Review Reports - Structural Equation Modeling of Genetic and Residual Covariance Matrices for Multiple-Trait Evaluation in Beef Cattle

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The study does not propose a fundamentally new statistical model at the methodological level; rather, its innovation lies in a systematic application and comparative evaluation. Unlike most existing studies, which tend to focus on a single form of SEM, this work applies FA and REC simultaneously and independently to the additive genetic and residual covariance matrices, and conducts a comprehensive comparison using real beef cattle breeding data. In particular, the application of REC models at the level of covariance structures remains relatively uncommon in multi-trait genetic evaluation of beef cattle. The paper establishes a clear comparative framework linking model choice, parameter parsimony, and the stability of breeding value predictions, which provides practical relevance for breeding programs.

Nevertheless, the innovation of the study is mainly reflected in methodological integration and empirical validation rather than in theoretical development. In addition, the exploration of potential biological or causal interpretations remains relatively conservative.

The main aspects that require further revision and improvement can be summarized as follows:

Unclear criteria for model selection
The choice of the number of factors and model structures relies largely on empirical comparisons, and more explicit and reproducible selection criteria should be provided.
Empirical nature of recursive path pruning
The threshold used to remove recursive effects in the REC models appears somewhat arbitrary; justification or sensitivity analyses are recommended.
Insufficient biological and causal interpretation
The biological meaning of the recursive relationships and their causal interpretation are not explored in sufficient depth.
Limited generalizability of the results
The analysis is based on a single breed and a limited number of traits, and the applicability of the approach to other data scenarios should be discussed.

Recommendation: Accept with minor revisions.

The manuscript meets the journal’s publication standards in terms of methodological soundness, robustness of results, and practical relevance. The authors are encouraged to further clarify the criteria for model selection and to more clearly delineate the scope of applicability of the proposed methods in the discussion. These revisions are primarily refinements and do not involve substantive changes to the core conclusions of the study.

Author Response

Response-Reviewer1: Dear Reviewer 1: The authors would like to thank the reviewers and the editor for their insightful and constructive suggestions. The manuscript was substantially improved as a result of their valuable contributions, and all comments were carefully addressed. The manuscript was revised in accordance with the recommendations provided. The English and grammar have been revised for better comprehension, as suggested by the reviewer. We agree that the primary innovation of this study lies in the methodological integration and empirical validation, rather than in theoretical development. The exploration of causal relationships was conducted conservatively, with the objective of demonstrating the independent application of structural equation modeling. Nevertheless, additional discussion regarding causal effects and related aspects has been incorporated into the revised manuscript. Modifications are indicated in blue.

The main aspects that require further revision and improvement can be summarized as follows:

1-Unclear criteria for model selection: The choice of the number of factors and model structures relies largely on empirical comparisons, and more explicit and reproducible selection criteria should be provided: Response-Reviewer1: Agree. We have revised as suggested. The text in “Model selection criteria” section was reviewed and rewritten according to the suggestion. Because the objective was to evaluate structural equation models applied simultaneously and independently, and given the limitation to six traits, the maximum number of latent factors that could be considered for each covariance structure was three (which proved not to be a good option). Although models with four factors were initially explored, they failed to converge due to the limited number of traits, an issue that is now explicitly discussed throughout the manuscript. The relevant sections—Factor analytic models, Recursive models, and Discussion—have been revised and rewritten in accordance with this suggestion.

