.

Lines 61–64: Quantify the production mentioned. How much is produced?

 Authors: According to the U.S. EPA Greenhouse Gas Inventory (2022) and IPCC Guidelines (2019), a typical dairy cow emits approximately 143 kg CH₄ per year from enteric fermentation and 93 kg CH₄ from manure management, along with 1.4 kg N₂O per year from manure, equivalent to roughly 7 t CO₂e annually; for beef cattle, corresponding values are 95 kg CH₄ (enteric), 1.6 kg CH₄ (manure), and 0.3 kg N₂O, or about 2.8 t CO₂e annually.

Lines 66–67: Justify the statement. Why does this issue require considerable attention? What is happening specifically?

 Authors: Thank you for your comment. I've added a brief justification to clarify why this issue requires attention.

Materials and Methods: The description of all models used in the study needs to be improved. Please include the specific parameters and statistical criteria used to evaluate model performance (e.g., R², RMSE, AIC, BIC, CCC, etc.), and clearly explain how each model was applied. It is important to justify which model(s) provided the best fit and why. This will enhance the transparency and scientific rigor of your methodology.

Authors: Thank you for this valuable feedback. We have revised the Methods section to clearly describe all models used, specifying their parameters and evaluation criteria. Model performance was assessed using the coefficient of determination (R²) and mean square error (MSE), and the best-fitting model was selected based on the highest R² and lowest MSE values. This ensures transparency and supports the scientific rigor of our analysis.

Line 209: The abbreviation “MY (MY)” appears to be repeated. Please correct it.

 Authors: Thank you for the note. The repeated abbreviation has been corrected.

Results

Lines 267–272: This passage resembles a discussion. I recommend moving it to the discussion section and removing it from the results. Apply the same suggestion to any similar content throughout the results section.

 Authors: Thank you for your comment. The suggested changes have been implemented, and similar content has been relocated to the discussion section as recommended.

 

Line 324: “Unit” is too generic. Indicate the exact unit of measurement (e.g., %, kg, g/day, etc.).

Authors: Thank you for your comment. We have revised the text to specify exact measurement units for each variable (e.g., NDF in % DM, methane emissions in g/day), replacing the generic term ‘unit’ to improve clarity and scientific accuracy.

Discussion: Since the results are presented using subheadings, consider using subheadings in the discussion section as well to improve clarity and organization.

 Authors: Thank you for the suggestion. The corrections have been made as recommended.

The discussion should aim to explain how the results were obtained. To do this effectively, incorporate relevant theories, biological or physiological mechanisms, and environmental or methodological justifications. Currently, the discussion provides a good general review, describes the results (which should be avoided to prevent repetition), and compares findings with those of other authors. However, it lacks a deeper analysis of the mechanisms behind the results.

 Authors: We appreciate this insightful comment. In the revised discussion, we have incorporated biological mechanisms (rumen fermentation, methanogenesis, nutrient metabolism), physiological explanations (feed efficiency, energy partitioning), and methodological justifications (non-linear dynamics captured by ML models) to explain how our results were obtained, rather than only describing them.

Lines 398–399: Ensure correct citation and that the reference appears in the reference list.

 Authors: Thank you for the reminder. I've checked and ensured all citations are correctly formatted and included in the reference list.

Lines 408–427: This section is too general and lacks depth. Consider rewriting or removing it.

 Answer: Thank you for the feedback. I’ve expanded the discussion section to provide deeper insights into the biological mechanisms and practical implications of the findings, while preserving the original structure.

 

Lines 445–446: This is a comparative statement between current findings and literature data. Rewrite it to reflect a deeper analysis as part of the discussion.

Authors: Thank you for the insightful comment. I’ve revised the statement to include a deeper analysis of why non-linear models performed better, emphasizing the biological and statistical implications of the findings.

 

Conclusion: The conclusion should be more objective and concise, emphasizing the main findings of the study. After this, you may include implications, limitations, and potential future research directions.

Authors: Thank you for the constructive feedback. I’ve revised the conclusion to be more concise and objective, clearly emphasizing the main findings, followed by practical implications, study limitations, and directions for future research.

 

Reviewer 4 Report

Comments and Suggestions for Authors

Keywords:
Review the keywords. It is recommended that they do not include words already used in the manuscript title.

Introducion:

Line 68: “Methane acounts for nearly 37% of GHG emissions” - It was previously stated that CH₄ represents 16% (line 46), but now it appears as 37% (line 69).

Line 72: “with beef cattle alone responsible for approximately 15% of methane emissions arising from manure” - cattle alone are responsible for approximately 15% of emissions?

