the importance of forest structure to biodiversity...

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Review History

RSOS-160521.R0 (Original submission) Review form: Reviewer 1 Is the manuscript scientifically sound in its present form?

Yes Are the interpretations and conclusions justified by the results?

Yes Is the language acceptable?

Yes Is it clear how to access all supporting data? Supplementary files need revisions (see attached files). R code is provided. Do you have any ethical concerns with this paper? No Have you any concerns about statistical analyses in this paper?

No

The importance of forest structure to biodiversity–

productivity relationships

Friedrich J. Bohn and Andreas Huth

Article citation details R. Soc. open sci. 4: 160521.

http://dx.doi.org/10.1098/rsos.160521

Review timeline

Original submission: 15 July 2016 1st revised submission: 13 October 2016 2nd revised submission: 18 November 2016 Final acceptance: 21 November 2016

Note: Reports are unedited and appear as submitted by the referee. The review history appears in chronological order.

Note: This manuscript was transferred from another Royal Society journal with peer review.

on May 19, 2018http://rsos.royalsocietypublishing.org/Downloaded from

http://rsos.royalsocietypublishing.org/

2

Recommendation?

Major revision is needed (please make suggestions in comments) Comments to the Author(s) The manuscript deals with the effect of forest structure on the relationship between tree species diversity and stand productivity. It relies on the use of a gap model (FORMIND3.0) and a specific procedure for stand initialization called “Forest Factory”. The main message is that density and height heterogeneity have a large influence on productivity (in their case study, greater than the effect of species richness and functional diversity) and that the relationship between diversity and productivity depends on stand structure. This topic is highly interesting and highly relevant. Although based on a static perspective, the fact that population or community size structure modifies significantly the effect of diversity on productivity is of major interest for plant ecologists. This is also a complex issue and the authors tackled it quite well. Moreover, the authors brought important modifications to comply with reviewers’ comments. I have however several concerns about the analysis itself, the structure of the paper and the way the topic is presented. First, the structure of the paper is quite unusual and could be a bit clarified. The analysis of underlying mechanisms (see pages 8-9) should be introduced in the method as the interest of this analysis does not really depend on the results obtained for the effect of species diversity on productivity. Of course, such a modification would imply to better integrate mechanisms in the introduction and the results sections. The introduction is quite general and doesn’t provide any clear hypotheses about the potential effects of structural attributes on productivity. For instance, the important positive effect of basal area on productivity is well-known. That is why many authors consider density (Zeide 2005) as different from forest structure (see for instance Pommerening 2002). In the same vein, several recent articles found negative effects of size heterogeneity in monospecific stands (e.g. Bourdier et al. 2016) and one recent study (Dănescu et al. 2016) revealed positive effects of size heterogeneity (and species diversity) in mixed stands (in Germany). These studies already indicate that the effect of size heterogeneity on productivity can be significant in both monocultures and mixed stands. I think the authors could thus better inform the reader about these effects and try to be more specific when presenting their hypotheses. This would also help the authors to clarify their discussion. For instance, the authors don’t discuss thoroughly the mechanisms that could explain the negative effect of size heterogeneity on productivity. Finally, the idea of comparing mechanisms (see Bauhus and Forrester 2016 for a review of processes) is interesting. Unfortunately, it is not mentioned in the questions of the introduction. I have two concerns about the analysis. First, the authors don’t consider mean size or succession stage to control for the diversity and the size heterogeneity effects. The authors justified this choice by the fact that basal area and mean height are correlated in their data. I think this is a problem and not a justification. It means that the effect of basal area and mean size are confounded and that the author cannot separate them with their constructed data set. This is a pity as, according to figure 1, tree height has a major effect on tree growth efficiency (see next paragraph). I think it should be at least discussed (see Lasky et al. 2013, Zhang et al. 2012). Second, and most importantly, the fact that the Factory Model selects species according to their ability to have positive growth under shade means that relative abundances of species within a mixture can vary with density and size heterogeneity. I think it is important that the author try to control for this effect. I was not convinced by the validation section. The fact that climate data used for simulations is different from climate experienced by inventory plots appears problematic. However, I think that the comparisons of results obtained for simulations and empirical data is more interesting and more relevant. It shows that results are coherent using different approaches (empirical data, simulations). I suggest the authors focus more on this comparison.