2- Empirical nature of recursive path pruning: The threshold used to remove recursive effects in the REC models appears somewhat arbitrary; justification or sensitivity analyses are recommended. Response-Reviewer1: Agree. We have revised as suggested. The exploration of causal relationships was conducted empirically, with the objective of demonstrating the effectiveness of recursive models when applied simultaneously and independently, as discussed in the Discussion section. In accordance with reviewers’ suggestions, additional discussion regarding model performance and effectiveness has been incorporated into the manuscript. The criteria used to exclude recursive effects in the REC models may appear somewhat arbitrary, as the primary objective of the causal exploration was to demonstrate the practical applicability of structural equation modeling through recursive formulations, particularly in scenarios where measurements of a given trait obtained at an earlier age may influence traits recorded at a later age, as discussed in the Discussion section. In the present study, because all traits were measured contemporaneously, we explored the empirically derived ordering from the fully recursive model (FRM) and removed small recursive effects. Specifically, an empirical threshold of approximately two standard deviations was applied in the REC1 model, whereas alternative empirical thresholds (e.g., 0.15) were adopted in the remaining models, as described in the Recursive models section. In accordance with reviewers’ suggestions, additional discussion regarding these remove recursive effects in the REC models has been incorporated into the manuscript.

3- Insufficient biological and causal interpretation. The biological meaning of the recursive relationships and their causal interpretation are not explored in sufficient depth. Response-Reviewer1: Agree. We have revised as suggested. We re-worked as suggested, and a text was inserted in the “Discussion” section.)

4- Limited generalizability of the results: The analysis is based on a single breed and a limited number of traits, and the applicability of the approach to other data scenarios should be discussed. Response-Reviewer1: Agree. We have revised as suggested. We re-worked as suggested, and a text was inserted in the “Discussion” section.

Recommendation: Accept with minor revisions.

Reviewer 2 Report

Comments and Suggestions for Authors

Major concerns

2. In the Discussion section, there are only two references 30 (2004), 31 (2001), the times are twenty years before.

3. Previous studies have used SEM for genetic evaluation, what is the novelty of this study?

4. Why choose Nellore cattle and its representativeness in Brazilian beef cattle breeding?

5. In the Discussion section, please explain why the FA model performs poorly when there is a high genetic correlation.

6. In the Discussion section, for the REC1 model, removing 6 recursive effects from the residual matrix could be discussed as to why these effects are not significant.

7. The limitations of this study should be added, such as dataset size, limited number of traits, and SC being limited to males only, which may affect the performance of models such as FA3.

8. English grammar and writing should be checked and revised throughout the manuscript.

Minor concerns

1. Line 22, ‘Structural equation models (SEM)’ VS Lines 27-28, ‘structured covariance matrices (SEM)’.

2. Lines 46, 130, 222, Table 2, 311, there are five ‘standard multiple-trait mixed models (SMTM)’.

3. Lines 61, 129, there are two ‘recursive (REC)’.

4. Lines 71, 129, there are two ‘factor analysis (FA)’.

5. A hypothesis of this study should be added at the end of Introduction section.

6. Line 118, revise ‘contemporary groups (CG)’ to ‘contemporary groups (CGs)’.

7. Lines 243, 276, there are two ‘deviance information criterion (DIC)’.

8. The format of references is inconsistent. For example,

Ref. 1, with DOI VS Ref. 6, without DOI.

Comments on the Quality of English Language

The English could be improved to more clearly express the research.

Author Response

In present work, Yokoo et al. try to use structural equation models (SEM) to estimate parameters for growth and ultrasound carcass traits in beef cattle. This study showed that mixed-effects multi-trait models in beef cattle could be successfully analyzed with FA or REC models. However, there are some concerns. Response-Reviewer2: Dear Reviewer 2: The authors would like to thank the reviewers and the editor for their insightful and constructive suggestions. The manuscript was substantially improved as a result of their valuable contributions, and all comments were carefully addressed. The manuscript was revised in accordance with the recommendations provided. The English and grammar have been revised for better comprehension, as suggested by the reviewer. Modifications are indicated in blue.

