Nonlinear Mixed-Effect Models to Describe Growth Curves of Pepper Fruits in Eight Cultivars Including Group Effects

Round 1

Reviewer 1 Report

Please find my comments in the pdf.

Comments for author File: Comments.pdf

N/A

Author Response

Thank you for review our manuscript. 

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors used Nonlinear Mixed-Effect Models (NLME) method using four models (Gompertz, 13 Logistic, Richards, and Von Bertalanffy) to describe 14 pepper genotypes' length and width growth.

The manuscript has the following minor and major concerns before acceptance of the article for publication.

 

Title: Considering the small number of genotypes in each group, it seems that the title should not be general (is it possible to estimate unbiased group effects with a 3-member group and a 5-member group?)

 Line 15: Please correct "three"

Line 16: Please add the coefficient of determination (R2)of the best models in the abstract

Introduction: The introduction section is short. It seems it is better to mention the importance of pepper cultivation in the world and then its place in Brazil at the beginning of the introduction section. It is suggested to use FAO statistics.

Line 37: Describe the advantage and superiority of this method over non-mixed methods in the application.

Line 67: It will be interesting for readers to see the difference between different genotypes in the picture.

Line 71: How many observation was used to fitting the model from each genotype? Did you use n=80 observations in model fitting? experimental design and number of replication and the sample size for each genotype should be mentioned.

It is vague.

Line 74: It is suggested to add pictures of pepper and bell pepper for supporting Table 1 information.

Table 2: Please write Logístico in English.

Results: This comparison cannot be generalized. The number of genotypes from each group is not enough to make a correct judgment about the difference between the two groups, one group has 3, and one group has 5 genotypes. By removing Vulcão, Jamaica Yellow, and Quadrado, the average of the two groups will be very close, or in another view, within-group differences are just as much as between-group differences. This requires a major revision of the presentation of your results.

Table 3: Please write Logístico in English.

Table 3: von Bertalanffy has a very low R2. Does this model has been convergence in the model fitting step?

Line 259: It is suggested to consider:

If the difference between AICc and the min AICc (as the best model), known to Δi, is less than 10, will indicate no significant difference and IF this difference is more than 10 will evidence that the model with larger AICc will not be a good fit (Burnham and Anderson, 2002).

Figure 3: Within-group differences appear to be greater than or equal to between-group differences

Line 356: Oliveira et al, (2021) studied nonlinear models in the fitting of growth curves in Vulcão, Picante para vaso, Peter, Cayene, and Jamaica Yellow. Some genotypes are similar to the present work. Do your achievements justify the superiority of your method to the method of these researchers? In the discussion section, compare and discuss the results of the two methods considering the similar plant materials between the present work and Oliveira et al, (2021) work.

Line 400: Due to this research's too-small sample size, it seems necessary to be more cautious in generalizing the results to the whole group. These results must achieve from a large sample size population and then must be validated in a larger population.

Comments for author File: Comments.pdf

 Moderate editing of English language required

Author Response

The authors used Nonlinear Mixed-Effect Models (NLME) method using four models (Gompertz, 13 Logistic, Richards, and Von Bertalanffy) to describe 14 pepper genotypes' length and width growth.

The manuscript has the following minor and major concerns before acceptance of the article for publication.

 

*Title: Considering the small number of genotypes in each group, it seems that the title should not be general (is it possible to estimate unbiased group effects with a 3-member group and a 5-member group?)

Answer: we changed the title, previously specifying the number of genotypes (line 3).

 

Line 15: Please correct "three"

Answer: Corrected (line 15).

 

Line 16: Please add the coefficient of determination (R2)of the best models in the abstract

Answer: The corrected coefficient of determination was added (line 18).

 

Introduction: The introduction section is short. It seems it is better to mention the importance of pepper cultivation in the world and then its place in Brazil at the beginning of the introduction section. It is suggested to use FAO statistics.

Answer: We were unable to find specific information about pepper in the context of Brazil. However, we added a paragraph (lines 26-34) at the beginning of the introduction highlighting the importance of growing peppers and understanding growth characteristics.

 

Line 37: Describe the advantage and superiority of this method over non-mixed methods in the application.

