An Economic Cost/Benefit Tool to Assess Bee Pollinator Conservation, Pollination Strategies, and Sustainable Policies: A Lowbush Blueberry Case Study

Round 1

Reviewer 1 Report

1. Carefully revise the manuscript for grammatical errors, typos, and inconsistencies in punctuation and punctuation, and formatting.

2. Ensure that in-text with the corresponding entries in the reference list and that all sources are properly sources are properly acknowledged.

3. Ensuring that all figures in the manuscript are in high resolution is crucial for maintaining the clarity and quality of visual representations.

4. Strengthen arguments by providing clear explanations, supporting evidence, and relevant examples

English very difficult to understand/incomprehensible

Author Response

Comments and Suggestions for Authors

1. Carefully revise the manuscript for grammatical errors, typos, and inconsistencies in punctuation and punctuation, and formatting.

We have carefully revised the manuscript for grammar, typos, and we have made the punctuation and formatting consistent. These changes are highlighted in yellow in the revised manuscript.

2. Ensure that in-text with the corresponding entries in the reference list and that all sources are properly sources are properly acknowledged.

We have made sure that the [#] in-text citations are consistent with what is listed in the References list so that all sources are properly acknowledged. We have made sure that the order of [#] are in order throughout the writing ending with what is cited in the Appendix. These edits to [#] citations in the writing are highlighted in yellow.

3. Ensuring that all figures in the manuscript are in high resolution is crucial for maintaining the clarity and quality of visual representations.

There are 3 figures that were not high resolution (Figure 6, Figure 7, and Figure A2). We have changed the resolution on these 3 figures to 600 dpi. All other figures were initially 600 dpi to begin with so were not changed.

4. Strengthen arguments by providing clear explanations, supporting evidence, and relevant examples

We have edited the entire manuscript to increase the clarify of explanations, the supporting evidence that we provide, as well as the case study examples that are described as well as what is currently happening from a pollinator conservation public policy perspective in Maine

Comments on the Quality of English Language

English very difficult to understand/incomprehensible

We have edited the entire manuscript for English corrections and edits to improve understanding, remove redundant statements, and simplify language to improve understanding. These edits are highlighted in yellow in the revised version of the manuscript. hanks very much for your valuable comments and edits.

Submission Date

26 January 2024

Date of this review

15 Feb 2024 07:33:03

Reviewer 2 Report

The study focused on the pollination role of honey bees and native bees in lowbush blueberry fields. The organization of the article is confusing. There is too much content in the title and the logic is unclear. The need and urgency of the research is not emphasized. It seems like that prediction is the main content of the study but the r2 is not enough to make the results credible. It may be a problem of the model or a problem of indicator selection. The current status of the manuscript is not sufficient for publication.

Author Response

Comments and Suggestions for Authors

The study focused on the pollination role of honey bees and native bees in lowbush blueberry fields. The organization of the article is confusing. There is too much content in the title and the logic is unclear.

We have reduced the length of the title to make clearer and to improve the logic and this is highlighted in yellow. We have improved the organization of the manuscript by increasing the number of paragraphs, deleting redundant statements, and writing out descriptions of variables used in equations.

The need and urgency of the research is not emphasized.

We have clarified the need and urgency of the research in the context of what is described in the Introduction regarding global pollinator declines from a producer perspective at the end of the first paragraph on page 3 of the Introduction section as well as at the end of the last paragraph of the Introduction that is also on page 3. We also clarified the context (global pollinator decline) for more economizing tools and strategies for pollination of pollinator-dependent crops in the last paragraph of the Conclusion section.

It seems like that prediction is the main content of the study but the r2 is not enough to make the results credible. It may be a problem of the model or a problem of indicator selection. The current status of the manuscript is not sufficient for publication.

In the pollination research literature, having r2 of 0.2 to 0.5 are considered acceptable and robust enough to justify modeling.

Submission Date

26 January 2024

Date of this review

02 Feb 2024 12:21:50

Reviewer 3 Report

The authors conducted a serious study. A deep sample was analyzed and significant statistical conclusions were made.  Between 1993 and 2021, authors sampled 209 commercial low- bush blueberry fields. The authors calculated how many bees are needed per 1 square meter to ensure maximum blueberry yield. Pollination decisions can be made based on the findings of this paper. The article has scientific novelty, theoretical and practical significance.

