PONE-D-20-12530

New genotypic adaptability and stability analyses using Legendre polynomials and genotype-ideotype distances

PLOS ONE

Dear Dr. de Souza,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

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Roberto Fritsche-Neto, Ph.D.

Academic Editor

PLOS ONE

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Partly

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: No

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3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: No

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4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: Overview

The proposed methodology could be an alternative to traditional models in the study of MET. It uses the phenotypic values of the genotypes across trials to create an environmental gradient and fits a reaction norm model using Legendre polynomials to predict the genotype performance. Although, using only the means of genotypes and general mean to create the environmental gradient may not be best alternative due disregard edaphoclimatic conditions.

The use of ideotypes to study the adaptability and stability seems to be a good alternative. It is possible to obtain four classes of ideotypes and from this select the desired genotypes.

A few considerations must be pointed:

The author may hypothesize why using Environmental gradient applying Finlay and Wilkinson is advantageous than environment traits to obtain the Environmental gradient;

The authors did not compare the proposed methodology to established methodologies. This could enhance the discussion;

Is it possible to use covariance matrix for the genotypic effect? It was used in the Phaseolus vulgaris L application?

A detailed description follows below:

Introduction:

Introduction underline the importance of genotype x environment studies. Although, it lacks reference that reinforce the proposed methodology and its theoretical background.

Line 35-36: Check the reference

Line 47-54: Need reference for theses affirmations

Line 66: imbalances or unbalanced? check in the text

Methods description (step by step):

Well written and understandable.

Application of the method with Phaseolus vulgaris L.

Results

Line 240: humidity to moisture

Line 267: witnesses to check

Discussion

Usually, in animals and plants, Legendre polynomials and other random regression are used to model the growth of the individual. In the presented methodology, it was not clear the “biological” meaning of modeling reaction norm using only environmental gradient with only the same priori information. see DOI 10.1007/s00122-013-2243-1. How the model deal with genotype x environment interaction? Is it feasible to extrapolate the presented methodology to unobserved environments? Since the Mixed model approach is used.

Line 424-425: How the presented methodology could incorporate the genomic matrix and environmental data in order to increase predictive ability?

Line 429-430: Which studies are these? What are the connections between the presented methodology and them?

Line 431-437: “The fact that an individuals' behavior is not predetermined, is an advantage of the proposed methodology in relation to the traditional methods of analysis of adaptability and stability.” I do not understand this affirmation. The model doesn’t use the environmental gradient defined a prioi from observed genotypes?

Line 446-454: Advantage over which other methodology? The presented work did not compare with the most common methodologies applied.

Line 452-454: It was not clear if it was used a cross-validation scenario to obtain these predictive accuracies. If it wasn’t, interpretation regarding predictive accuracy must be pondered.

Line 460-461: Comparison among mixed models and others approach must be careful since the present work did not evaluate any other approach.

Line 482-524: These paragraphs focus mainly on bean recommendation. Although very important, these do not seem to be the main focus of the study.

Reference

Many references are in Portuguese or are from books. These type of refences should be avoided in order to ensure access to the readers.

Reviewer #2: The authors applied random regression models (RRM) to investigate the reaction norms in common bean cultivars. This is a timely topic because understanding the genotype by environment is increasingly becoming important given the recent climate change. Although the topic discussed here is fascinating, there are a number of subjects that the authors may want to expand.

The authors argued as if they developed RRM to investigate phenotypic plasticity  or reaction norm. For instance, this is reflected in the title, "We propose a new methodology" in the Abstract, and "Thus, the objectives of this investigation were to propose a new methodology for ..." However, this is incorrect as the use of RRM for phenotypic plasticity analysis has been an active research area in animal breeding and ecology for more than decades. You are applying the previously developed methodology to study phenotypic plasticity in plants by treating multi-environment trials as environmental gradients. This manuscript would be much more appealing to plant breeders if written in the context of those works by others.

My second reservation pertains to the Introduction section that lacks a good structure. First, start by framing why adaptability/stability analysis is an important research area in the context of multi-environment trials (MET) and genotype by environment (GEI). Note that MET and GEI were never mentioned in the Introduction in the current version. The term MET first appears in the Methods section and GEI is only referred to in the Discussion section. Second, briefly review rich literature on how and why RRM has been widely used to study plasticity or GEI in animal breeding and ecology. Lastly, clearly state the objective of this paper, which is the application of RRM to investigate reaction norms in plant breeding. Also, just saying linear mixed models coupled with Legendre polynomials is not sufficient. Explicitly mention that the model you are using is RRM. I suggest entirely rewriting the Introduction.