Answer: The advantages of using the NLME over non-mixed methods are described in the following paragraph (lines 53-60), where after their advantages, examples from the literature of works that used this method are used. However, it was probably not clear what these advantages were over non-mixed models. Therefore, we add a sentence making this advantage clearer in lines 52-53.

 

Line 67: It will be interesting for readers to see the difference between different genotypes in the picture.

Answer: We were unable to find specific information about pepper in the context of Brazil. However, we added a paragraph at the beginning of the introduction highlighting the importance of growing peppers and understanding growth characteristics.

 

Line 71: How many observation was used to fitting the model from each genotype? Did you use n=80 observations in model fitting? experimental design and number of replication and the sample size for each genotype should be mentioned. It is vague.

Answer: As noted in lines 85-88, the eight experimental units were measured over 10 specific time periods, totaling N = 80 observations. About the experiment, we agree that little information was provided. To improve this, we have added a more complete description of the experiment referring to this work (lines 81-88).

 

Line 74: It is suggested to add pictures of pepper and bell pepper for supporting Table 1 information.

Answer: We were unable to find specific information about pepper in the context of Brazil. However, we added a paragraph at the beginning of the introduction highlighting the importance of growing peppers and understanding growth characteristics.

 

 

Table 2: Please write Logístico in English

Answer: Corrected for Tables 2, 3 and 4.

 

Results: This comparison cannot be generalized. The number of genotypes from each group is not enough to make a correct judgment about the difference between the two groups, one group has 3, and one group has 5 genotypes. By removing Vulcão, Jamaica Yellow, and Quadrado, the average of the two groups will be very close, or in another view, within-group differences are just as much as between-group differences. This requires a major revision of the presentation of your results.

Answer: The sample used in the work is, in fact, small. However, our intention in carrying out this research was not to generalize the results, not least because no statistical test was carried out in order to compare the two groups. The main gain of the methodology presented in terms of adjustment was that it was possible to insert the type of pepper (pepper and sweet pepper) as a covariate, being represented by the fixed effect, and uniting this estimate with that of individual effects, in turn represented by random effects. We can observe that, mainly in terms of MAE, MSE and , the models were able to efficiently predict the growth of the genotypes in the study, even considering a small sample. To emphasize this, we have added a sentence in the conclusions section to make this clearer (lines 442-445).

 

Table 3: Please write Logístico in English

Answer: Corrected for Tables 2, 3 and 4.

 

Table 3: von Bertalanffy has a very low R2. Does this model has been convergence in the model fitting step?

Answer: Yes, there was convergence for all models. However, even with convergence in parameter estimation, it is possible that some equations are not capable of, in that specific situation, providing a good fit for the data. To make it clearer about the convergence of the models, we add a sentence to the results (lines 210-211).

 

Line 259: It is suggested to consider:

If the difference between AICc and the min AICc (as the best model), known to Δi, is less than 10, will indicate no significant difference and IF this difference is more than 10 will evidence that the model with larger AICc will not be a good fit (Burnham and Anderson, 2002).

Answer: We added a sentence with this citation in the discussion, when discussing about comparison criteria (lines 398-403).

 

Figure 3: Within-group differences appear to be greater than or equal to between-group differences.

Answer: This is a great observation. We added a sentence about this on the lines 285-286 of the uploaded file. However, in the methodology used, the parameters used to estimate the fixed effect (responsible for the differences between the types of pepper) and random effects (individual differences between the means of each group) were able to capture this variation, which can be measured by the MSE and MAE close to zero. This was one of the great results of the work.

 

Line 356: Oliveira et al, (2021) studied nonlinear models in the fitting of growth curves in Vulcão, Picante para vaso, Peter, Cayene, and Jamaica Yellow. Some genotypes are similar to the present work. Do your achievements justify the superiority of your method to the method of these researchers? In the discussion section, compare and discuss the results of the two methods considering the similar plant materials between the present work and Oliveira et al, (2021) work. Answer: It would be very difficult to carry out an objective comparison since in the work by Oliveira et al. (2021) the adjustments were made individually. This changes the comparison criteria, since the sample size is different, in addition to the likelihood being modified as well. Furthermore, in your sample, only pepper genotypes were used, and in our research, pepper genotypes were included. However, we added a part to the discussion that addresses some similarities between the works (lines 392-397).