3

In the main text, we lack some justifications for several important choices made by the authors (the reader has to read appendix files very carefully to understand these choices). Why do the authors standardise (normalise?) tree productivity according to tree crown area (page 4 line 10)? Why do you sum these values at the stand scale? Why is the maximum diameter value set to 50cm (a low value for a temperate forest)? I have read carefully the Appendix files. There are too many language mistakes (see corrections in the attached files). It is important that the authors explain on which basis they define their 15 stand structures (empirical data?) as some diameter distributions appear highly unrealistic (e.g. stand 15). I didn’t get what rule 1 consists of (how does it work?). Figure A4 (Appendix A): these graphs are of major importance for your results. They indicate that height of the trees impact tree growth efficiency (growth per unit of crown area). If I understand correctly, small and large trees are less efficient for all species (for Hainich environmental conditions). Is this pattern (which is important for your study) really supported by empirical studies? I was surprised by some values: for instance, your model predicts that small beech trees (a shade tolerant species) cannot grow when they receive less than 80% of available light at the top of their crown. Such a value appears very high. Figure 2 is difficult to read (even with subsamples). I suggest the authors provide the distribution of plots for each number of species in separate graphs (in a supplementary material). The number of inventory plots varies in your text: 2418 page 6 and 2415 page 7 References -Bourdier T, Cordonnier T, Kunstler G, Piedallu C, Lagarrigues G, Courbaud B. 2016. Tree size inequality reduces forest productivity: An analysis combining inventory data for ten European species and a light competition model. PLoS ONE 11. -Dănescu A, Albrecht AT, Bauhus J. 2016. Structural diversity promotes productivity of mixed, uneven-aged forests in southwestern Germany. Oecologia: 1-15. -Forrester, D.I., Bauhus. J. 2016. A review of processes behind diversity—productivity relationships in forests. Current Forestry Reports 2: 45-61. -Lasky JR, Uriarte M, Boukili VK, Erickson DL, John Kress W, Chazdon RL. 2014. The relationship between tree biodiversity and biomass dynamics changes with tropical forest succession. Ecology Letters 17: 1158-1167. -Pommerening A. 2002. Approaches to quantifying forest structures. Forestry 75: 305-324. -Zhang Y, Chen HYH, Reich PB. 2012. Forest productivity increases with evenness, species richness and trait variation: A global meta-analysis. Journal of Ecology 100: 742-749. -Zeide B. 2005. How to measure stand density. Trees 19: 1-14.

Review form: Reviewer 2 (David Coomes) Is the manuscript scientifically sound in its present form?

Yes Are the interpretations and conclusions justified by the results?

Yes Is the language acceptable? No Is it clear how to access all supporting data? Yes



4

Do you have any ethical concerns with this paper?

Yes Have you any concerns about statistical analyses in this paper? Yes Recommendation? Accept with minor revision (please list in comments) Comments to the Author(s) The authors explore the relationship between tree biodiversity and productivity of forests using a simulation modelling approach. They create a large number of forest stands in silico, each of which has a realistic stem-size distribution and is comprised of randomly generated mixtures of species. They then use a well-known spatially-explicit size-structured forest model within which trees compete with one another for light depending on the relative size, position and foliar density of their crowns. This model is used to calculate the annual aboveground woody growth of each constituent stem, and thence the above-ground wood production (AWP) of the whole stand. The authors repeat this exercise for almost 400,000 stands, and then explore the covariance between species richness and AWP estimates in these simulations. They find that forest structure (i.e. basal area and height heterogeneity) have a very strong influence on AWP, and that the productivity-biodiversity effect is small and contingent upon forest structure. This is an exciting piece of research, underpinned by very substantial computational work, that elegantly complements (and to some extent challenges) observational studies based on repeated measurements made in inventory plots. The journal has provided me with responses to previous reviews. I see that the authors have added new sections exploring “underlying mechanism” and “validation” of the simulations. I found the new mechanistic section of particular interest. I found the science compelling, but I would encourage the authors to focus on restructuring the text, in order that the paper gets the positive attention that it deserves. My comments below are aimed at improving the flow and wording of the manuscript. I have just two scientific points to raise: (a) Assumption iii included in the new section on page 9 got me thinking! The authors simulate stands in which the species identity of stems is initially random, but it light demanding trees (e.g. birch) have been placed beneath a dense canopy then the simulator will calculate that they have negative growth rates. Instead of using these negative growth rates when calculating AWP, the authors have instead replaced the offending stems by species that are more shade tolerant. Whilst this make sense in terms of re-creating realistic forests, this step is in effect replicating successional processes inside the simulator: it’s increasing the likelihood of complementarity effects in old-growth forests (i.e. those with high BA and low height heterogeneity). I haven’t thought through the consequence of this, but I suggest that it’s considered more explicitly in the discussion (b) Please would the authors provide a slightly longer explanation of the inner workings of FORMIND in the text (for those unwilling wade through lengthy SI sections) and particularly its main assumptions. I think it assumes that all plant “traits” including light-response curves for photosynthesis and respiration, allocation and allometry are invariant of the competitive environment a tree is found in. I’m not unhappy about these assumptions – a line must be drawn somewhere! – but feel that readers would benefit from having all this information in one place. “Minor” comments. The summary contains numerous grammatical errors. Please check this particularly carefully, as many readers never get beyond the summary!



