Enhancing Genomic Prediction Accuracy in Beef Cattle Using WMGBLUP and SNP Pre-Selection

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

While the manuscript is generally well-structured and addresses an important challenge in multi-population genomic selection, significant clarifications and additional analyses are needed—particularly around parameter justification, sensitivity to key design choices, deeper discussion of limitations, and, ideally, validation on real data—before it is suitable for publication.

1. You simulate five populations (A–E) with specific sizes, replacement rates, growth rates, etc. (Table 1). Can you provide more rationale—based on real Chinese beef-cattle breeding programs—for why these exact values were chosen and how sensitive your results are to them?
2. You divide each population into a GWAS group (3,200), a GP training set (4,000), and a test set (800). Why these proportions? Have you tested alternative splits (e.g., smaller GWAS group) to ensure your conclusions hold? ​
3. POPCORN was used to select A, B, E based on “varying kinship” (Fig. 3), but details of how thresholds were set are missing. What cutoff did you use, and why? Can you include the numeric correlations and a brief interpretation in the main text? ​
4. You include significant PCs (P < 0.05) as covariates in the MLM (Eq. 1). How many PCs were retained per scenario? Could population structure confound the discovery of truly causal SNPs, especially in small simulated populations?
5. You evaluate top 5–25% SNPs by GWAS P-value. Why was 25% chosen as the upper bound? Have you explored finer gradations (e.g. 2%, 1%) or a data-driven cutoff (e.g. Bonferroni)? ​
6. The weight for locus k is defined as –log₁₀(pₖ). Can you justify this choice versus other weighting schemes (e.g. squared effect size, Bayesian posterior variance)? How sensitive are results to the logarithmic transform? ​
7. You fit GBLUP in GCTA and WMGBLUP/MGBLUP in DMUAI (DMU). What convergence criteria and priors (if any) were used? Did all runs converge reliably across replicates?
8. Apart from GBLUP, MGBLUP, WMGBLUP, there are other single-step or Bayesian models (e.g. ssGBLUP, BayesB). Why were these not included, and how might they perform relative to your WMGBLUP?
9. All analyses are based on simulation. To demonstrate practical utility, can you apply your top-performing WMGBLUP (top 5% SNPs) to an actual beef-cattle dataset, even if smaller, and report empirical accuracy?
10. You observe that adding population E (closer kinship) improves accuracy more than adding B (more distant) at 3:1 and 1:1 ratios. Can you discuss how this finding might inform the design of reference panels in practice?
11. Please expand on limitations: e.g., only additive effects simulated, no dominance/epistasis; no environmental interactions; fixed heritability of 0.3. How might these factors alter your conclusions
12. Figures 1–3 and Tables 1–7 contain a wealth of detail but are dense. Consider moving some tables to Supplementary Material and summarizing key trends in the main text.
13. Will you make your QMSim scripts, GCTA/DMU configuration files, and analysis code publicly available (e.g., GitHub) to ensure reproducibility?

Author Response

Comments 1: You simulate five populations (A–E) with specific sizes, replacement rates, growth rates, etc. (Table 1). Can you provide more rationale—based on real Chinese beef-cattle breeding programs—for why these exact values were chosen and how sensitive your results are to them?

Response 1: Thank you for pointing this out. The parameter values in Table 1 were determined by referring to two relevant literatures on beef cattle simulation parameters and the actual breeding parameters of Chinese beef cattle breeds such as Huaxi Cattle. In the actual beef cattle breeding in China, there is a rich variety of breeding models. Large-scale farms usually have a relatively large number of breeding cows. Considering the functions and management costs of bulls, the number of bulls is relatively small. In our simulated population A, we set the initial number of cows to 2,800 and the initial number of bulls to 60. These parameters are based on the actual situation of medium-sized farms in China, conforming to the reasonable ratio of bulls to cows in actual breeding and contributing to the efficient conduct of breeding activities. What’s more, regarding the setting of replacement rates, as the semen quality and reproductive capacity of bulls decline with age, in actual breeding, a new batch of bulls usually needs to be replaced every 2-3 years. Therefore, we set the bull replacement rate in the range of 0.5-0.6. Specifically, the bull replacement rate for populations A and B is 0.5, and for populations C and E is 0.6, which is highly consistent with the actual breeding scenario. In the case of cows, taking Huaxi cattle as an example, a replacement rate of around 30% is common in the industry. This rate can not only eliminate individuals with poor reproductive performance but also introduce high-quality genes, effectively maintaining the genetic diversity and reproductive efficiency of the population. Based on this, we uniformly set the cow replacement rate for each simulated population to 0.3. In this study, the parameters of the simulated populations were slightly modified based on those of the real populations to achieve the effect of simulating the real populations. Therefore, no horizontal comparison was conducted among different parameter settings.