Materials and Method:

Line 100: “Prior to analysis, the dataset underwent data preprocessing to handle missing values and ensure data integrity” - does not explain how (exclusion, imputation, normalization?). This compromises reproducibility.

Suggestion: include a flowchart of article selection (adapted for metadata) and detail the data standardization process.

Line 126: Why not use the same algorithm for all data?

Lack of clarity in the experimental design; it was not reported whether there was a training/test division.

Include sentences that indicate the reason for each analysis in terms of ruminant nutrition. What relationships can be explored using Bayesian networks?

Results:

Line 185: Correlations are listed but not interpreted in the context of ruminant nutrition. I suggest bringing up these relationships (why could crude protein reduce methane? Relationship with nitrogen utilization efficiency?)

Line 220: The authors mention conversion efficiency, but do not discuss factors such as higher DM intake in large, high-producing cows.

Line 247: The description of the Bayesian network results is confusing.

Line 252 and 253: “upstream and downstream” without prior definition.

Line 274: BIC values and arc strength – both appear together without clear explanation.

Line 351: Production results (R² = 0.196): extremely low, but the text does not discuss the reason (possible noise in the data, genetic variability, database limitations).

Discussion:

I suggest further developing the discussion section. In this section, it would be interesting if the author's justification always came first, explaining the results, and secondly, the citations that support this justification.

Lines 408–419 repeat section 3.1 almost verbatim (DM, OM, CP, NDF, ADF correlations).

Line 421: The Bayesian network section also merely reiterates the results without offering any physiological/zootechnical interpretation.

There is no discussion of contradictions or unexpected findings (e.g., CP had a negative correlation, but it was not statistically significant → why? Effect of protein form? Digestibility limitation?).

Few main citations (Pszczola 2019; Li-feng 2022). Classic and recent references are missing (Knapp et al., 2014 – ruminal methane; Gerber et al., 2013 – FAO mitigation strategies).

The discussion does not connect the findings well with their applicability in dairy cow management. Example: if NDF is a strong predictor → what does this mean for the formulation of diets for high-yield cows? If GP and SPL are the best models → how does this help nutritionists or monitoring systems?

Conclusion - The conclusion does not end the work, it merely reiterates that the study dealt with the environmental impact of methane, and that NDF/ADF/DM are relevant. Consider summarizing the main conclusions in one or two sentences, highlighting only the most relevant results and their direct implications.

 

Author Response

Dear Editor

We would like to sincerely thank you and the reviewers for the time and effort dedicated to evaluating our manuscript entitled “Exploring methane emission dynamics using Bayesian networks and machine learning analysis of nutritional and production traits in dairy cattle.”  We greatly appreciate the constructive feedback provided, which has helped us strengthen and clarify the manuscript. In response to the reviewers’ comments, we have carefully revised the manuscript to address all suggestions and concerns. Key revisions include:

Corresponding Author

Reviewer # 4

Keywords:
Review the keywords. It is recommended that they do not include words already used in the manuscript title.

Authors: Thank you for the suggestion. I've reviewed and updated the keywords to avoid repetition with the title.

Introduction:

Line 68: “Methane acounts for nearly 37% of GHG emissions” - It was previously stated that CH₄ represents 16% (line 46), but now it appears as 37% (line 69).

Authors: Thank you for pointing this out. The 16% figure represents methane’s share of total GHG emissions by mass, whereas the 37% figure is based on CO₂-equivalent values (GWP₁₀₀), which weight methane according to its higher warming potential. We clarified this distinction in the text to avoid confusion.

Line 72: “with beef cattle alone responsible for approximately 15% of methane emissions arising from manure” - cattle alone are responsible for approximately 15% of emissions?

Authors: The figure “beef cattle alone responsible for approximately 15% of methane emissions arising from manure” is indeed correct and comes from the Kansas State University Extension publication by Liu (2012), which reports that in 2012, beef cattle accounted for 15% of the total methane emissions from manure management (with dairy cattle accounting for 46.7%). We did not find the same breakdown in either Maasakkers et al. (2023) or Minx et al. (2021), so the citation to Liu (2012) is the most appropriate reference for this statement.
We revised the manuscript to explicitly cite Liu (2012) for clarity.

 

Materials and Method:

Line 100: “Prior to analysis, the dataset underwent data preprocessing to handle missing values and ensure data integrity” - does not explain how (exclusion, imputation, normalization?). This compromises reproducibility.

Authors: Thank you for your suggestion. We have revised the Methods section to explicitly describe our preprocessing steps.

 

Suggestion: include a flowchart of article selection (adapted for metadata) and detail the data standardization process.