Author Response

Comments and Suggestions for Authors

The authors conducted a serious study. A deep sample was analyzed and significant statistical conclusions were made.  Between 1993 and 2021, authors sampled 209 commercial low- bush blueberry fields. The authors calculated how many bees are needed per 1 square meter to ensure maximum blueberry yield. Pollination decisions can be made based on the findings of this paper. The article has scientific novelty, theoretical and practical significance.

Thanks very much for highlighting the amount of field research and data analyses that were involved in this manuscript submission. We agree and hope our research can be used for making more informed pollination decisions.

Submission Date

26 January 2024

Date of this review

06 Feb 2024 13:46:38

Reviewer 4 Report

TITLE

 The Pollination Role of Honey Bees and Native Bees in Low-bush Blueberry Fields.

ABSTRACT

 It is suggested to include the objective, experimental design, treatments, repetitions, analyzed variables and conclusion.

KEY WORDS

 It is suggested to use words that are not in the title and help to locate the paper, such as the scientific name of the pollinators and the culture.

INTRODUCTION

 The purpose of the introduction is to support the discussion of the results. Therefore, I suggest that each variable analyzed should have more scientific articles listed in the Introduction.

MATERIAL AND METHODS

 Shorter paragraphs make it easier to understand.

 Wouldn’t the first paragraph of this chapter be better in the Introduction?

 The title of tables and figures must be self-explanatory, for example: Table 1 – Yield components of the wheat crop (Triticum aestivum), cultivar Tbio Itaipu®, controlled by the application of fungicides without and with adjuvants, 2023 harvest, Farm Sacramento ( California – USA).

RESULTS AND DISCUSSION

 Discuss the results based on the articles presented in the Introduction.

 Mention the scientific name of each crop, insect, etc...

CONCLUSION

 Respond to the objective of the paper.

REFERENCES

 I suggest checking if the References are in the standards and checking if all citations in the text are in the references and vice versa.

I recommend accepting the paper.

Author Response

Comments and Suggestions for Authors

TITLE

ü The Pollination Role of Honey Bees and Native Bees in Low-bush Blueberry Fields.

We have simplified the title more in line with what is suggested: “Pollination Role and Monetary Value of Honey Bees and Native Bees in Lowbush Blueberry Fields: Assessing More Sustainable Conservation Policy or Pollination or Pollination Strategies.”

ABSTRACT

ü It is suggested to include the objective, experimental design, treatments, repetitions, analyzed variables and conclusion.

We have edited the abstract to include and/or clarify the objective, details about how pollinator field sampling was conducted, analyzed variables, and conclusions.

KEY WORDS

ü It is suggested to use words that are not in the title and help to locate the paper, such as the scientific name of the pollinators and the culture.

We have done as you suggested and added the scientific name for lowbush blueberries, honey bees, and bumble bees was keywords.

INTRODUCTION

ü The purpose of the introduction is to support the discussion of the results. Therefore, I suggest that each variable analyzed should have more scientific articles listed in the Introduction.

We initially cited more articles in the Introduction or that could have been included in the Introduction but MDPI journals have a limit of 10% of the cited references that can be self-citations by co-authors on the manuscript. Dr. Drummond has a long history of research in lowbush blueberry in Maine. Many of these articles dealt with the variables analyzed by the research. Thus the current citations used were the best fitting journal articles we could find given this limitation of not being able to cite the following 18 references:

Butler, R.G.; Dobrin, S.; Staples, J.; Venturini, E.; Frank, J.; Drummond, F.A. Maine’s bumble bee (Hymenoptera: Apidae) assemblage—Part 1: Composition, seasonal and regional distribution, and resource use. Environ. Entomol. 2021, 50(6), 1344–1357. https://doi.org/10.1093/ee/nvab095

Drummond, F.A.; Dibble, A.C.; Stubbs, C.; Bushmann, S.; Ascher, J.; Ryan, J. A Natural History of Change in Native Bees Associated with Lowbush Blueberry in Maine. Northeastern Naturalist, 2017, 24(m15), 49–68. https://doi.org/10.1656/045.024.m1502

Stubbs, C.S.; Jacobson, H.A.; Osgood, E.A.; Drummond, F.A. Alternative forage plants for native (wild) bees associated with lowbush blueberry, Vaccinium spp., in Maine. Maine Agricultural Experiment Station Technical Bulletin, 1992, 148, 54 pp. Available online: https://digitalcommons.library.umaine.edu/cgi/viewcontent.cgi?article=1048&context=aes_techbulletin (accessed 2 November 2023).