Comments 2: You divide each population into a GWAS group (3,200), a GP training set (4,000), and a test set (800). Why these proportions? Have you tested alternative splits (e.g., smaller GWAS group) to ensure your conclusions hold?

Response 2: Thank you for raising this important question regarding the partitioning of populations into GWAS (3,200), GP training (4,000), and test (800) sets. The GWAS (3,200) was chosen to balance the need for sufficient samples to detect significant SNPs under limited computational resources, while the GP training set (4,000) was referenced from the actual reference population size of 4,000 head in the Huaxi Cattle breeding program. It provides a reference for the use of real data in the future. The focus of this study is not on the proportion of the number of samples in the GWAS group and the GS group. Therefore, alternative splits have not been tested. 

Comments 3: POPCORN was used to select A, B, E based on “varying kinship” (Fig. 3), but details of how thresholds were set are missing. What cutoff did you use, and why? Can you include the numeric correlations and a brief interpretation in the main text?

Response 3: Thank you for pointing this out. The POPCORN software we use calculates the kinship among populations, and the magnitude of the numerical value directly represents the closeness of the relationship, without setting a threshold. Based on the results, we directly selected three populations, including both the pair with the closest relationship (A and E) and the pair with a relatively distant relationship (A and B), to compare the impact of the kinship among populations on the prediction accuracy when conducting multi-population genomic selection (GS) for population A. 

Comments 4: You include significant PCs (P < 0.05) as covariates in the MLM (Eq. 1). How many PCs were retained per scenario? Could population structure confound the discovery of truly causal SNPs, especially in small simulated populations?

Response 4: Thank you for pointing this out. In the GWAS analysis, the specific number of principal components (PCs) used as covariates in each scenario is not fixed. The significant principal components are determined through the EIGENSTRAT software. The specific approach is as follows: First, calculate the principal components using the EIGENSTRAT software, and then determine whether each principal component has significant statistical significance. The principal components that have a significant impact on the population structure with a P-value less than 0.05 are included in the association analysis. In various scenarios, the number of such principal components may be 1, 3, 4, 6, or other numbers. This approach can be referred to in the paper "GWAS Identifies Novel Susceptibility Loci on 6p21.32 and 21q21.3 for Hepatocellular Carcinoma in Chronic Hepatitis B Virus Carriers".

Comments 5: You evaluate top 5–25% SNPs by GWAS P-value. Why was 25% chosen as the upper bound? Have you explored finer gradations (e.g. 2%, 1%) or a data-driven cutoff (e.g. Bonferroni)?

Response 5: Thank you for pointing this out. The selection of the 25% cutoff was aimed at investigating the impact of including SNPs with lower significance levels on model performance. While this study did not examine finer gradations (e.g., 1-2%), we acknowledge that more stringent thresholds (such as Bonferroni) could preferentially select high-confidence SNPs. However, such an approach might exclude loci with small yet biologically relevant effects.

Comments 6: The weight for locus k is defined as –log₁₀(pₖ). Can you justify this choice versus other weighting schemes (e.g. squared effect size, Bayesian posterior variance)? How sensitive are results to the logarithmic transform?

Response 6: Thank you for pointing this out. In Su et al.'s research on weighting factors, five factors, including squared effect size, Bayesian posterior variance, and –log₁₀(pₖ) of GWAS results, were used as weights for the G matrix in genomic prediction. The results showed that the best weighting factor was the posterior variance estimated by the Bayesian model. However, using the method of combining the Bayesian model with GBLUP increased the computational burden. Therefore, the second-best weighting factor, –log₁₀(pₖ) from GWAS results, was chosen.