 

Line 400: Due to this research's too-small sample size, it seems necessary to be more cautious in generalizing the results to the whole group. These results must achieve from a large sample size population and then must be validated in a larger population.

Answer: As mentioned before, our intention in carrying out the research was not to generalize to any type of fruit (pepper or bell pepper), but rather to present a methodology that allows the adjustment of the growth curves of pepper fruits with the inclusion of groups. We try to remove or change sentences that might make the reader think about it. And one of our changes was to highlight that the method was effective even using a small sample, and that it can present even better results if it is more robust (lines 442-445), in conclusion.

Author Response File: Author Response.docx

Reviewer 3 Report

1.     The statement of objectives near the end of the Introduction seems to contain a lot of information, which makes it somewhat confusing. To enhance clarity, consider breaking down the objective statement into bullet points or separate sentences. Each goal could be described and explained in a separate sentence or two.

2.     It could be beneficial to further clarify why NLMEs are particularly suitable for your study as opposed to other methods in Introduction. Providing a brief comparison of NLMEs and other approaches could enhance your argument. Specifically, what are the limitations of the traditional approach of adjustment per individual, and why is NLME an effective alternative?

3.     The introduction explains that growth characteristics of pepper plants depend on the cultivar and growing conditions, and that NLME can include this information. However, the importance of these variables (cultivar, growing conditions) in pepper plant growth could be elaborated on further. Additionally, some context or background information on the specific challenges or importance of understanding growth in pepper plants would add relevance and urgency to your study. Are there specific problems in pepper farming that this research could help solve? How might your research contribute to better cultivation methods or productivity for pepper and bell pepper cultivars?

4.     The section 2.1 lacks in providing a clear methodology and step-by-step detail of the experimental procedures. For example, it does not clearly define how the peppers were grown or managed in the greenhouse, or the specific metrics by which they were assessed. The experimental setup and conditions are not explicitly explained, including the control measures to standardize the conditions, any steps taken to prevent cross-pollination, etc.

5.     In Results, when discussing the asymptotic length, it's mentioned that the bell pepper species have a higher value than pepper fruits, but without any explanation of what "asymptotic length" means.

6.     The Results section has numerous references to 'pepper' and 'bell pepper,' which can be confusing as both terms are referring to the same species, just different variants. Furthermore, the usage of the term 'pepper fruits' is somewhat confusing and may not be accurate. It would be better to establish a clear distinction between these two types and maintain consistent usage throughout.

7.     In Discussions, the relationship between the asymptotic width and the time to the inflection point is presented as "close to zero correlation," but the authors did not explain the implications of this. Specifically, how does this finding relate to the overall study? What does it mean for the prediction or understanding of the growth patterns of pepper and bell pepper fruits? The explanation should go beyond mere reporting of the results and should attempt to interpret what this means in the context of their research. This could be expanded upon to strengthen the discussion and conclusions drawn from their findings.

8.     The conclusion could benefit from specifying the potential implications or applications of these findings in real-world contexts.

Author Response

1. The statement of objectives near the end of the Introduction seems to contain a lot of information, which makes it somewhat confusing. To enhance clarity, consider breaking down the objective statement into bullet points or separate sentences. Each goal could be described and explained in a separate sentence or two.

Answer: We rewrote the objectives trying our best to describe what was done in the work without making the paragraph too long. We found it more interesting to separate them into topics to better describe each step. Changes are on lines 66-74.

 

2. It could be beneficial to further clarify why NLMEs are particularly suitable for your study as opposed to other methods in Introduction. Providing a brief comparison of NLMEs and other approaches could enhance your argument. Specifically, what are the limitations of the traditional approach of adjustment per individual, and why is NLME an effective alternative?

Answer: The main advantages of the NLME over the traditional approach are described in lines 53-60. We added a sentence to make it clearer what the advantages presented were in relation to traditional (non-mixed) methods (lines 52-53).