Major concerns

1. The key methods used in this study are very old. Please see the Statistical Analyses section, the references 24 (2014), 25 (2014), 26 (1992), 27 (2007), 28 (2002), 29 (2014), the times are ten years before. In addition, the present study used data from 2,942 Nellore animals collected over 3 years (Line 102), from which year? Response-Reviewer2: As noted by the first reviewer, this study does not propose a novel statistical model from a methodological standpoint. Rather, its contribution lies in the methodological integration that enables the simultaneous and independent application of structural equation modeling within additive genetic and residual (co)variance matrices, combining concepts from earlier foundational studies through the use of recursive and factor-analytic models in genetic evaluation. This approach differs from most existing studies, which focus on a single structural equation modeling framework. This aspect is now discussed in greater depth in the revised manuscript, in accordance with the reviewers’ suggestions. Given that recursive and factor-analytic methodologies are well established and theoretically sound in other fields, the use of these earlier references is therefore justified. The data used in this study were collected between 2004 and 2006 and, in order to avoid reliance on simulated data, a real dataset was analyzed, comprising six traits measured on the same animals, on the same day, and under identical conditions. This characteristic is particularly important for comparing models that estimate causal relationships, an issue that is now explicitly discussed throughout the manuscript following the reviewers’ recommendations.

2. In the Discussion section, there are only two references 30 (2004), 31 (2001), the times are twenty years before. Response-Reviewer2: It is important to acknowledge the pioneering studies in this field; however, more recent and up-to-date references have also been incorporated into the revised manuscript.

3. Previous studies have used SEM for genetic evaluation, what is the novelty of this study? Response-Reviewer2: The novelty of this study resides in the independent and/or joint application of structural equation modeling approaches. Specifically, within a single evaluation framework, recursive structures may be specified for the genetic covariance matrix, while factor-analytic structures may be simultaneously applied to the residual covariance matrix, provided that model fit is improved. These considerations and methodological extensions have now been incorporated into the manuscript in response to the reviewers’ suggestions.

4. Why choose Nellore cattle and its representativeness in Brazilian beef cattle breeding? Response-Reviewer2: The Nelore cattle dataset was selected to avoid reliance on simulated data and because it comprises real phenotypic records collected on the same animals on the same day, a feature that is particularly important for the objectives of this study. In addition, Nelore is the predominant beef cattle breed in Brazil, representing approximately 70% of the national beef cattle population.

5. In the Discussion section, please explain why the FA model performs poorly when there is a high genetic correlation. Response-Reviewer2: Agree. We have revised, rewrote and added more explanation to the text as suggested in the "Discussion" section.

6. In the Discussion section, for the REC1 model, removing 6 recursive effects from the residual matrix could be discussed as to why these effects are not significant. AR2.: Response-Reviewer2: Agree. We have revised, rewrote and added more explanation to the text as suggested in the "Discussion" section.

7. The limitations of this study should be added, such as dataset size, limited number of traits, and SC being limited to males only, which may affect the performance of models such as FA3. Response-Reviewer2: Agree. We have revised the manuscript as suggested. We have rewrote and added more explanation to the text as suggested in the "Discussion" section.

8. English grammar and writing should be checked and revised throughout the manuscript. Response-Reviewer2: Agree. We checked the grammar, writing, and English throughout the article, and corrections were made as suggested.

Minor concerns

1. Line 22, ‘Structural equation models (SEM)’ VS Lines 27-28, ‘structured covariance matrices (SEM)’. Response-Reviewer2: Agree. We have revised as suggested.

2. Lines 46, 130, 222, Table 2, 311, there are five ‘standard multiple-trait mixed models (SMTM)’. Response-Reviewer2: Agree. We have revised as suggested.

3. Lines 61, 129, there are two ‘recursive (REC)’. Response-Reviewer2: Agree. We have revised as suggested.

4. Lines 71, 129, there are two ‘factor analysis (FA)’. Response-Reviewer2: Agree. We have revised the manuscript as suggested.

5. A hypothesis of this study should be added at the end of Introduction section. Response-Reviewer2: Agree. We have revised as suggested. A paragraph describing the hypothesis of this study has been added at the end of the Introduction section, as suggested.