The third major concern is the lack of methodological clarity and smoothness. The current Methods section is written like a step by step software manual with a disconnection between them. Not quite sure how Ij defined in step 1 is relevant to the subsequent steps. Steps in L131 and L144 can be combined with others because they are well-known statistics. I believe the methodology part can be significantly improved.

The utility of RRM is limited in this study because the authors did not use any genetic data (pedigree or genomics). Consider adding one or two paragraphs, regarding the impact of genetics on adaptability and stability analyses in the Discussion section.

Below are my specific comments.

Data availability statement. It is a bit strange to say that the data will be available upon acceptance of this manuscript. The data should be made available for reviewers and editors through the reviewing process if you intend to make them open.

L47: It was not clear to me what you are referring to by current technologies and lower level technologies.

L123: How is the vector of phenotypes constructed? Is it ordered by genotypes or trials? This will determine how you specify the variance-covariance terms for g and e. There is an inconsistency in your notation because Kg is on the left side of the Kronecker product, while Sigma_e is on the right side of the Kronecker product.

L155, L163, L168: It is misleading to say "at the original scale". You are just predicting breeding values from estimated random regression coefficients.

L157: What BLUPs are you referring to? I do not see any connection between this and the preceding subsections.

L173: Clarify how PEV was computed from a random regression model.

Equation 9: A reference is needed.

L204: I did not understand this paragraph. What does it mean by "through the invariance in multi environment trials (MET)."?

Genetic material (L216) and Trials (L223) should be placed before the Methods description (L83) according to the flow.

L218: How population structure of Carioca grains and Black grains were accounted for. I believe this will impact the interpretation of results.

L322: It is not evident in Figure 1, which ones are environmental gradients six and eight.

L324: This is essential information. I suggest you show a table or a figure related to variance components.

Figure 1: Clarify why the x-axis is ranging from -1 to 1. This does not agree with Table 1.

L340: You previously mentioned in L264 that the cultivars of minimal adaptability will not be considered for recommendations. Why do the cultivars of minimal adaptability appear here again?

L406: Introduce the concept of genotype by environment interactions first in the Introduction section rather than in the Discussion.

L426: This paragraph should be placed in the Introduction section.

L446: You did not propose the method (reaction norm analysis using RRM), but you applied.

Minor comments.

L117: Consider replacing order of adjustment with order of polynomials

L122, L293, L308: residue -> residual or residuals

L200: Why na appears twice for k = 1 and k = 4?

L281: table 1 -> Table 1.

L293: Consider replacing grade six with order six. Also, see L306.

Table 2: The column LOG L is redundant if all models converged.

L313: There is no need to redefine DEG, AIC, BIC, PAL, LRT, H, and D again.

L322: figure 1 -> Figure 1

L401-402: Be consistent with the use of trials vs. environments

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Reviewer #1: No

Reviewer #2: No

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PONE-D-20-12530R1

Adaptability and stability analyses of plants using random regression models

PLOS ONE

Dear Dr. de Souza,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Oct 11 2020 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols

We look forward to receiving your revised manuscript.

Kind regards,

Roberto Fritsche-Neto, Ph.D.

Academic Editor

PLOS ONE

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: (No Response)

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: I would like to thank the authors for having accepted my suggestions and or clarified my doubts. The application of random regressions models and ideotypes proved to be suitable in the studies of genotype by environment interaction (GEI) in beans. Although the authors did not use any genomic/pedigree data or environmental information, the methodologies used provide opportunities for further research regarding the use of environmental and genomics data using Random Regression models in multi environmental trials studies.

A detailed description with minor review follows below:

L.48: Replace “imbalance” to “unbalanced”

L.155: Replace “Genetic imbalance” to “Genetic Unbalanced”

L. 293: Replace "Witnesses" to "check"

L. 294: Replace "as witnesses to check" "as check"

L.248: Equation 9. Reference needed

L.381: Replace "Witnesses" to "check"

L. 657: Remove

Reviewer #2: The authors have addressed most of my comments adequately. Below are my additional comments to improve the readability and strengthen the manuscript.

L103: This is incorrect. Henderson proposed BLUP, linear mixed model, and mixed model equations, but not RRM. The initial form of RRM was first proposed by Kirkpatrick et al. 1990 [1] and later extended by Schaeffer and Dekkers 1994 [2] and Meyer and Hill 1997 [3].

[1] Kirkpatrick et al. 1990 Analysis of the inheritance, selection and evolution of growth trajectories. Genetics 124: 979–993.