 

3. The introduction explains that growth characteristics of pepper plants depend on the cultivar and growing conditions, and that NLME can include this information. However, the importance of these variables (cultivar, growing conditions) in pepper plant growth could be elaborated on further. Additionally, some context or background information on the specific challenges or importance of understanding growth in pepper plants would add relevance and urgency to your study. Are there specific problems in pepper farming that this research could help solve? How might your research contribute to better cultivation methods or productivity for pepper and bell pepper cultivars?

Answer: Specifically, the methodology proposed in this work applied to pepper data helps us to model the behavior pattern of width and fruit growth of pepper cultivars. We added a paragraph in the introduction (lines 26-34) highlighting the importance of knowledge of pepper fruit growth.

 

4. The section 2.1 lacks in providing a clear methodology and step-by-step detail of the experimental procedures. For example, it does not clearly define how the peppers were grown or managed in the greenhouse, or the specific metrics by which they were assessed. The experimental setup and conditions are not explicitly explained, including the control measures to standardize the conditions, any steps taken to prevent cross-pollination, etc.

Answer: We have added some additional information about the experiment, provided by our team, in order to clarify how it was carried out (lines 81-88).

 

5. In Results, when discussing the asymptotic length, it's mentioned that the bell pepper species have a higher value than pepper fruits, but without any explanation of what "asymptotic length" means.

Answer: We added in the parameter description part what is the asymptotic weight and a practical interpretation (lines 154-155).

 

6. The Results section has numerous references to 'pepper' and 'bell pepper,' which can be confusing as both terms are referring to the same species, just different variants. Furthermore, the usage of the term 'pepper fruits' is somewhat confusing and may not be accurate. It would be better to establish a clear distinction between these two types and maintain consistent usage throughout.

Answer: We had difficulties to define the nomenclatures that we would use in this work, and this was the best we found after some suggestions. However, we try to correct some points where the term "pepper" is used erroneously referring to what would be "bell pepper".

 

7. In Discussions, the relationship between the asymptotic width and the time to the inflection point is presented as "close to zero correlation," but the authors did not explain the implications of this. Specifically, how does this finding relate to the overall study? What does it mean for the prediction or understanding of the growth patterns of pepper and bell pepper fruits? The explanation should go beyond mere reporting of the results and should attempt to interpret what this means in the context of their research. This could be expanded upon to strengthen the discussion and conclusions drawn from their findings.

Answer: We have added a sentence (lines 425-429) highlighting what this correlation entails. Because it is a new application for the methodology, we had difficulties in finding works in the literature that performed a similar procedure. Therefore, we describe this relationship in terms of implications related to the results found.

 

8. The conclusion could benefit from specifying the potential implications or applications of these findings in real-world contexts.

Answer: We add at the end of the conclusions (lines 442-445) some considerations aimed at the possible application of the methodology in longitudinal data, and especially with larger samples.

Author Response File: Author Response.docx

Reviewer 4 Report

Comments for agronomy-2482997-v1

The authors applied nonlinear mixed-effect models to fit the pepper fruits’ (bell peppers and peppers) length and width during the growth. The length and width data come from a greenhouse study. Overall, the NLME modeling works well to fit the length and width of all pepper fruits. In addition, the authors compared four types of models in terms of modeling performance and indicated that Richards’ and Logistic models have the best performance for length and width, respectively. In summary, this manuscript is well-written and has sound results. I recommend considering accepting after minor revisions.

1.      Authors keep confusing the names for “bell pepper and pepper.” For example, Figure 2 names “pepper and red pepper;” Line 67 – 68 “five pepper genotypes … three pepper genotypes.” Please double-check and be consistent.

2.      Please clarify how you evaluated the standard deviations presented in Table 1. Specifically, how many replicates were performed? Are the replicates done for the same fruit or for several different fruits?

3.      According to results in Table 3 and Table 4, the performance of different models is not obvious, especially for Compertz, Logistico, and Richards models. Please provide a further justification for selecting Richars and Logistico as the best models over others. I am not convinced by the minor differences in Tables 3 and 4.

 

4.      The authors mentioned that the pepper’s length is positively correlated with the time (to the inflection point); while the width is unrelated to the time. Please provide a potential explanation for this observation.