6. Line 118, revise ‘contemporary groups (CG)’ to ‘contemporary groups (Cgs)’. Response-Reviewer2: Agree. We have revised as suggested.

7. Lines 243, 276, there are two ‘deviance information criterion (DIC)’. Response-Reviewer2: Agree. We have revised the manuscript as suggested.

8. The format of references is inconsistent. For example, Ref. 1, with DOI VS Ref. 6, without DOI. Response-Reviewer2: Agree. We have revised the manuscript as suggested.

Reviewer 3 Report

Comments and Suggestions for Authors

Title: Structural equation modelling of additive genetic and residual covariance matrices in beef cattle

General Comments

This study evaluated the use of structural equation models, specifically factor-analytic and recursive parameterizations, as parsimonious alternatives to standard multi-trait mixed models for estimating additive genetic and residual covariance matrices in Nellore cattle.

Major Comments

The criteria used to zero-out recursive effects appear ad hoc and appear to be insufficiently justified and are arbitrary. Please clarify or justify the choice of these thresholds.

This dataset includes only six traits with an uneven number of records across traits. These limitations may impact the performance of FA models but this is only acknowledged briefly. I would consider expanding the discussion on how sample size, trait imbalance, and number of traits may influence stability and usefulness of FA and REC models.

Minor Comments

There is some redundancy between your Results and Discussion sections that could be reduced to improve readability.

Author Response

General Comments

Overall, this manuscript is well written and addresses a topic relevant to modern livestock breeding programs. The statistical methodology is sound and results are clearly presented. However, this study appears to confirm patterns already reported in literature rather than providing substantial new methodology or biological insights. Interpretation of latent factors and recursive relationships appears to be limited in some areas. Additionally, some modelling choices and claims are weakly justified. Addressing these issues would strengthen your manuscript as a whole. Response-Reviewer3: Dear Reviewer 3: The authors would like to thank the reviewers and the editor for their insightful and constructive suggestions. The manuscript was substantially improved as a result of their valuable contributions, and all comments were carefully addressed. The manuscript was revised in accordance with the recommendations provided. Modifications are indicated in blue.

Major Comments

The advantages and limitations of FA and REC models in multi-trait genetic evaluations have been discussed in previous studies, many of which you have cited. I think your manuscript would benefit from discussing what is fundamentally new or different when compared to prior research. Has this type of modelling been done specifically with Nellore cattle before? Please clarify what is specifically novel about this study. Response-Reviewer3: As noted by the first reviewer, this study does not introduce a novel statistical model from a methodological perspective. Rather, its contribution lies in the methodological integration that allows the simultaneous and independent specification of structural equation modeling within the additive genetic and residual (co)variance matrices, combining concepts from earlier foundational studies through the joint use of recursive and factor-analytic models in genetic evaluation. This approach differs from most existing studies, which typically focus on a single structural equation modeling framework. This aspect is now discussed in greater depth in the revised manuscript, in accordance with the reviewers’ suggestions. Given that recursive and factor-analytic methodologies are well established and theoretically sound across other species and breeds, the application to the Nellore dataset is both appropriate and informative.

Your FA and REC models/effects are discussed primarily from a statistical perspective, which is a strength of this manuscript. However, this manuscript would benefit from greater biological interpretation and speculation of latent factors and recursive relationships. As SEMs are often promoted for their interpretability, additional biological context could strengthen results. Response-Reviewer3: Agree. We have revised the manuscript as suggested. These discussions regarding the interpretation of causal effects, the biological context, and other related topics were added to the discussion section.