5

Page 7 Line 26. Might I suggest replacing “horizontal tree density measures (basal area)” with “basal area”? In my view, basal area isn’t a good measure of tree density! Page 7 Line 21 “We compiled a large set of forest stands by using a new forest modelling approach, which we refer to as the forest factory approach”. I think “simulated a large set of forest stands by randomising species identities” would be a better word than “compiled” here. Page 7 Line 32. “For every forest stand, we measure productivity as above ground wood production per hectare for one year (AWP) using a process-based forest gap model”. Consider writing “we estimate the wood production of every tree in the stand using physiological relationships encoded in a process-based forest gap model (FORMIND) and then estimate instantaneous aboveground wood production by summing the wood production of all trees in the simulated stands”. I’ve included “instantaneous” here because your model isn’t accounting for mortality, so will give a high AWP than measured in permanent plots ( see papers by Coomes et al http://onlinelibrary.wiley.com/doi/10.1111/gcb.12622/abstract and Jucker et al. 2016 http://onlinelibrary.wiley.com/doi/10.1002/ece3.2175/pdf for similar approach being used in permanent plots, with some discussion on the subject) Page 7 Line 36. Please define “canopy structure” at this point or even before. Page 8: Consider including a nice explanatory figure here. Page 8 Line 11: “These species vary by allometry parameterisation, productivity and responses to climatic patterns”…. Suggest… “These species vary markedly in SHADE TOLERANCE (key to you finding any effect of biodiversity using your modelling approach), allometry, productivity and responses to climate” Page 8 Line 20: Again I suggest “estimate” instead of “measure” as you’re not going out and measuring things, you’re estimating them from a complex model. Page 8 Line 23: “The model considers establishment, 2 mortality, competition and growth processes.” I suggest “The model simulates the establishment, mortality, growth processes of trees that are competing for light” Page 8 Line 34 “as a proxy year for a typical climate regime of the temperate zone” suggest “which has a temperate climate” [ i.e. no need to assert this study necessarily applies elsewhere ] Page 9 Line 12: is it really “per area” for AGBtree ?

Page 10 “Only the structure class with a high BA and high Θ contains forest stands with a

maximum of seven species” … please follow this line through by stating why. Page 11 The authors should be praised for their efforts to compare modelling predictions with field measurements, but I don’t think that comparisons with inventory datasets should be described as “validation”. My suggestion would be that the eddy flux measurements are left where they are – simply mentioned in the methods as “validation” of the ecophysiological modelling approach. In my mind they’re contributing very little to the biodiversity issues that are central to the paper. I would suggest that comparisons with inventory datasets are given more prominence throughout the paper, as it’s now a selling point. Ps. it’s a great pity that the figures pertaining to the inventory results are tucked away in appendices. I’d love to see them in the main body of the text. Page 11 Up to you, but I suggest “Comparisons with field datasets” rather than “validation” here. Page 12 Line 10 “Second”…. Please make clearer what “First” is in the previous paragraph Page 12 Line 20 … There’s a tremendous amount of fascinating stuff summarised in this one paragraph! I suggest you describe your findings in a little more detail Page 12 Line 32… isn’t it 379,000 stands? That’s quite a lot more than 300,000 Page 13 Line 26. Again, do you need to use basal area as a proxy for stem density? Why not just stick with basal area as a measure of “forest structure”? In self thinning stands, the two variables are strongly negatively correlated! Page 13: Underlying mechanisms. There are several really neat ideas in this new section. To my mind, it’s this section that really lifts the paper to a high standard. But it’s not very tightly written at present, and it feels “tacked on” to the original manuscript rather than being integrated into it. I’d encourage the authors to include reference to this section in the summary, introduction and methods.



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Page 14: “The forest factory approach”. This section makes many good points, but it needs consolidating into paragraphs (currently it has too many one sentence paragraphs) and perhaps shortening. Page 16: “Comparison with other studies”. I think this section is all about inventory analyses. Thus might you consider moving the “a. Comparison with the German forest inventory” section down here? There are several other inventory studies you could mention here, including the two I mentioned above. Several have included basal area alongside biodiversity in their regression or path analyses. I’m not aware of any that have also included height heterogeneity, so that’s a neat addition to the literature.