Bushmann, S.; Drummond F.A. Abundance and diversity of wild bees (Hymenoptera: Apoidea) found in lowbush blueberry growing regions of Downeast Maine. Environ. Entomol. 2015, 44(4), 1–15. https://doi.org/10.1093/ee/nvv082

Drummond, F. A.; Ballman, E.; Collins, J. Are they weeds or a life force? Or sustainability on the edge. Spire, The Maine Journal of Conservation and Sustainability, 2017. Available online: https://umaine.edu/spire/2017/05/04/drummond-et-al/ (accessed 2 November 2023).

Drummond, F.A. Wild blueberry fruit drop: A consequence of seed set? Special Issue: Pollinator Diversity and Pollination in Agricultural Systems. Agronomy 2020, 10(7), 939. https://doi.org/10.3390/agronomy10070939

Drummond F.A. Behavior of bees associated with the wild blueberry agroecosystem in the USA. Int. J. Entomol. Nematol. 2016, 2(1), 27–41.

Hoshide, A.K.; Dalton, T.J.; Smith, S.N. Profitability of coupled potato and dairy farms in Maine. Renew. Agric. Food Sys. 2006, 21, 261–272. https://doi.org/10.1079/RAF2006146

Yarborough, D.E.; Drummond, F.A.; Annis, S.; D’Appollonio, J. Maine Wild blueberry systems analysis. ActaHortic. 2017, 1180, 151–160. https://doi.org/10.17660/ActaHortic.2017.1180.21

Stubbs, C.S.; Drummond, F.A. Management of the alfalfa leafcutting bee, Megachile rotundata (Hymenoptera: Megachilidae), for pollination of wild lowbush blueberry. J. Kans. Entomol. Soc. 1997, 70(2), 81–93. Available online: https://www.jstor.org/stable/25085759 (accessed 5 January 2024).

Drummond, F.A. Commercial bumble bee pollination of lowbush blueberry. Int. J. Fruit Sci. 2012, 12(1–3), 54–64. https://doi.org/10.1080/15538362.2011.619120

Butler, R.G.; Lage, C.; Dobrin, S.; Staples, J.K.; Venturini, E.; Frank,_, J.; Drummond, F.A. Maine’s Bumble Bees (Hymenoptera: Apidae) – Part 2: Composition, Seasonal and Regional Distribution, and Resource Use. Environ. Entomol. 2021, 50(6), 1344–1357. https://doi.org/10.1093/ee/nvab095

Drummond, F.A.; Stubbs, C. Wild Bee Conservation for Wild Blueberry Fields. Fact Sheet No. 630, University of Maine Cooperative Extension, No. 2111. Available online: https://extension.umaine.edu/blueberries/630-wild-bee-conservation-for-wild-blueberry-fields/ (accessed 13 December 2023).

Stubbs, C.S.; Drummond, F.A. Yarborough, D.E. Field Conservation Management of Native Leafcutting and Mason Osmia Bees. Fact Sheet No. 301, University of Maine Cooperative Extension, No. 2420. Available online: https://extension.umaine.edu/blueberries/301-field-conservation-management-of-native-leafcutting-and-mason-osmia-bees/ (accessed 13 December 2023).

Venturini, E.M.; Drummond, F.A.; Hoshide, A.K.; Berg Stack, L.; Dibble, A. Enhancing Wild Bees for Crop Pollination: Sowing Bee Pasture for New England’s Wild Blueberry. University of Maine Cooperative Extension. Available online: https://extension.umaine.edu/blueberries/wp-content/uploads/sites/41/2015/03/2015-Bee-Pasture-Fact-Sheet.pdf (accessed 13 December 2023).

Stubbs, C.S.; Drummond, F.A.; Allard, S.L. Bee conservation and increasing Osmia spp. in Maine lowbush blueberry fields. Northeast. Nat. 1997, 4, 133–144.

Drummond, F.A. Estimating the Strength of Your Pollinator Force in Wild Blueberry. University of Maine Cooperative Extension, Maine Wild Blueberries. Available online: https://extension.umaine.edu/blueberries/estimating-the-strength-of-your-pollinator-force-in-wild-blueberry/ (accessed 13 December 2023).