The criteria used to zero-out recursive effects appear ad hoc and appear to be insufficiently justified and are arbitrary. Please clarify or justify the choice of these thresholds. Response-Reviewer3: Agree. We have revised as suggested. The exploration of causal relationships was conducted empirically, with the objective of demonstrating the effectiveness of recursive models when applied simultaneously and independently, as discussed in the Discussion section. In accordance with reviewers’ suggestions, additional discussion regarding model performance and effectiveness has been incorporated into the manuscript. The criteria used to exclude recursive effects in the REC models may appear somewhat arbitrary, as the primary objective of the causal exploration was to demonstrate the practical applicability of structural equation modeling through recursive formulations, particularly in scenarios where measurements of a given trait obtained at an earlier age may influence traits recorded at a later age, as discussed in the Discussion section. In the present study, because all traits were measured contemporaneously, we explored the empirically derived ordering from the fully recursive model (FRM) and removed small recursive effects. Specifically, an empirical threshold of approximately two standard deviations was applied in the REC1 model, whereas alternative empirical thresholds (e.g., 0.15) were adopted in the remaining models, as described in the Recursive models section. In accordance with reviewers’ suggestions, additional discussion regarding these remove recursive effects in the REC models has been incorporated into the manuscript.

Trait ordering in REC models is only briefly mentioned in L 270 – L 274, where causal flow is assumed from left to right. Please justify your chosen trait ordering and consider briefly discussing whether alternative orderings were considered or could impact your results. Response-Reviewer3: Agree. We have revised as suggested. The table 5 header has been rewritten for better understanding of the results. In addition, one sentence was rewritten for better understanding.

Minor Comments

There is some redundancy between your Results and Discussion sections that could be reduced to improve readability. Response-Reviewer3: Agree. We have revised the manuscript as suggested and some sentences have been rewritten in these two sections to remove redundancies and improve reading flow.

You introduce the FA3F model in your Methods (L225 – L228) without a clear biological or statistical justification. It is later shown to be the poorest performing model (L280 – L284). Although its poor performance is later discussed (L330 – L348), the rationale for its inclusion in the model set should be clarified. Response-Reviewer3: Agree. We have revised the manuscript as suggested and we explain the criteria for choosing all FA models in more detail in the “Factor analytic models” section.

Reviewer 4 Report

Comments and Suggestions for Authors

I am reviewing the manuscript entitled "Structural equation modelling of additive genetic and residual covariance matrices in beef cattle" by Yokoo et al, submitted to MDPI Animals.

In this manuscript, the authors tested two SEM approaches in a six-trait beef cattle dataset and compared the fit and the parameter reduction when compared to a traditional multi-trait model.

The manuscript is well written, and the methodology contains many details that are important for readers who are not familiar with the methodology. There are a few small flaws in the method, but they do not harm research reproducibility.

Some results could be further explored, especially the recursive effects and causality.

Finally, the suggestion of implementing such approaches in large datasets cannot be confirmed, since the authors only examined 3k animals. This reviewer doesn't think it harms the manuscript; however, such conclusions must be made with an extra level of caution.

Specific comments:

L26: first sentence states the importance of changes due to the large number of records, but only 3k animals were tested.

L32: Please, explain this sentence better as it is a bit confusing.

L47: define unstructured covariance matrices

L 106: rewrite this 'ultrasson methodology was applied' sentence, as it sounds a bit odd

L 119: define management group

L 125 to 129: This paragraph is a bit odd under this header; perhaps moving it up or rewording can improve it

L 130: Why not an animal model?

L 160: Please, clarify that u is the ebv vector.

L 199: Not all equations are numbered and equation (4) is not numbered

L210: Assuming the models will be described below (they were, but please consider adding it into the text)

Results: Any difference expected or observed with the se/pev of ebvs?

Table 5: is there a better way to show those results? Perhaps some sort of graph would be easier to interpret than a table

L 316: This was not tested, so it may be too early to make such recommendations

L 366: Can results from REC1 be used in this manuscript to make such interpretations? I would be very interested in looking into this discussion if that fits the author's objectives

Author Response

General Comments

I am reviewing the manuscript entitled "Structural equation modelling of additive genetic and residual covariance matrices in beef cattle" by Yokoo et al, submitted to MDPI Animals.