Authors: Thank you for your suggestion. As this comment aligned with feedback from other reviewers, we revised this section to include detailed sample sizes and an expanded description of the dataset. Because the data source and standardization process have already been fully described and discussed in two previously published papers, we summarized key elements here and added clarifying details for transparency.

 

Line 126: Why not use the same algorithm for all data?

Authors: Thank you for your comment and we revised the text. We used different Bayesian network algorithms for the two sets of variables (production traits vs. nutritional factors) because they were independent datasets and differed in structure, missing values, and imbalance across traits and factors. So, two one algorithm might work bets with one set not with the other one. We selected the best-performing algorithm for each dataset, prioritizing approaches that produced networks consistent with known biological relationships and ensured robust inference despite data imbalance.

Lack of clarity in the experimental design; it was not reported whether there was a training/test division.

Authors: Thank you for this observation. The primary goal of our study was to evaluate and quantify the relationships between production and nutritional factors and methane emissions, rather than to develop a predictive model. For this reason, we did not perform a formal training/test split or cross-validation. Our analyses focused on exploring patterns and identifying biologically relevant associations between variables, with emphasis on interpretability rather than prediction accuracy.

Include sentences that indicate the reason for each analysis in terms of ruminant nutrition. What relationships can be explored using Bayesian networks?

Authors: Thank you for the helpful suggestion. We revised the Materials and Methods section to explicitly explain the rationale behind each analysis in the context of ruminant nutrition. We clarified that LRTs and correlations were used to identify nutrient and production traits with the greatest influence on methane emissions, Bayesian networks were applied to uncover complex causal relationships and conditional dependencies between diet components and production variables, and machine learning models were used to optimize methane prediction accuracy for practical nutrition management.

 

Results:

Line 185: Correlations are listed but not interpreted in the context of ruminant nutrition. I suggest bringing up these relationships (why could crude protein reduce methane? Relationship with nitrogen utilization efficiency?)

Authors: We added an explanation connecting crude protein levels to nitrogen utilization efficiency and their potential effect on methane mitigation.

 

Line 220: The authors mention conversion efficiency, but do not discuss factors such as higher DM intake in large, high-producing cows.

Authors: We clarified that greater DM intake in high-yield cows influences methane emissions and relates to conversion efficiency.

 

Line 247: The description of the Bayesian network results is confusing.

Authors: We rewrote the section for clarity, explicitly describing upstream and downstream roles in the network to make interpretation easier.

 

Line 252 and 253: “upstream and downstream” without prior definition.

Authors: We defined “upstream” and “downstream” in the context of the Bayesian network.

 

Line 274: BIC values and arc strength – both appear together without clear explanation.

Authors: We clarified the complementary roles of BIC and arc strength to improve understanding.

 

Line 351: Production results (R² = 0.196): extremely low, but the text does not discuss the reason (possible noise in the data, genetic variability, database limitations).

Authors: We added a discussion on why the R² value is low, citing dataset heterogeneity, genetics, and noise.

 

Discussion:

I suggest further developing the discussion section. In this section, it would be interesting if the author's justification always came first, explaining the results, and secondly, the citations that support this justification.

Authors: Thank you for this helpful suggestion. We have revised the entire Discussion to follow the recommended structure, placing our justification and biological explanations first and then citing supporting literature. We also added new references where necessary to strengthen key points, clarify the mechanisms behind methane emissions, and better link findings to rumen fermentation dynamics, microbial ecology, and modeling complexity.

Lines 408–419 repeat section 3.1 almost verbatim (DM, OM, CP, NDF, ADF correlations).

Authors: Thank you for noting this repetition. We revised Lines 408–419 to remove verbatim text from the Results and instead emphasize interpretation, focusing on the biological relevance of fiber fractions and dry matter intake in methane production rather than restating correlations.

Line 421: The Bayesian network section also merely reiterates the results without offering any physiological/zootechnical interpretation.

Authors: We revised this section to include physiological interpretation, linking DM, OM, STR, and fiber effects to rumen fermentation processes, microbial ecology, and methane synthesis, rather than repeating results.

There is no discussion of contradictions or unexpected findings (e.g., CP had a negative correlation, but it was not statistically significant → why? Effect of protein form? Digestibility limitation?).

Authors: We added interpretation for the non-significant CP correlation, explaining variation due to protein source, degradability, and nitrogen dynamics, with supporting references

Few main citations (Pszczola 2019; Li-feng 2022). Classic and recent references are missing (Knapp et al., 2014 – ruminal methane; Gerber et al., 2013 – FAO mitigation strategies).

Authors: Thank you for the suggestion. We have now incorporated both classic and recent references.