Du Clos, B.; Loftin, C.S.; Drummond, F.A. BeeMapper Quick Guide. The University of Maine. Available online: https://umaine.edu/beemapper/wp-content/uploads/sites/353/2017/07/BeeMapper-Quick-Guide-for-Web.pdf (accessed 13 December 2023).

MATERIAL AND METHODS

ü Shorter paragraphs make it easier to understand.

We have converted longer run-on paragraphs to shorter paragraphs organized by topic area and this includes the Materials and Methods section.

ü Wouldn’t the first paragraph of this chapter be better in the Introduction?

We have moved the first paragraph of the Materials and Methods section to make up the two paragraphs before the last paragraph of the Introduction section.

ü The title of tables and figures must be self-explanatory, for example: Table 1 – Yield components of the wheat crop (Triticum aestivum), cultivar Tbio Itaipu®, controlled by the application of fungicides without and with adjuvants, 2023 harvest, Farm Sacramento ( California – USA).

We have made edits and clarifications highlighted in yellow to all titles of tables and figures as suggested so they are both stand-alone in understanding from the rest of the manuscript and self-explanatory.

RESULTS AND DISCUSSION

ü Discuss the results based on the articles presented in the Introduction.

We have contrasted our results in the Discussion section to research cited in the Introduction section, namely [26], [27], [31], and [58].

ü Mention the scientific name of each crop, insect, etc...

We have included the scientific names (Genus species) for sweet lowbush blueberries and honey bees as well as the Genus names for sampled native bees at the start of both the Results section and the Discussion section.

CONCLUSION

ü Respond to the objective of the paper.

We made edits in 3 areas to re-inforce the objectives of the research in the Conclusion section as suggested.

REFERENCES

ü I suggest checking if the References are in the standards and checking if all citations in the text are in the references and vice versa.

We have checked and made edits so that all [#] are consistent with what is listed numerically in the References section and all [#] are in numerical order from the start of the Introduction through the Methods, Results, Discussion, and the table in the Appendix.

I recommend accepting the paper.

Thanks very much for your valuable comments and edits.

Submission Date

26 January 2024

Date of this review

06 Feb 2024 20:38:33

Round 2

Reviewer 2 Report

In the section of Induction, there are so much redundant information such as the brief description of the lowbush blueberry cropping system. In the section of Induction, the content of the background, the value of research, the review of the study, and the contribution should be highlighted. The authors described “we summarize the data collected during our farm surveys over a 29 year-period. Using these data, we conducted Monte Carlo simulations on the economic uncertainty in lowbush blueberry pollination. In addition, we proposed, formulated, and used an "Economic Pollinator Level" (EPL) metric for evaluating future conservation and pollination policies and strategies using case study examples. Long-term data of the impact of pollinators on crop fruit set and yield as well as metrics such as the EPL can be used help producers more efficiently focus limited resources to optimize the impacts of more efficient pollination strategies.”, but it was not introduced why the simulations on the economic uncertainty in lowbush blueberry pollination need to be conducted. Is there any studies focus on the different effects from honey bees and native bees? The review was absented.

Why the Monte Carlo model was used? Is the model suitable for the study? Where has the model already been applied? The review for simulations, metrics, and long-term data of the impact of pollinators on crop fruit set and yield was absented in the Introduction section. The organization of the article is still confusing.

The authors demonstrated that “Mixed linear models were used to estimate bee-to-bee and bee-to-pollination relationships.”, why the models can be used to estimate the relationships? Is there any evidence for the feasibility?

In the results from Figure 3 to Figure 5, low levels of fit (R²) are difficult to predict trends accurately. It could not accurately describe the trends.

In my opinion, the logic of the research is poor, and the research design is not rigorous. The results are not convinced.

Author Response

Dear Reviewer,

We thank you for your suggestions that will make our manuscript a better contribution to the current knowledge of pollination sustainability.

The first comments that we address is that you have suggested that we must improve the seven aspects of our paper listed below. Because there is no specific advice, we have decided to go through each and try and improve it in a way that we think will result in an improved manuscript.

Is the content succinctly described and contextualized with respect to previous and present theoretical background and empirical research (if applicable) on the topic?

We have put subheadings in the Introduction to clarify our logic and the manner that we are introducing the literature review so one can see the relationship of our literature review to the greater context of our goal and objectives which have also been outlined to make them clear.