In this manuscript, the authors tested two SEM approaches in a six-trait beef cattle dataset and compared the fit and the parameter reduction when compared to a traditional multi-trait model.

Some results could be further explored, especially the recursive effects and causality.

Response-Reviewer4: Agree. Dear Reviewer#4, we agree with your comments, and additional discussion has been included in the Discussion section addressing the role of causal effects to further emphasize model interpretability and causality. Furthermore, as pointed out, the conclusions and discussions regarding the application of these models were carefully rewritten, addressing the size of the dataset and the number of traits, as well as the breed in question.

Specific comments:

L26: first sentence states the importance of changes due to the large number of records, but only 3k animals were tested. Response-Reviewer4: Agree. We have revised the manuscript as suggested. As highlighted by Reviewer 4, we rewrote and expanded the discussion to more explicitly address the number of animals and traits evaluated, the applicability of the proposed models, and the specific breed under study.

L32: Please, explain this sentence better as it is a bit confusing. Response-Reviewer4: Agree. We have revised the sentence as suggested.

L47: define unstructured covariance matrices. Response-Reviewer4: Agree. We have revised the sentence as suggested.

L 106: rewrite this 'ultrasson methodology was applied' sentence, as it sounds a bit odd.Response-Reviewer4: Agree. We have revised the sentence as suggested.

L 119: define management group. Response-Reviewer4: Agree. We revised the sentence as suggested and defined the management group.

L 125 to 129: This paragraph is a bit odd under this header; perhaps moving it up or rewording can improve it. Response-Reviewer4: Agree. We have revised and rewrote the sentence as suggested.

L 130: Why not an animal model?.Response-Reviewer4: For all models, breeding values were estimated using a sire model exclusively to reduce computational burden and ensure feasibility of the genetic evaluations.

L 160: Please, clarify that u is the ebv vector. Response-Reviewer4: Agree. We have revised the sentence as suggested.

L 199: Not all equations are numbered and equation (4) is not numbered. Response-Reviewer4: Agree. We have revised the equations as suggested.

L210: Assuming the models will be described below (they were, but please consider adding it into the text). Response-Reviewer4: Agree. We have revised and rewrote the sentence as suggested.

L 247: The authors use both estimated and predicted breeding values in the manuscript. Please, choose one for consistency. - I would dare to preach to the authors about the differences, I am just stating that for consistency:). Response-Reviewer4: Agree. Every manuscript was reviewed and the word "estimated" was used instead of "predicted", as suggested.

Results: Any difference expected or observed with the se/pev of ebvs? Response-Reviewer4: Agree. We have revised as suggested. For all models, breeding values were estimated using a sire model exclusively to reduce computational burden and ensure feasibility of the genetic evaluations. Under this modeling choice, direct comparison of breeding value accuracies across models based on the heritability estimates derived from each approach. Accordingly, heritability estimates obtained from each model were used as an objective and theoretically justified proxy for comparing expected selection accuracy. This rationale and its implications have now been explicitly discussed in the Discussion section.

Table 5: is there a better way to show those results? Perhaps some sort of graph would be easier to interpret than a table. Response-Reviewer4: Agree. We have revised as suggested. The table header has been rewritten for better understanding of the results. In addition, one sentence was rewritten for better understanding.

L 297: Authors do not explain how the EBVs were calculated. Did you fix the variances and ran another round of iterations? Or used the average ebv across the 146k samples? Please, include that in the methods. Response-Reviewer4: We agree that the sentence in line 297 was poorly formulated and have therefore rewritten it. In the present study, breeding values were estimated jointly with all other model parameters, without fixing any variance components. The intention of the original sentence was to clarify that, in routine genetic evaluation programs adopting SEM, breeding values are typically predicted using BLUP for computational efficiency; under such circumstances, variance components are necessarily fixed in order to preserve the estimation of breeding values and their accuracies across different genetic evaluations. Some of the materials and methods explaining the estimates were also rewritten.