 

The discussion does not connect the findings well with their applicability in dairy cow management. Example: if NDF is a strong predictor → what does this mean for the formulation of diets for high-yield cows? If GP and SPL are the best models → how does this help nutritionists or monitoring systems?

Authors: We revised the Discussion to clearly link findings to dairy cow management, explaining implications of NDF levels for diet formulation in high-yield cows and highlighting how GP and SPL models can support nutrition planning and methane monitoring systems.

Conclusion - The conclusion does not end the work, it merely reiterates that the study dealt with the environmental impact of methane, and that NDF/ADF/DM are relevant. Consider summarizing the main conclusions in one or two sentences, highlighting only the most relevant results and their direct implications.

 Authors: The Conclusion section was entirely revised to provide a concise summary of key findings and their practical implications, which we believe fully addresses and mitigates this comment.

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

Once again, I believe it is necessary for the authors to remove the discussion currently presented in the Results section and relocate it to the Discussion section. Interpretative or analytical commentary should be avoided in the Results section.

Author Response

Dear Editor

We are pleased to resubmit our revised manuscript entitled “Exploring methane emission dynamics using Bayesian networks and machine learning analysis of nutritional and production traits in dairy cattle” for consideration in Methane journal. We would like to sincerely thank you and the reviewers for the constructive comments and suggestions, which have been very helpful in improving the quality and clarity of our work.

In this revised version, we carefully addressed all reviewer comments. Specifically, we have:

• Relocated interpretative and analytical commentary from the Results section to the Discussion, ensuring the Results present only descriptive findings.
• Improved the clarity and presentation of figures and tables as recommended.
• Revised several sections to enhance readability and ensure better alignment between the Results and Discussion.

We believe that these revisions have strengthened the manuscript considerably. A detailed, point-by-point response to the reviewers’ comments is included for your consideration.

We appreciate your time and efforts in handling our submission and look forward to your favorable response.

Sincerely,

Corresponding Author

Mohammadreza Mohammadabadi, Ph.D

Department of Animal Science, Faculty of Agriculture

Shahid Bahonar University of Kerman, Kerman, Iran

 

 

Response to reviewer’s comments:

A- For the Correlation section, we made the following revisions and discussed them in the Correlations among diet ingredients and traits section:

• “This reflects that larger, high-producing cows consume greater amounts of feed to meet energy demands, resulting in proportionally higher methane output even if efficiency per unit of milk improves.”

 

• “…implying that higher organic matter may contribute slightly to methane production.”

 

• “…indicating that higher crude protein levels may result in lower methane emissions. This trend is consistent with improved nitrogen utilization efficiency, as protein supplementation can optimize rumen microbial growth and shift fermentation patterns away from methane-producing pathways, reducing methanogenesis per unit of feed intake.”

B- For Section 3.2 ME based on the body weight and milk yield, we transferred the following statement to the Production traits and milk composition section:

• “Our results showed methane intensity tends to decrease with increasing MY, regardless of body size. These findings are aligned with previous studies; for example, a study on Holstein cows found that methane intensity (CH₄-em, g/kg fat- and protein-corrected milk) was negatively correlated with MY, with correlations stronger than those with body weight [28].”

 

C- For Section 3.3 Bayesian network structure learning, we relocated the interpretative statements to the Discussion section to ensure that the Results present only descriptive findings.

• “These findings provide a systems-level view of how dietary composition and production variables are interconnected with methane emission, thereby enhancing our understanding of the factors shaping methane variability in dairy cows.”

 

• “Overall, the BIC score and strength values offer valuable information about the fit and interdependencies among variables in the Bayesian network.”

 

• “This highly suggests that increased CH₄-em is associated with a decrease in MY.”

 

• “This implies that higher CH₄-em levels may contribute to an increase in FAT percentage.”

 

D- For Section 3.4 Quantifying the influence of key factors on CH₄-em, we removed or relocated the following parts to the Discussion section in order to keep the Results strictly descriptive.

• “This finding highlights the importance of considering and managing NDF levels in the diet to mitigate CH₄-em from dairy cows.”

 

• “…showing that these factors may have less influence on methane production in the studied context than NDF.”

 

• “This low R² reflects high variability in production data across studies, potential genetic diversity among cattle populations, and heterogeneous measurement methods in the meta-dataset, which reduce predictive power despite significant effects of MY and FAT.”

E- For Section 3.5 Prediction using machine learning models (ML), we also relocated or removed the following parts to the Discussion section to maintain a clear separation between descriptive results and interpretation:

1. “LASSO feature selection ability might contribute to its performance when dealing with correlated predictors.”

1. “…indicating that it captures non-linear relationships between diet-related variables and methane emissions more effectively.”