The sub headings are:

• Bee Pollinator Decline – a significant concern
• Economics of Pollination – not thoroughly studied
• Sustainable Pollinator or Pollination Protection Policies – a global perspective
• Lowbush Blueberry – A Unique Native North American Wild Crop – a unique native North American wild crop
• 5 Goals and Objectives for Lowbush Blueberry Sustainable Pollination

Our goal and objectives have been more concisely presented as:

Using these data, our goal was to conduct a risk assessment of the economics of pollination in Maine lowbush blueberry along with the development of a tool that can be used by growers, pollination researchers, economists and policy makers to assess the viability and robustness of novel pollination tactics. Our objectives are as follows:

1) Determine that both native bees and managed honey bees contribute, in part, to fruit set;

2) Determine the relationship between honey bee hive stocking density and honey bee forager populations in the field;

3) Estimate the relationship between fruit set and yield;

4) Propose, formulate, and use an “Economic Pollinator Level” (EPL) metric for evaluating future conservation and pollination policies and strategies using case study examples.

5) Conduct Monte Carlo simulations on the economic uncertainty or risk in lowbush blueberry pollination by way of using the EPL to test pollination tactics.

                                We also included a justification of our objectives at the end, just prior to the Methods section

“Change is occurring at a rapid rate to global markets, climate, pollinator community diversity and abundance. These changes are already beginning to impact lowbush blueberry production and economics. One of the critical inputs to the existence of lowbush blueberry production is the continued sustainability of pollination. Long-term data of the impact of pollinators on crop fruit set and yield as well as metrics such as the EPL can be used help producers more efficiently focus limited resources to optimize the impacts of more efficient pollination strategies. This is extremely important specifically in light of how climate change may alter pollinator community diversity and abundance as well as the yields and economics of lowbush blueberry production as is occurring in other cropping systems.”

• Are all the cited references relevant to the research?

We are familiar with the literature supporting the research in pollinator ecology, economics, and policy. We have had to leave some papers out due to the volume of research that has been conducted in this area. Many of our own papers were not included (more than 100 papers published on bees and lowbush blueberry) due to the editors request that we limit the number of self-citations. However, we read over our citations and do not feel that we have included any citations that are not relevant to our research. If there are nay citations that you feel we have missed and are important please alert us to them and we will include them. WHAT WE HAVE DONE to improve relevancy of our citations is to add a bit more detail regarding what the citations specific contributions are where we think it might help the reader.    

• Are the research design, questions, hypotheses and methods clearly stated?

We have added an outline of our objectives in the Introduction section and in the Methods, we have tried to improve the description of the experimental design and the analytical methods where they appear (see below and Methods section).

• Are the arguments and discussion of findings coherent, balanced and compelling?

We have reread our Discussion and have rewritten some of the sentences to improve the clarity of our arguments and included more comparison with other literature where possible (see text of manuscript).

• For empirical research, are the results clearly presented?

We have added a few more sentences to hopefully clarify our results (see below).

• Is the article adequately referenced?

We have more than 100 references cited and so we think that the article is adequately referenced. If the reviewer feels that we have missed some key references please let us know and we will be happy to include them.

• Are the conclusions thoroughly supported by the results presented in the article or referenced in secondary literature?

We have rewritten our conclusions and tried to make our conclusions clear and understandable, and supported by our research findings or supported by the literature (see text of Conclusion section).

Comments and Suggestions for Authors

In the section of Induction, there are so much redundant information such as the brief description of the lowbush blueberry cropping system.

We have attempted to better organize the Introduction by adding subheadings so that the writing better follows a logical process. I think rearranging a few paragraphs with the subheadings makes our Introduction clear now. Thank you. However, we did not delete or cut the description of lowbush blueberry culture because it is a unique wild crop only grown commercially in northeastern North America and it is not similar to the production of highbush blueberry which is grown all over the world. Therefore, we thought that if we deleted the paragraph describing lowbush blueberry that there might be confusion among readers.

In the section of Induction, the content of the background, the value of research, the review of the study, and the contribution should be highlighted.

Thank you for the good advice. We have put subheadings in the Introduction (see above) and added an outlined text of our goal and objectives for this paper, see above. In addition, we added a justification for this research after the objectives, see above.