Comments for author File: Comments.pdf

Author Response

Comments for agronomy-2482997-v1

The authors applied nonlinear mixed-effect models to fit the pepper fruits’ (bell peppers and peppers) length and width during the growth. The length and width data come from a greenhouse study. Overall, the NLME modeling works well to fit the length and width of all pepper fruits. In addition, the authors compared four types of models in terms of modeling performance and indicated that Richards’ and Logistic models have the best performance for length and width, respectively. In summary, this manuscript is well-written and has sound results. I recommend considering accepting after minor revisions.

1. Authors keep confusing the names for “bell pepper and pepper.” For example, Figure 2 names “pepper and red pepper;” Line 67 – 68 “five pepper genotypes … three pepper genotypes.” Please double-check and be consistent.

Answer: We seek to correct all sentences where there may be confusion between terms, including elsewhere in the text.

 

2. Please clarify how you evaluated the standard deviations presented in Table 1. Specifically, how many replicates were performed? Are the replicates done for the same fruit or for several different fruits?

Answer: The sample sizes used to calculate both the mean and the standard deviation are specified in the first row of the table (n = 5 pepper fruits and n = 3 bell pepper fruits). Some information about the experiment in general has been added, so that reviewers and readers can understand how each experimental unit considered was taken (lines 81-88).

 

3. According to results in Table 3 and Table 4, the performance of different models is not obvious, especially for Compertz, Logistico, and Richards models. Please provide a further justification for selecting Richars and Logistico as the best models over others. I am not convinced by the minor differences in Tables 3 and 4.

Answer: When discussing the work, our team had the same thought about the proximity of performance between the models, and this was even mentioned in the work at times. However, to describe the genotypes graphically and in terms of estimates of random effects, we needed a model that best described each variable. For this, we took care to choose five comparison criteria widely used in the literature. As we needed a model per variable, no matter how close the results are, the chosen one was the one that best met the requirements of the criteria used. In the manuscript, we cite some works that compared models such as Wubs et al. (2012) for pepper data, Hojjati and Hossein-Zadeh (2018) for Mehraban Sheep growth. In these articles, there was a high proximity between the models, however, the researchers chose what, according to their criteria, best adjusted the data. It is important to emphasize that, due to the idea in the development of the models being similar, it is natural that they present similar performances, but each in a specific situation, some of them will be chosen as the best. It does not mean that the Richards and Logistic models will always present the best results, but that according to these five criteria and for this data, however close and efficient the results may have been, we decided to opt for these two.

 

4. The authors mentioned that the pepper’s length is positively correlated with the time (to the inflection point); while the width is unrelated to the time. Please provide a potential explanation for this observation.

Answer: We complement the discussion with some possible implications on the results. As this type of analysis is being proposed for the first time in this context, we have no material in the literature to provide a potential explanation for the occurrence of this fact. However, the last paragraph of the discussion aimed to identify some implications of this result, and as already mentioned, we included a new part to complement this discussion (lines 425-429).

 

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

I would like to thank all the authors for patiently addressing my comments. However, I still think the MS needs further improvement regarding the INTRODUCTION and number of REFERENCES.

-The INTRODUCTION is too short. It looks like just a mere depiction of quoting others' results. Please follow the proper structure and make it coherent. Give more study results to support your scientific points. Moreover, I think the number of references is very less, so add more references. 

I think after addressing the above-mentioned comments, the MS can be considered for publication.

The quality of English can be improved.

Author Response

Dear editors,

We would like to thank you for the review and suggestions. Our team did their best to serve you. As for the English review, we did a new check to try to improve the work. As for the introduction and references, we added a paragraph at the beginning showing from quotes the importance of pepper fruits. Furthermore, in the penultimate paragraph we delve a little deeper into some of the good results found by applying the proposed methodology to some concepts. In all, approximately 8 more works were added to the references. If necessary, we are available for further questions and suggestions. All said changes have been added to the attached file.

Best Regards.

Author Response File: Author Response.docx

Reviewer 2 Report

 Comments and suggestions have been satisfactorily addressed by the authors. Therefore, the revised manuscript can be accepted.

Minor editing of English language required

Author Response

Dear editors,

We would like to thank you for the review and suggestions. Our team did their best to serve you. As for the English review, we did a new check to try to improve the manuscript. All the changes in the manuscript have been added to the attached file.

Best Regards.

Author Response File: Author Response.docx