Decision letter (RSOS-160521) 12-Sep-2016 Dear Mr Bohn, The editors assigned to your paper ("Forest structure shapes biodiversity-productivity relationships.") has now received comments from reviewers. We would like you to revise your paper in accordance with the referee and Subject Editor suggestions which can be found below (not including confidential reports to the Editor). Please note this decision does not guarantee eventual acceptance. Please submit a copy of your revised paper within three weeks (i.e. by the 05-Oct-2016). If we do not hear from you within this time then it will be assumed that the paper has been withdrawn. In exceptional circumstances, extensions may be possible if agreed with the Editorial Office in advance.We do not allow multiple rounds of revision so we urge you to make every effort to fully address all of the comments at this stage. If deemed necessary by the Editors, your manuscript will be sent back to one or more of the original reviewers for assessment. If the original reviewers are not available we may invite new reviewers. To revise your manuscript, log into http://mc.manuscriptcentral.com/rsos and enter your Author Centre, where you will find your manuscript title listed under "Manuscripts with Decisions." Under "Actions," click on "Create a Revision." Your manuscript number has been appended to denote a revision. Revise your manuscript and upload a new version through your Author Centre. When submitting your revised manuscript, you must respond to the comments made by the referees and upload a file "Response to Referees" in "Section 6 - File Upload". Please use this to document how you have responded to the comments, and the adjustments you have made. In order to expedite the processing of the revised manuscript, please be as specific as possible in your response. In addition to addressing all of the reviewers' and editor's comments please also ensure that your revised manuscript contains the following sections as appropriate before the reference list:

• Ethics statement (if applicable) If your study uses humans or animals please include details of the ethical approval received, including the name of the committee that granted approval. For human studies please also detail whether informed consent was obtained. For field studies on animals please include details of all permissions, licences and/or approvals granted to carry out the fieldwork.



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Please list the source of funding for each author. Once again, thank you for submitting your manuscript to Royal Society Open Science and I look forward to receiving your revision. If you have any questions at all, please do not hesitate to get in touch. Yours sincerely, Andrew Dunn Senior Publishing Editor Royal Society Open Science on behalf of Kevin Padian Subject Editor, Royal Society Open Science [email protected]



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Comments to Author: Reviewers' Comments to Author: Reviewer: 1 Comments to the Author(s) The manuscript deals with the effect of forest structure on the relationship between tree species diversity and stand productivity. It relies on the use of a gap model (FORMIND3.0) and a specific procedure for stand initialization called “Forest Factory”. The main message is that density and height heterogeneity have a large influence on productivity (in their case study, greater than the effect of species richness and functional diversity) and that the relationship between diversity and productivity depends on stand structure. This topic is highly interesting and highly relevant. Although based on a static perspective, the fact that population or community size structure modifies significantly the effect of diversity on productivity is of major interest for plant ecologists. This is also a complex issue and the authors tackled it quite well. Moreover, the authors brought important modifications to comply with reviewers’ comments. I have however several concerns about the analysis itself, the structure of the paper and the way the topic is presented. First, the structure of the paper is quite unusual and could be a bit clarified. The analysis of underlying mechanisms (see pages 8-9) should be introduced in the method as the interest of this analysis does not really depend on the results obtained for the effect of species diversity on productivity. Of course, such a modification would imply to better integrate mechanisms in the introduction and the results sections. The introduction is quite general and doesn’t provide any clear hypotheses about the potential effects of structural attributes on productivity. For instance, the important positive effect of basal area on productivity is well-known. That is why many authors consider density (Zeide 2005) as different from forest structure (see for instance Pommerening 2002). In the same vein, several recent articles found negative effects of size heterogeneity in monospecific stands (e.g. Bourdier et al. 2016) and one recent study (Dănescu et al. 2016) revealed positive effects of size heterogeneity (and species diversity) in mixed stands (in Germany). These studies already indicate that the effect of size heterogeneity on productivity can be significant in both monocultures and mixed stands. I think the authors could thus better inform the reader about these effects and try to be more specific when presenting their hypotheses. This would also help the authors to clarify their discussion. For instance, the authors don’t discuss thoroughly the mechanisms that could explain the negative effect of size heterogeneity on productivity. Finally, the idea of comparing mechanisms (see Bauhus and Forrester 2016 for a review of processes) is interesting. Unfortunately, it is not mentioned in the questions of the introduction. I have two concerns about the analysis. First, the authors don’t consider mean size or succession stage to control for the diversity and the size heterogeneity effects. The authors justified this choice by the fact that basal area and mean height are correlated in their data. I think this is a problem and not a justification. It means that the effect of basal area and mean size are confounded and that the author cannot separate them with their constructed data set. This is a pity as, according to figure 1, tree height has a major effect on tree growth efficiency (see next paragraph). I think it should be at least discussed (see Lasky et al. 2013, Zhang et al. 2012). Second, and most importantly, the fact that the Factory Model selects species according to their ability to have positive growth under shade means that relative abundances of species within a mixture can vary with density and size heterogeneity. I think it is important that the author try to control for this effect. I was not convinced by the validation section. The fact that climate data used for simulations is different from climate experienced by inventory plots appears problematic. However, I think that the comparisons of results obtained for simulations and empirical data is more interesting and