The authors described “we summarize the data collected during our farm surveys over a 29 year-period. Using these data, we conducted Monte Carlo simulations on the economic uncertainty in lowbush blueberry pollination. In addition, we proposed, formulated, and used an "Economic Pollinator Level" (EPL) metric for evaluating future conservation and pollination policies and strategies using case study examples. Long-term data of the impact of pollinators on crop fruit set and yield as well as metrics such as the EPL can be used help producers more efficiently focus limited resources to optimize the impacts of more efficient pollination strategies.”, but it was not introduced why the simulations on the economic uncertainty in lowbush blueberry pollination need to be conducted. Is there any studies focus on the different effects from honey bees and native bees? The review was absented.

You are absolutely correct about our confusing writing. We have now rewritten the last section of the introduction (as mentioned above) and rewritten the Methods to better explain our research approach and central questions.  Thank you.

Why the Monte Carlo model was used? Is the model suitable for the study? Where has the model already been applied? The review for simulations, metrics, and long-term data of the impact of pollinators on crop fruit set and yield was absented in the Introduction section. The organization of the article is still confusing.

Hopefully we have clarified the logic of our research approach by use of subheadings and writing explanatory descriptions of the methods where necessary. The Monte Carlo method is a common economic tool used to assess economic risk based upon a probabilistic rationale. It is a technique that is described in introductory econometrics text books and a quick search of Monte Carlo simulation in Google will reveal hundreds of topics in economics. The book by Hardaker et al. [64] which we cite is the premier reference for the conduct of Monte Carlo simulation in agricultural Risk Assessment. In this book they discuss how to conduct Monte Carlo risk assessment and provide many case studies. The peer reviewed literature on using Monte Carlo simulation to assess economic uncertainty or risk is voluminous. We used it in a previous economic study evaluating pollination risk in four lowbush blueberry production systems (high input, medium input, low input conventional systems and organic production systems), Asare et al. 2017 [26].

In this current study we used Monte Carlo simulations to evaluate the risk of pollination tactics by setting up a pollination strategy using the Economic Pollinator Level or EPL. We then simulated the variation in parameters in the EPL representing a given pollination tactic. This is done by selecting input parameters within the EPL equation that there exist frequency distributions for each parameter selected. These frequency distributions represent the variation in the input parameters. Solving for one or more output parameters the simulations are run by the software program (@Risk) by selecting input values randomly from the frequency distributions. These simulations are run 100 to 100,000 iterations in @Risk where with each iteration the program selects random inputs and calculates the outputs. We chose to run the simulations with 1000 iterations Variables used to calculate the EPL for honey bees and native bees that had available times series data included the monetary cost of pollination (C), the value (V) of lowbush blueberries ($/kg) in Maine, the number of flowers set per m² per bee (P), and B which is the weight of one marketable individual lowbush blueberry in kg (equation 2). In order to run stochastic Monte Carlo simulations in @Risk [63], historical data for C, V, P, and B were fit to functional forms for probability distributions (Table 1). The values of C and V were calculated in U.S. dollars (USD). FROM these Monte Carlo simulations we were able to conduct a sensitivity analysis. A sensitivity analysis is where one identifies the variables that contributed most to the variation of uncertainty to the economic measure of interest, in our case it is the EPL. The Tornado diagrams capture the sensitivity analysis by showing each variable of interest and its effect on the sensitivity or impetus for change by the EPL. We have added more explanation into the Methods section so that it is hopefully clear to the reader about what the objective was of our Monte Carlo simulations. We hope this clarifies our Monte Carlo analyses.

The authors demonstrated that “Mixed linear models were used to estimate bee-to-bee and bee-to-pollination relationships.”, why the models can be used to estimate the relationships? Is there any evidence for the feasibility?