1. “The GP probabilistic nature allows it to model uncertainty and capture complex non-linear relationships in the data.”

4. “These models, which assume linear relationships between production-related variables and methane emissions, appear to have limited predictive ability in capturing the variability in methane emissions based on production traits.”

 

Reviewer 4 Report

Comments and Suggestions for Authors

Hello, authors!

I would like to congratulate you on the care and attention you have taken in revising the manuscript. I was very pleased to see that all suggestions were considered and incorporated, from clarifications on methane emissions to detailed explanations of the analyses and physiological interpretation of the results. The way you connected the findings to ruminant nutrition and practical applications in dairy cow management made the study much clearer and more relevant.

Congratulations on your work!

Author Response

Dear Editor

We are pleased to resubmit our revised manuscript entitled “Exploring methane emission dynamics using Bayesian networks and machine learning analysis of nutritional and production traits in dairy cattle” for consideration in Methane journal. We would like to sincerely thank you and the reviewers for the constructive comments and suggestions, which have been very helpful in improving the quality and clarity of our work.

In this revised version, we carefully addressed all reviewer comments. Specifically, we have:

• Relocated interpretative and analytical commentary from the Results section to the Discussion, ensuring the Results present only descriptive findings.
• Improved the clarity and presentation of figures and tables as recommended.
• Revised several sections to enhance readability and ensure better alignment between the Results and Discussion.

We believe that these revisions have strengthened the manuscript considerably. A detailed, point-by-point response to the reviewers’ comments is included for your consideration.

We appreciate your time and efforts in handling our submission and look forward to your favorable response.

Sincerely,

Corresponding Author

Mohammadreza Mohammadabadi, Ph.D

Department of Animal Science, Faculty of Agriculture

Shahid Bahonar University of Kerman, Kerman, Iran

 

 

Response to reviewer’s comments:

A- For the Correlation section, we made the following revisions and discussed them in the Correlations among diet ingredients and traits section:

• “This reflects that larger, high-producing cows consume greater amounts of feed to meet energy demands, resulting in proportionally higher methane output even if efficiency per unit of milk improves.”

 

• “…implying that higher organic matter may contribute slightly to methane production.”

 

• “…indicating that higher crude protein levels may result in lower methane emissions. This trend is consistent with improved nitrogen utilization efficiency, as protein supplementation can optimize rumen microbial growth and shift fermentation patterns away from methane-producing pathways, reducing methanogenesis per unit of feed intake.”

B- For Section 3.2 ME based on the body weight and milk yield, we transferred the following statement to the Production traits and milk composition section:

• “Our results showed methane intensity tends to decrease with increasing MY, regardless of body size. These findings are aligned with previous studies; for example, a study on Holstein cows found that methane intensity (CH₄-em, g/kg fat- and protein-corrected milk) was negatively correlated with MY, with correlations stronger than those with body weight [28].”

 

C- For Section 3.3 Bayesian network structure learning, we relocated the interpretative statements to the Discussion section to ensure that the Results present only descriptive findings.

• “These findings provide a systems-level view of how dietary composition and production variables are interconnected with methane emission, thereby enhancing our understanding of the factors shaping methane variability in dairy cows.”

 

• “Overall, the BIC score and strength values offer valuable information about the fit and interdependencies among variables in the Bayesian network.”

 

• “This highly suggests that increased CH₄-em is associated with a decrease in MY.”

 

• “This implies that higher CH₄-em levels may contribute to an increase in FAT percentage.”

 

D- For Section 3.4 Quantifying the influence of key factors on CH₄-em, we removed or relocated the following parts to the Discussion section in order to keep the Results strictly descriptive.

• “This finding highlights the importance of considering and managing NDF levels in the diet to mitigate CH₄-em from dairy cows.”

 

• “…showing that these factors may have less influence on methane production in the studied context than NDF.”

 

• “This low R² reflects high variability in production data across studies, potential genetic diversity among cattle populations, and heterogeneous measurement methods in the meta-dataset, which reduce predictive power despite significant effects of MY and FAT.”

E- For Section 3.5 Prediction using machine learning models (ML), we also relocated or removed the following parts to the Discussion section to maintain a clear separation between descriptive results and interpretation:

1. “LASSO feature selection ability might contribute to its performance when dealing with correlated predictors.”

1. “…indicating that it captures non-linear relationships between diet-related variables and methane emissions more effectively.”

1. “The GP probabilistic nature allows it to model uncertainty and capture complex non-linear relationships in the data.”

4. “These models, which assume linear relationships between production-related variables and methane emissions, appear to have limited predictive ability in capturing the variability in methane emissions based on production traits.”