9

more relevant. It shows that results are coherent using different approaches (empirical data, simulations). I suggest the authors focus more on this comparison. In the main text, we lack some justifications for several important choices made by the authors (the reader has to read appendix files very carefully to understand these choices). Why do the authors standardise (normalise?) tree productivity according to tree crown area (page 4 line 10)? Why do you sum these values at the stand scale? Why is the maximum diameter value set to 50cm (a low value for a temperate forest)? I have read carefully the Appendix files. There are too many language mistakes (see corrections in the attached files). It is important that the authors explain on which basis they define their 15 stand structures (empirical data?) as some diameter distributions appear highly unrealistic (e.g. stand 15). I didn’t get what rule 1 consists of (how does it work?). Figure A4 (Appendix A): these graphs are of major importance for your results. They indicate that height of the trees impact tree growth efficiency (growth per unit of crown area). If I understand correctly, small and large trees are less efficient for all species (for Hainich environmental conditions). Is this pattern (which is important for your study) really supported by empirical studies? I was surprised by some values: for instance, your model predicts that small beech trees (a shade tolerant species) cannot grow when they receive less than 80% of available light at the top of their crown. Such a value appears very high. Figure 2 is difficult to read (even with subsamples). I suggest the authors provide the distribution of plots for each number of species in separate graphs (in a supplementary material). The number of inventory plots varies in your text: 2418 page 6 and 2415 page 7 References -Bourdier T, Cordonnier T, Kunstler G, Piedallu C, Lagarrigues G, Courbaud B. 2016. Tree size inequality reduces forest productivity: An analysis combining inventory data for ten European species and a light competition model. PLoS ONE 11. -Dănescu A, Albrecht AT, Bauhus J. 2016. Structural diversity promotes productivity of mixed, uneven-aged forests in southwestern Germany. Oecologia: 1-15. -Forrester, D.I., Bauhus. J. 2016. A review of processes behind diversity—productivity relationships in forests. Current Forestry Reports 2: 45-61. -Lasky JR, Uriarte M, Boukili VK, Erickson DL, John Kress W, Chazdon RL. 2014. The relationship between tree biodiversity and biomass dynamics changes with tropical forest succession. Ecology Letters 17: 1158-1167. -Pommerening A. 2002. Approaches to quantifying forest structures. Forestry 75: 305-324. -Zhang Y, Chen HYH, Reich PB. 2012. Forest productivity increases with evenness, species richness and trait variation: A global meta-analysis. Journal of Ecology 100: 742-749. -Zeide B. 2005. How to measure stand density. Trees 19: 1-14. Reviewer: 2 Comments to the Author(s) The authors explore the relationship between tree biodiversity and productivity of forests using a simulation modelling approach. They create a large number of forest stands in silico, each of which has a realistic stem-size distribution and is comprised of randomly generated mixtures of species. They then use a well-known spatially-explicit size-structured forest model within which trees compete with one another for light depending on the relative size, position and foliar density of their crowns. This model is used to calculate the annual aboveground woody growth of each constituent stem, and thence the above-ground wood production (AWP) of the whole stand. The authors repeat this exercise for almost 400,000 stands, and then explore the covariance between species richness and AWP estimates in these simulations. They find that



10

forest structure (i.e. basal area and height heterogeneity) have a very strong influence on AWP, and that the productivity-biodiversity effect is small and contingent upon forest structure. This is an exciting piece of research, underpinned by very substantial computational work, that elegantly complements (and to some extent challenges) observational studies based on repeated measurements made in inventory plots. The journal has provided me with responses to previous reviews. I see that the authors have added new sections exploring “underlying mechanism” and “validation” of the simulations. I found the new mechanistic section of particular interest. I found the science compelling, but I would encourage the authors to focus on restructuring the text, in order that the paper gets the positive attention that it deserves. My comments below are aimed at improving the flow and wording of the manuscript. I have just two scientific points to raise: (a) Assumption iii included in the new section on page 9 got me thinking! The authors simulate stands in which the species identity of stems is initially random, but it light demanding trees (e.g. birch) have been placed beneath a dense canopy then the simulator will calculate that they have negative growth rates. Instead of using these negative growth rates when calculating AWP, the authors have instead replaced the offending stems by species that are more shade tolerant. Whilst this make sense in terms of re-creating realistic forests, this step is in effect replicating successional processes inside the simulator: it’s increasing the likelihood of complementarity effects in old-growth forests (i.e. those with high BA and low height heterogeneity). I haven’t thought through the consequence of this, but I suggest that it’s considered more explicitly in the discussion (b) Please would the authors provide a slightly longer explanation of the inner workings of FORMIND in the text (for those unwilling wade through lengthy SI sections) and particularly its main assumptions. I think it assumes that all plant “traits” including light-response curves for photosynthesis and respiration, allocation and allometry are invariant of the competitive environment a tree is found in. I’m not unhappy about these assumptions – a line must be drawn somewhere! – but feel that readers would benefit from having all this information in one place.