Good question! The broad wide spread use of Linear Mixed Models is fairly new (within the last two decades) across multiple disciplines in sciences, especially sciences that involve analysis of complex noisy systems such as ecology (Boker et al. 2009). This statistical modeling approach is now commonly being taught in introductory statistics courses and a survey of recent published studies in ecology or agricultural field work is used to collect data in mensurative experiments (those experiments that measurements are made in more than one place in time or space). Linear mixed models are also used in analysis of medical clinical studies were there are more columns of data (variables) than rows (samples), a situation where standard Analysis of Variance will not work. The power of linear mixed models is that they can be used to directly model nested data where the nested elements represent variable sample sizes. They also can be used to model data where correlations between independent variables exist because the covariance matrix can be modeled directly. In our case we used mixed models because we had unbalanced designs where differences in the number of fields sampled varied from year to year. Mixed model loose no power in situations like this. In addition, because the models are estimated with Maximum Likelihood Algorithms instead of Least Squares, transformation of data is often not necessary, because the residuals will often conform to the probability distribution of the chosen error distribution. The default distribution is Gaussian, but linear mixed models can also be fit with binomial, Poisson, or other distributions. The selection of a fixed effect or multiple fixed effects set the predictors. The selection of random effects allows one to account for variation such as year to year variation or site to site variation that might obscure the effects of the predictors. In our models we chose “year” to be the random effect so that the variation in our dependent variables affected by year was accounted for and this allowed us to have a better assessment of the effects of our predictors on the dependent variables. We have added a few sentences in the Methods to justify our use of linear mixed models.

Boker, B.M., Brooks, M.E., Clark, C.J., Geange, S.W., Poulsen, J.R., Stevens, M.H.H., White, J.S. General linear mixed models: a practical guide for ecology and evolution. Trends in Ecology and Evolution, 2009, 24, 127-135.     

In the results from Figure 3 to Figure 5, low levels of fit (R²) are difficult to predict trends accurately. It could not accurately describe the trends.

Thank you for this comment so we can explain our stance on these models as we possibly haven’t explained our perspective on the use of our models. First of all, the models were constructed to determine if the independent variables were significant predictors in a model when no other predictors that might affect the values of the dependent variables were in the model. In other words, our question is, for example: can yield be determined by fruit set when it is the only predictor and we know that lots of other factors affect yield? A significant model suggests that yes fruit set alone can predict yield and a significant F statistic suggests that the AVERAGE TREND in yield as fruit set changes is predictable, BUT individual data points can probably not be predicted with any accuracy if the r² is low. So, in direct answer to your question, the statistical models that we present throughout this paper, and specifically in Figures 3-5 suggest that the r² range from is low to moderate (0.21-0.53) in explanatory ability of the independent variables to explain the VARIANCE in the dependent variable and so it is correct that the models do not explain a high level of variation in the dependent variable. Therefore, what this suggests is that if one wanted to predict an individual data point (field) that one would have little power in doing so.  But, this is very different from predicting an average trend. The F statistic tells us how significant the ability of the model to predict the average trend is. All of these models have P values < 0.0001 and the standard errors of the slopes are 15% of the slopes or less, a high level of precision, especially for field ecology research. These two statistics, the F value and the high slope precision, tell us that the average trend can be predicted well, with much power, even though the ability to predict any INDIVIDUAL data points is low based upon r² (Freedman 2009). We have now pointed this out in the Results section.

David A. Freedman. Statistical Models: Theory and Practice. Cambridge University Press, 2009. ISBN 978-1-139-47731-4.

In my opinion, the logic of the research is poor, and the research design is not rigorous. The results are not convinced.

We have attempted to improve the clarity of our research approach and its logic by rewriting portions of the Introduction, Methods, Results, and Discussion sections in order to improve out manuscript. In our conclusion we have justified our study by suggesting that, to our knowledge, our data set is the most extensive pollinator, fruit set, and yield survey in fields representing a single crop that exists globally. This data is very labor intensive to obtain (multiple visits per field to measure bee activity density, fruit set, and yield, as well as components of yield such as berry size and weight) and represents the relationships between honey bee and wild native bee activity density and fruit set, fruit set and yield, and the relationship between honey bee hive density and honey bee forager activity density. In addition, variation in fruit set, yield, berry size and weight, honey bee activity densities, and wild native bee activity densities on per field basis for more than 200 grower managed fields over a period of 26 years. The fields were randomly sampled each year and the metrics were fairly consistent over the field survey period.  In addition, our within-field sampling yielded estimates with standard errors 10-20% of the mean which is considered high precision for field studies. Because of this we believe that our research design was rigorous to the point were few if any other crop pollination researchers have as powerful as a dataset to conduct economic analyses on and we have used “state of the art” analytical methods to explore our data. Because of this we have to disagree with you that our research is not rigorous and of poor quality.

Submission Date

26 January 2024

Date of this review

16 Mar 2024 15:03:26

Author Response File: Author Response.pdf

Round 3

Reviewer 2 Report

The article has been extensively revised to reach the state of acceptance for publication. I have the greatest respect for the authors’ revision.