Comments 7: You fit GBLUP in GCTA and WMGBLUP/MGBLUP in DMUAI (DMU). What convergence criteria and priors (if any) were used? Did all runs converge reliably across replicates?

Response 7: Thank you for pointing this out. Maybe I didn't explain it clearly. We fit GBLUP/ WMGBLUP/MGBLUP in DMUAI (DMU). We did not set additional convergence criteria or prior conditions. All runs converged reliably across replicates.

I have revised the last sentence in "2.5. MGBLUP model and WMGBLUP model" of "2. Materials and Methods" from "The DMUAI program of the DMU software is used to estimate the genomic estimated breeding values (GEBVs)." to "The R software is used to construct the G matrix and g matrix. And The DMUAI program of the DMU software is used to estimate the genomic estimated breeding values (GEBVs).”

Comments 8: Apart from GBLUP, MGBLUP, WMGBLUP, there are other single-step or Bayesian models (e.g. ssGBLUP, BayesB). Why were these not included, and how might they perform relative to your WMGBLUP?

Response 8: We appreciate your comment. In this study, we did not include models such as ssGBLUP and BayesB mainly for two reasons. First, our beef cattle dataset lacks pedigree information, so the ssGBLUP method may not be suitable for our research context. Second, Bayesian models like BayesB require long computation times and substantial computational resources. Therefore, improving the GBLUP model is one of the main research focuses.

Comments 9: All analyses are based on simulation. To demonstrate practical utility, can you apply your top-performing WMGBLUP (top 5% SNPs) to an actual beef-cattle dataset, even if smaller, and report empirical accuracy?

Response 9: Thank you for your suggestions. Unfortunately, there is no phenotypic information in the public dataset. Moreover, we are currently collecting real data, and we will conduct verification in the future.

Comments 10: You observe that adding population E (closer kinship) improves accuracy more than adding B (more distant) at 3:1 and 1:1 ratios. Can you discuss how this finding might inform the design of reference panels in practice?

Response 10: Thank you for pointing this out. This finding is of great significance for the design of reference panels. When constructing a reference panel, populations with close kinship to the target population should be prioritized. For example, in beef cattle breeding, selecting individuals from the same or closely related breeds to form a reference panel can improve the accuracy of genomic prediction. The proportion of added populations also affects accuracy. For populations with low genetic diversity, the proportion of closely related populations can be appropriately increased to supplement more genetic information, while for those with high genetic diversity, the proportion needs to be carefully adjusted. In addition, a genetic analysis of the participating populations should be carried out during the design process. Understanding the kinship and genetic structure differences is conducive to scientifically selecting populations and determining their proportions.

Comments 11: Please expand on limitations: e.g., only additive effects simulated, no dominance/epistasis; no environmental interactions; fixed heritability of 0.3. How might these factors alter your conclusions

Response 11: Thank you for pointing this out. Our simulations only focused on the simple scenario of additive genetic effects and did not consider complex factors such as dominance effects, epistatic effects, and environmental interactions. Dominance effects and epistatic effects may bring about additional genetic variations that have not been considered, and the epistatic effects may lead to an overestimation of the prediction accuracy in this study. In actual beef cattle breeding, environmental conditions (such as the farm environment, nutrition, etc.) will have a significant impact on phenotypic and heritability estimations. Heritability can vary greatly depending on the traits, populations, and environmental conditions. A higher heritability will result in greater prediction accuracy. We have added the limitations of this part of the simulation to the discussion section. Thank you very much for your valuable comments.

Comments 12: Figures 1–3 and Tables 1–7 contain a wealth of detail but are dense. Consider moving some tables to Supplementary Material and summarizing key trends in the main text.

Response 12: Thank you for pointing this out. We agree with this comment. Therefore, I have moved Table 3 and Figure 2, which present the simulation results, to Supplementary Material. And I have made revisions to the content.

Comments 13: Will you make your QMSim scripts, GCTA/DMU configuration files, and analysis code publicly available (e.g., GitHub) to ensure reproducibility?