“Minor” comments. The summary contains numerous grammatical errors. Please check this particularly carefully, as many readers never get beyond the summary! Page 7 Line 26. Might I suggest replacing “horizontal tree density measures (basal area)” with “basal area”? In my view, basal area isn’t a good measure of tree density! Page 7 Line 21 “We compiled a large set of forest stands by using a new forest modelling approach, which we refer to as the forest factory approach”. I think “simulated a large set of forest stands by randomising species identities” would be a better word than “compiled” here. Page 7 Line 32. “For every forest stand, we measure productivity as above ground wood production per hectare for one year (AWP) using a process-based forest gap model”. Consider writing “we estimate the wood production of every tree in the stand using physiological relationships encoded in a process-based forest gap model (FORMIND) and then estimate instantaneous aboveground wood production by summing the wood production of all trees in the simulated stands”. I’ve included “instantaneous” here because your model isn’t accounting for mortality, so will give a high AWP than measured in permanent plots ( see papers by Coomes et al http://onlinelibrary.wiley.com/doi/10.1111/gcb.12622/abstract and Jucker et al. 2016 http://onlinelibrary.wiley.com/doi/10.1002/ece3.2175/pdf for similar approach being used in permanent plots, with some discussion on the subject) Page 7 Line 36. Please define “canopy structure” at this point or even before. Page 8: Consider including a nice explanatory figure here. Page 8 Line 11: “These species vary by allometry parameterisation, productivity and responses to climatic patterns”…. Suggest… “These species vary markedly in SHADE TOLERANCE (key to



11

you finding any effect of biodiversity using your modelling approach), allometry, productivity and responses to climate” Page 8 Line 20: Again I suggest “estimate” instead of “measure” as you’re not going out and measuring things, you’re estimating them from a complex model. Page 8 Line 23: “The model considers establishment, 2 mortality, competition and growth processes.” I suggest “The model simulates the establishment, mortality, growth processes of trees that are competing for light” Page 8 Line 34 “as a proxy year for a typical climate regime of the temperate zone” suggest “which has a temperate climate” [ i.e. no need to assert this study necessarily applies elsewhere ] Page 9 Line 12: is it really “per area” for AGBtree ?

Page 10 “Only the structure class with a high BA and high Θ contains forest stands with a

maximum of seven species” … please follow this line through by stating why. The authors should be praised for their efforts to compare modelling predictions with field measurements, but I don’t think that comparisons with inventory datasets should be described as “validation”. My suggestion would be that the eddy flux measurements are left where they are – simply mentioned in the methods as “validation” of the ecophysiological modelling approach. In my mind they’re contributing very little to the biodiversity issues that are central to the paper. I would suggest that comparisons with inventory datasets are given more prominence throughout the paper, as it’s now a selling point. Ps. it’s a great pity that the figures pertaining to the inventory results are tucked away in appendices. I’d love to see them in the main body of the text. Page 11 Up to you, but I suggest “Comparisons with field datasets” rather than “validation” here. Page 12 Line 10 “Second”…. Please make clearer what “First” is in the previous paragraph Page 12 Line 20 … There’s a tremendous amount of fascinating stuff summarised in this one paragraph! I suggest you describe your findings in a little more detail Page 12 Line 32… isn’t it 379,000 stands? That’s quite a lot more than 300,000 Page 13 Line 26. Again, do you need to use basal area as a proxy for stem density? Why not just stick with basal area as a measure of “forest structure”? In self thinning stands, the two variables are strongly negatively correlated! Page 13: Underlying mechanisms. There are several really neat ideas in this new section. To my mind, it’s this section that really lifts the paper to a high standard. But it’s not very tightly written at present, and it feels “tacked on” to the original manuscript rather than being integrated into it. I’d encourage the authors to include reference to this section in the summary, introduction and methods. Page 14: “The forest factory approach”. This section makes many good points, but it needs consolidating into paragraphs (currently it has too many one sentence paragraphs) and perhaps shortening. Page 16: “Comparison with other studies”. I think this section is all about inventory analyses. Thus might you consider moving the “a. Comparison with the German forest inventory” section down here? There are several other inventory studies you could mention here, including the two I mentioned above. Several have included basal area alongside biodiversity in their regression or path analyses. I’m not aware of any that have also included height heterogeneity, so that’s a neat addition to the literature.

Author's Response to Decision Letter for (RSOS-160521) See Appendix C.



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RSOS-160521.R1 (Revision) Review form: Reviewer 1 Is the manuscript scientifically sound in its present form? Yes Are the interpretations and conclusions justified by the results?

Yes Is the language acceptable?

Yes Is it clear how to access all supporting data? Supplementary materials have been improved and are now clear and adequate. Do you have any ethical concerns with this paper? No Have you any concerns about statistical analyses in this paper? No Recommendation?