L316: This was not tested, so it may be too early to make such recommendations. Response-Reviewer4: Agree. We have removed that sentence as suggested.

L366: Can results from REC1 be used in this manuscript to make such interpretations? I would be very interested in looking into this discussion if that fits the author's objectives. Response-Reviewer4: Agree. REC1 can not make such interpretations. We have removed those two sentences as suggested.

Reviewer 5 Report

Comments and Suggestions for Authors

This manuscript presents a well-structured and scientifically sound evaluation of factor-analytic and recursive models for multi-trait genetic evaluation in beef cattle. The methodology looks appropriate, the results are clearly presented, and the conclusions are supported by the findings.

Minor clarifications could further strengthen the manuscript. In particular, the discussion could briefly address why heritability estimates were not discussed in greater detail and how they could affect genetic selection, especially given their central role in genetic evaluation. Additionally, some statements regarding the limitations of factor-analytic models for estimating high correlations may benefit from further contextualization, and references to “causal effects” in recursive models could be softened to emphasize interpretability rather than definitive causality.

Overall, this is a strong study that would benefit only from minor revision.

Author Response

General Comments

Overall, this is a strong study that would benefit only from minor revision.

Response-Reviewer5: Agree. Dear Reviewer#5, we agree with your comments, and additional discussion has been included in the Discussion section addressing how heritability estimates—and consequently selection—are affected by the choice of model, the limitations of factor-analytic (FA) structures under high correlations with appropriate contextualization, and the role of causal effects to further emphasize model interpretability.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Thanks for author’s responses. However, this Reviewer STILL does not agree with publication in Animals.

Table 1, only descriptive statistics of ultrasound carcass and growth traits in Nellore cattle. However, there is no an ultrasound image.
This study only reported using digital data which are easy to change. Raw data should be provided for review.
In the Discussion section, there are only several references, and there is no a reference in some paragraphs (Lines 310-326, 337-345, 346-358, 386-402, and 419-440).
In general, the data is limited for publication in Animals.

Comments on the Quality of English Language

The English could be improved to more clearly express the research.

Author Response

Dear Reviewer 2: Once again, the authors would like to thank you for this second round of review. The manuscript has been improved. The manuscript has been revised according to your recommendations. Throughout the manuscript, as suggested, the English and grammar have been revised for better comprehension. The modifications are indicated in purple.

Table 1, only descriptive statistics of ultrasound carcass and growth traits in Nellore cattle. However, there is no an ultrasound image. Dear Reviewer 2: Two ultrasound images have been added.

This study only reported using digital data which are easy to change. Raw data should be provided for review. Dear Reviewer 2: The data has been made available.

In the Discussion section, there are only several references, and there is no a reference in some paragraphs (Lines 310-326, 337-345, 346-358, 386-402, and 419-440). Dear Reviewer 2, all of these paragraphs mentioned have been duly discussed with the corresponding citations.

In general, the data is limited for publication in Animals. Dear Reviewer 2: The data were used because they represent real data and did not need to be simulated. The data has been made available.

Comments on the Quality of English Language
The English could be improved to more clearly express the research.
Dear Reviewer 2: As suggested, the manuscript has had its English and grammar revised for better comprehension. The modifications are indicated in purple.

Reviewer 3 Report

Comments and Suggestions for Authors

My only change is a minor grammatical change at L101 where "be apply" should be "be applied." Other than that, I am satisfied and thank you for your thoughtful and detailed responses to my questions, comments, and concerns.

Author Response

Dear Reviewer 3: Once again, the authors would like to thank you for this second round of review. The manuscript has been improved. The manuscript has been revised according to your recommendations. Throughout the manuscript, as suggested, the English and grammar have been revised for better comprehension. The modifications are indicated in purple.