Response 13: Thank you for pointing this out. I'm more than happy to share my code. If any scholars are interested in my research, they can contact me via email to ensure the reproducibility of the research.

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript addresses a highly relevant and timely issue in the field of animal breeding, specifically the challenge of improving genomic prediction (GP) accuracy in beef cattle where small reference populations and incomplete data pose practical challenges. The study is well-structured, and the methodology is sound. However, the manuscript requires significant revisions to improve its clarity, interpretability, and impact.

Comments:

Major 

Biological Relevance and Practical Application

The manuscript would benefit from a stronger discussion of the biological relevance of the trait simulated and the implications of the findings for real-world beef cattle breeding programs.

Justification of SNP Pre-selection Thresholds

The rationale behind selecting the top 5% to 25% SNPs should be clarified, with references to relevant literature or empirical justification.

Generalizability and Limitations of Simulation

The manuscript should discuss the limitations of simulation studies and explicitly state that the findings need validation on real datasets.

Statistical Significance of Model Comparisons

Although the models are compared using correlation values, no statistical tests (e.g., paired t-tests) are presented to assess whether differences are significant.

Clarification of Population Naming

Terms like '3000A_1000B' are used without clear explanation. A legend or consistent format would enhance readability.

Minor

Abstract and Conclusion Clarity

The abstract is too technical and should be made more concise. The conclusion should summarize key takeaways more clearly.

Comments on the Quality of English Language

The manuscript contains numerous grammatical errors and awkward constructions. A thorough proofreading is essential.

Examples:

Line 13: "Genomic selection (GS) is pivotal in livestock and poultry breeding." → Unnecessary to specify both; just “livestock breeding” suffices.

Line 67: “test a weighted multi-population multi-G matrix model (WMGBLUP)” → Revise for clarity: “evaluate a weighted multi-population G-matrix model (WMGBLUP)”.

Recommendation, a full language polishing pass is needed, ideally by a native English-speaking editor.

Author Response

Comments 1: Biological Relevance and Practical Application. The manuscript would benefit from a stronger discussion of the biological relevance of the trait simulated and the implications of the findings for real-world beef cattle breeding programs.

Response 1: We greatly appreciate this constructive comment, which points out a crucial aspect for improving our manuscript. We have briefly supplemented it in the newly added Section 4.4 of the discussion. Thank you again for your valuable feedback.

Comments 2: Justification of SNP Pre-selection Thresholds. The rationale behind selecting the top 5% to 25% SNPs should be clarified, with references to relevant literature or empirical justification.

Response 2: Thank you for your valuable comments. In the discussion section, we cited a reference on the SNP proportion. To explore the appropriate SNP proportion when combining genomic selection (GS) with genome - wide association study (GWAS), we conducted comparisons at several levels starting from 5% with an increment of 5%. A 5% SNP proportion is at a significant level. If the SNP proportion is smaller, the pre-selected SNP set may exclude some loci that, although having small effects, are biologically significant. Therefore, we chose the range of 5% - 25%.

Comments 3: Generalizability and Limitations of Simulation. The manuscript should discuss the limitations of simulation studies and explicitly state that the findings need validation on real datasets.

Response 3: Thank you for pointing this out. We agree with this comment. Therefore, we have supplemented the limitations of the simulation at the end of the discussion section.

Comments 4: Statistical Significance of Model Comparisons. Although the models are compared using correlation values, no statistical tests (e.g., paired t-tests) are presented to assess whether differences are significant.

Response 4: Thank you for the questions you raised. In most current studies related to genomic selection (GS), the correlation coefficient $r$ is used for comparison. $r$ is calculated as the Pearson correlation coefficient between the genomic estimated breeding values (GEBV) and the true breeding values (TBV). Almost no statistical tests are performed on the differences between models.

Comments 5: Clarification of Population Naming. Terms like '3000A_1000B' are used without clear explanation. A legend or consistent format would enhance readability.

Response 5: Thank you for pointing this out. Thank you for pointing out these detailed issues. I have supplemented the legends at the first occurrence, as shown in Table 2 and Table 3.