Accept with minor revision (please list in comments) Comments to the Author(s)

The authors improved the manuscript in many ways. They performed new analyses and answered the main issues I raised in my first review. At this stage, I have only very minor comments. Abstract line3: specify the structural attributes considered (i.e. stand density and height heterogeneity) within brackets. line6: add “species” before “diversity”. line10: the mechanisms involved (?) Material and methods Correct equations AWPS and AWPN by replacing s=1 and n=1 by i=1 and by replacing AWPs,n by AWPs,i and AWPi,n. line24 section f: correct than (then) line26 section f: correct add (added) section f: why do you need to define psi (not used in the result section and in the figures)? Results In order to be homogeneous, please use BA for basal area when you use theta for height heterogeneity. line 3-5 section b: provide just a sentence to explain why this is interesting to quantify selection and complementarity effects (this comes a bit abruptly). Discussion: Zeide 2005 and Pommering et al. (2011) are not in the reference list. Do you mean Pommerening ? You could quote Pommerening (2002) instead of using these two references. Figure 2: the caption appears incomplete (?) Figure 8: it would be useful to represent standards deviations. Appendix A: validate all your modifications (see reference list). Appendix B: correct the reference of Morin et al.



13

Reference Pommerening, A. 2002. Approaches to quantifying forest structures. Forestry 75, 305-324

Decision letter (RSOS-160521.R1) 11-Nov-2016 Dear Mr Bohn: On behalf of the Editors, I am pleased to inform you that your Manuscript RSOS-160521.R1 entitled "The importance of forest structure to biodiversity-productivity relationships." has been accepted for publication in Royal Society Open Science subject to minor revision in accordance with the referee suggestions. Please find the referees' comments at the end of this email. The reviewers and Subject Editor have recommended publication, but also suggest some minor revisions to your manuscript. Therefore, I invite you to respond to the comments and revise your manuscript.

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14

We suggest the following format: AB carried out the molecular lab work, participated in data analysis, carried out sequence alignments, participated in the design of the study and drafted the manuscript; CD carried out the statistical analyses; EF collected field data; GH conceived of the study, designed the study, coordinated the study and helped draft the manuscript. All authors gave final approval for publication.

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15

please ensure these are accurate and informative so that your files can be found in searches. Files on figshare will be made available approximately one week before the accompanying article so that the supplementary material can be attributed a unique DOI. Once again, thank you for submitting your manuscript to Royal Society Open Science and I look forward to receiving your revision. If you have any questions at all, please do not hesitate to get in touch. Best wishes Andrew Dunn Senior Publishing Editor Royal Society Open Science [email protected] on behalf of Kevin Padian Subject Editor, Royal Society Open Science Comments to Author: Reviewer: 1 Comments to the Author(s) The authors improved the manuscript in many ways. They performed new analyses and answered the main issues I raised in my first review. At this stage, I have only very minor comments. Abstract line3: specify the structural attributes considered (i.e. stand density and height heterogeneity) within brackets. line6: add “species” before “diversity”. line10: the mechanisms involved (?) Material and methods Correct equations AWPS and AWPN by replacing s=1 and n=1 by i=1 and by replacing AWPs,n by AWPs,i and AWPi,n. line24 section f: correct than (then) line26 section f: correct add (added) section f: why do you need to define psi (not used in the result section and in the figures)? Results In order to be homogeneous, please use BA for basal area when you use theta for height heterogeneity. line 3-5 section b: provide just a sentence to explain why this is interesting to quantify selection and complementarity effects (this comes a bit abruptly). Discussion: Zeide 2005 and Pommering et al. (2011) are not in the reference list. Do you mean Pommerening ? You could quote Pommerening (2002) instead of using these two references. Figure 2: the caption appears incomplete (?) Figure 8: it would be useful to represent standards deviations. Appendix A: validate all your modifications (see reference list). Appendix B: correct the reference of Morin et al. Reference Pommerening, A. 2002. Approaches to quantifying forest structures. Forestry 75, 305-324



16

Author's Response to Decision Letter for (RSOS-160521.R1) Many thanks for rereading the manuscript. According to the suggestions we did the following changes: Abstract line3: specify the structural attributes considered (i.e. stand density and height heterogeneity) within brackets. Done. line6: add “species” before “diversity”. We follow the suggestion. line10: the mechanisms involved (?) We revised the sentence. Material and methods Correct equations AWPS and AWPN by replacing s=1 and n=1 by i=1 and by replacing AWPs,n by AWPs,i and AWPi,n. We have corrected the equation following the suggestions. line24 section f: correct than (then);line26 section f: correct add (added) We have corrected the mistakes. section f: why do you need to define psi (not used in the result section and in the figures)? We deleted the formula and the previous sentence. Results In order to be homogeneous, please use BA for basal area when you use theta for height heterogeneity. We follow the suggestion. line 3-5 section b: provide just a sentence to explain why this is interesting to quantify selection and complementarity effects (this comes a bit abruptly). We reformulate this passage. Discussion: Zeide 2005 and Pommering et al. (2011) are not in the reference list. Do you mean Pommerening ? You could quote Pommerening (2002) instead of using these two references. We deleted Zeide 2005 and correct the name and year of Pommerening (2002). Figure 2: the caption appears incomplete (?) We revised the caption. Figure 8: it would be useful to represent standards deviations. We modified the figure and add standard deviations. Appendix A: validate all your modifications (see reference list). Done. Appendix B: correct the reference of Morin et al. We deleted the unused reference. Reference Pommerening, A. 2002. Approaches to quantifying forest structures. Forestry 75, 305-324