[2] Schaeffer LR, Dekkers JCM. Random regressions in animal models for test-day production in dairy cattle. Proc 5th World Congress on Genetics Applied to Livestock Production; 1994; Guelph, 18:443-446.

[3] Meyer K, Hill WG. Estimation of genetic and phenotypic covariance functions for longitudinal or repeated records by restricted maximum likelihood. Livest Prod Sci. 1997; 47:185–200.

It is important to note that the current work is not the first time to apply RRM to univariate or multivariate plant breeding data. The authors failed to refer to the earlier work of Sun et al. 2017 [4], Ly et al. 2018 [5], Momen et al. 2019 [6], and Baba et al. 2020 [7] in the Introduction section. Put them after animal breeding literature you referred and mention their contribution/relevance with respect to the current work.

[4] Sun et al. Multitrait, random regression, or simple repeatability model in high-throughput phenotyping data improve genomic prediction for wheat grain yield. Plant Genome. 2017; 10. pmid:28724067

[5] Ly et al. Whole-genome prediction of reaction norms to environmental stress in bread wheat (Triticum aestivum 736 L.) by genomic random regression. F Crop Res. 2018;216.

[6] Momen et al. Predicting longitudinal traits derived from high-throughput phenomics in contrasting environments using genomic Legendre polynomials and B-splines. G3: Genes, Genomes, Genetics. 2019.  9:3369-3380.

[7] Baba et al. Multi-trait random regression models increase genomic prediction accuracy for a temporal physiological trait derived from high-throughput phenotyping. PLoS ONE 2020. 15(2): e0228118.

In sum, the introduction section should be framed in the context of earlier work by others.

L185: I believe you meant the lowest and highest averages rather than lower and higher averages.

L191-194: What do you mean by "adjusted"? Perhaps "adjusted" is not the best term to use here.  

L196, Equation 3: Why don't you include fixed random regression coefficients designed to capture the mean trajectory of environmental gradients? Almost all of the previous RRM literature include this term to account for the mean trend. 

L248: Provide a reference for equation 9.

L264: Remove "thus"

L293, L375: What witnesses are? I am not familiar with this term. I believe you meant checks?

Table 2: Clarify what H or D means (first column) in the table caption.

L765: Smith et al. 2015 has been cited twice. Ref 1 and Ref 73.

Ref 20. Wrong journal title. Should be Journal of Dairy Science.

Ref 38: It says "Available: file:///C:/Users/Sandrinho/Downloads/artículo_redalyc_253021631009.pdf". Note that this is the author's locale file on a computer. Readers will not have access to it.

Lastly, I agree with reviewer 2 that references are used to support or defend your claims you made in your research. Note that PLOS ONE has a wide range of readers from around the world. I could not assess many references such as 9, 38-39, 42, 48-52, 61, 72, 76 because they are not written in English. Consider replacing them, if possible, with more suitable references that everyone can read, understand, and discuss.

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Reviewer #1: No

Reviewer #2: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

PONE-D-20-12530R2

Adaptability and stability analyses of plants using random regression models

PLOS ONE

Dear Dr. de Souza,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Dec 04 2020 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols

We look forward to receiving your revised manuscript.

Kind regards,

Paulo Eduardo Teodoro, Dr.

Academic Editor

PLOS ONE

Additional Editor Comments (if provided):

Dear authors, your manuscript was returned to the initial reviewers. One accepted and another requested Minor Revision. I am also requesting some corrections. Answer the comments point-to-point so that I can make the Final Decision in the next round.

- Throughout the text use "common bean" instead of just "bean";

- quote all R packages used for the analyzes;

- In the Discussion, insert a final paragraph about what advances the proposed method has in relation to the dozens of methods in the literature;

- Add in the conclusions the best genotypes identified by RR models.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: (No Response)

Reviewer #2: All comments have been addressed

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: (No Response)

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: (No Response)

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: (No Response)

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: (No Response)

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The authors addressed most of my comments. Follows some additional suggestions to improve the manuscript:

Please, check if the term "imbalances" is correct

I did not understand equation 9 and I did not find a direct connection between the citation. Considering that part of your conclusions is based on it, I recommend that you explain it better or reference it.

Reviewer #2: (No Response)

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7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

Adaptability and stability analyses of plants using random regression models

PONE-D-20-12530R3

Dear Dr. de Souza,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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Kind regards,

Paulo Eduardo Teodoro, Dr.

Academic Editor

PLOS ONE