Comments 6: Abstract and Conclusion Clarity. The abstract is too technical and should be made more concise. The conclusion should summarize key takeaways more clearly.

Response 6: We are extremely grateful for your valuable comments, which have clearly pointed out the direction for our improvement. We have reorganized the language and simplified the content of both the abstract and the conclusion. This is to ensure that readers can effortlessly understand the content of our research briefly. Thank you again for your precious input, which will undoubtedly contribute to enhancing the overall quality of our manuscript.

Comments 7: Comments on the Quality of English Language. The manuscript contains numerous grammatical errors and awkward constructions. Thorough proofreading is essential.

Examples:

Line 13: "Genomic selection (GS) is pivotal in livestock and poultry breeding." → Unnecessary to specify both; just “livestock breeding” suffices.

Line 67: “test a weighted multi-population multi-G matrix model (WMGBLUP)” → Revise for clarity: “evaluate a weighted multi-population G-matrix model (WMGBLUP)”.

Recommendation, a full language polishing pass is needed, ideally by a native English-speaking editor.

Response 7: Thank you for pointing out the issues concerning the English language quality of our manuscript. We are fully cognizant of the significance of presenting a manuscript with accurate grammar and lucid expressions. Regarding the specific examples you provided, we have already made amendments to the original text. To tackle the overall language quality problem, we conduct thorough proofreading of the entire manuscript, aiming to rectify all the grammatical errors and stiff expressions. Once again, we sincerely appreciate your constructive comments.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have taken an appreciable effort to conduction a simulation study. However, there are a few concerns with this study one of them being the novelty of this study and its practical utility. In the present digital era, simulation studies are well appreciated especially for the fact that it can provide a theoretical expected outcome. The effects of some of the factors observed in a practical scenario seemed to be missing in the present simulation study, for instance, breed, location, farm management, nutrition, etc. Below mentioned are some more comments:

1. It is crucial to mention the specific trait considered while simulating this study. Though the heritability is mentioned, it would be ideal to enlist the traits too as some of them are influenced by factors like breed, management, environment, etc.
2. Most of the findings presented in this study, especially the fact that MGBLUP and WMGBLUP models can improve the prediction accuracy that GBLUP model, doesn’t seem to be a new finding. Wasn’t there already established facts?
3. One of the major concerns with simulation studies is their similarity/accuracy with practical research. As the authors have indicated well in their research that smaller population size and other on-field factors significantly influence the GEBV predictions. Therefore to bridge this difference, the simulations models are set with factors pertaining to practical conditions. Quite a lot of such factors seems to be overlooked here in this study, for instance, the details on differences between breeds, location, environment/season, feeding/farm factors, age, etc.
4. Furthermore, in table 1, the authors have mentioned that the mating design opted was random. Is this case in the present scenario? As globally livestock breeding adopts selective breeding.
5. Line 106: specify the trait for which the heritability was indicated
6. Table 1: what was the basis for grouping the founder population into 5 groups? Was it decided by the authors or the simulation program?
7. Lines 380-384: are the reductions in accuracy indicated significant or of high concerns. For instance a decline in accuracy of 0.250 to 0.241 is a difference of 0.09 while for some it is as low as 0.012 (0.287 to 0.275).

Author Response

We sincerely appreciate your comprehensive review and the time you've spent providing such incisive feedback on our simulation study. We're truly grateful for your recognition of the efforts we've put into this research. Regarding your concerns about the novelty and practical application value of our study, we fully understand your perspective. In terms of novelty, although there are some overlapping concepts with previous studies, our research is specifically focused on beef cattle breeding. We systematically explored the preselection proportion of SNPs and comprehensively analyzed population-related factors. This has brought new knowledge to the field and promoted the development of genomic selection in beef cattle breeding. When it comes to practical application value, we acknowledge the gap between our simulation study and practical factors. However, the conclusions drawn from our simulation study exhibit a certain degree of stability and hold practical significance as a reference for actual beef cattle breeding. Although our current simulation did not explicitly incorporate factors such as breed, geographical location, farm management, and nutrition, we regard this as an opportunity for future research. 

Comments 1: It is crucial to mention the specific trait considered while simulating this study. Though the heritability is mentioned, it would be ideal to enlist the traits too as some of them are influenced by factors like breed, management, environment, etc.

Response 1: We sincerely appreciate your valuable comments. You are that traits can be influenced by factors such as breed, management, and environment. To facilitate the testing of different models, we simplified these complex factors. Therefore, the simulated trait represents a trait with a heritability of 0.3.

Comments 2: Most of the findings presented in this study, especially the fact that MGBLUP and WMGBLUP models can improve the prediction accuracy that GBLUP model, doesn’t seem to be a new finding. Wasn’t there already established facts?

Response 2: We sincerely appreciate your profound insights regarding the novelty of our research findings. Indeed, the general concept that models like MGBLUP and WMGBLUP may enhance genomic prediction accuracy compared to GBLUP has been explored in some previous studies. However, our research makes several unique contributions, which validate the significance of our research results. Firstly, our study is centered around beef cattle breeding. Beef cattle breeding is characterized by many breeds, small reference populations, and incomplete records, which pose challenges to genomic prediction. The performance of related models in beef cattle breeding was previously unknown. By simulating beef cattle populations and testing these models, we have filled this research gap. Secondly, we systematically investigated the impact of different preselected SNP proportions on prediction accuracy. This aspect has not been explored in detail in previous studies. Thirdly, we comprehensively studied the influence of population kinship, reference population size, and population composition ratio on prediction accuracy. This has great significance for constructing multi-population reference sets in real beef cattle populations.

Comments 3: One of the major concerns with simulation studies is their similarity/accuracy with practical research. As the authors have indicated well in their research, smaller population size and other on-field factors significantly influence the GEBV predictions. Therefore, to bridge this difference, the simulations models are set with factors pertaining to practical conditions. Quite a lot of such factors seem to be overlooked here in this study, for instance, the details on differences between breeds, location, environment/season, feeding/farm factors, age, etc.

Response 3: The core of this study is to evaluate the impact of models and other factors on genomic prediction. To highlight this, we simplified real - world aspects such as geographical location, season, and farm - specific conditions. If we incorporated too many factors into the simulation, the study could become overly complex, making it difficult to determine the true effects of the models. Although these practical factors were not considered, the reliability and stability of the conclusions can still be demonstrated through the prediction results of different populations. This is of great significance for guiding GS in actual beef cattle breeding. The limitations of this study also point the way for future research. Future studies can gradually incorporate the factors that were previously overlooked, building on the foundation of this research.

Comments 4: Furthermore, in table 1, the authors have mentioned that the mating design opted was random. Is this case in the present scenario? As globally livestock breeding adopts selective breeding.

Response 4: The random mating design in this study is a deliberate choice based on research objectives. It does not represent the actual situation in global livestock farming, where selective breeding is the mainstream. The use of random mating in the simulation is aimed at simplifying the initial genetic background. This makes it easier to observe the impacts of different models and kinship among populations on prediction accuracy without the influence of genetic selection based on complex mating patterns.

Comments 5: Line 106: specify the trait for which the heritability was indicated

Response 5: Our focus is on the prediction accuracy of different models for traits with a heritability of 0.3, rather than on any complex trait in reality.

Comments 6: Table 1: what was the basis for grouping the founder population into 5 groups? Was it decided by the authors or the simulation program?

Response 6: We divided the population into five groups not only based on previous studies but also to select three groups with different degrees of relatedness from them according to kinship for research. The aim is to provide a reference for how to select populations when conducting multi - population genomic selection on multiple practical populations. The format of the simulated populations is determined by the researchers themselves, not by the simulation program.

Comments 7: Lines 380-384: are the reductions in accuracy indicated significant or of high concerns. For instance a decline in accuracy of 0.250 to 0.241 is a difference of 0.09 while for some it is as low as 0.012 (0.287 to 0.275).

Response 7: The situation of accuracy reduction should be highly concerned. In genomic prediction, generally, both the improvement and reduction of accuracy are paid attention to, but the significance of the accuracy reduction as an indicator is rarely focused on. 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

My comments have been addressed. Thanks.

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript has been corrected appropriately.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors addressed all my queries satisfactorily