Decision letter (RSOS-160521.R2) 21-Nov-2016 Dear Mr Bohn, I am pleased to inform you that your manuscript entitled "The importance of forest structure to biodiversity-productivity relationships." is now accepted for publication in Royal Society Open Science.



17

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Appendix A - Additional information about the method and validation

A.1 Climate data

Two climate time series are used in this study. The first one (fig A1) consists of one “typical” year and is needed

in the forest factory for the creation process of the forest stands. The second one (fig A2) consists of five years,

which are used to calculated average productivities of these five independent scenario years. Note, tree allometries

stay constant for all five scenarios.

Figure A1: Overview of climate conditions used as input for the forest stand creation. The climate data set was measured at FLUXNET-station Hainich in 2007. (a) daily precipitation [mm], (b) daily air temperature [°C], (c) daily incoming radiation [photoactive photon flux density µmol/(m²s)].

Figure A2: Overview of climate conditions used as input for the final productivity calculation. The climate data set was measured at FLUXNET-station Hainich from 2000 to 2004. (a) daily precipitation [mm], (b) daily air temperature [°C], (c) daily incoming radiation [photoactive photon flux density µmol/(m²s)].

Appendix A on May 19, 2018http://rsos.royalsocietypublishing.org/Downloaded from


A.2 Detailed description of generation of the forest patches.

The used stem size distributions are based on a Weibull-distribution (e.g.: Ryniker et al. 2006, Taubert et

al. 2013). We define that every species identities can be assigned to every tree size of the stem size

distribution. As the maximal stem diameter is 50 cm due to the species-parameterization the maximal

stem size in every stem size distribution is set to 50 cm. The peaks of the stem size distribution are set at

a stem diameter of 5,15,25,35 and 45 cm whereby the 95% quintile are set at a stem diameter of

6,16,26,36 and 46 cm (fig. A3).

Figure A3: Overview of the different stem size distributions.

For every combination of species mixtures and stem size distributions we generate 100 patches of

400m² (= 4 hectare in total). For every hectare (25 patches) we execute step one and step two.

Step one: we determine how many trees can be found per hectare by adding tree per tree

reproducing the stem size distribution as good as possible (rule 2). Thereby the only limitation is the

space occupied by their crowns (rule 1) and species identities of trees are chosen randomly from the

current species pool. This results in a maximal stem number per hectare.

Step two: We start the placement of trees in the 25 patches of the stem size distribution resulting

from step 1 with the largest tree (defined by the largest stem diameter) followed by the next smaller

one. Every tree is assigned to one of the patches randomly. Before every tree placement we check



a) …if there is enough space in the patch for the tree crown. If not another patch is selected

randomly. If no patch could take up the tree the total number of trees for the current hectare is

reduced and the filling process of step two restarts.

b) …if the assigned species identity of the tree has a positive productivity under the current light

and environmental conditions (see fig 1 in the paper). If this is not the case another species

identity (if available) is tested for positive productivity. If no species identity (of the current

mixture) has a positive productivity, another patch is selected and the placement starts with the

original species identity. If no patch could host the current tree the total number of trees in the

hectare is reduced and the filling process of step two restarts.

c) … if the change in light conditions results in a negative productivity of any other tree in the

patch. If this is the case, we check if a species identity with same stem diameter and positive

productivity is available, which shades other trees less than the original one so that all trees have

a positive productivity. If not all criteria are fulfilled another patch is selected. If no patch could

host the tree the total number of trees for the current hectare is reduced and the filling process

of step two restarts.

Note, if the tree number of the stem size distribution must be reduced, the reduction is executed in a

way that keeps the shape of distribution at the hectare scale as good as possible.

The described procedure is implemented in R.



Figure A4: productivity per projected crown area of all eight species. Productivity depends on tree height and available light at the top of the tree under the given environmental conditions (Hainich 2007). Light-height combination with negative productivity is not plotted (white area).

References

Ryniker K, Bush J, Van Auken O. Structure of quercus gambelii communities in the Lincoln

national forest, New Mexico, USA. Forest Ecol. and Manag. 2006; 233: 69–77 (doi:

10.1016/j.foreco.2006.06.008)

Taubert F, Hartig F, Dobner HJ, Huth A. On the challenge of fitting tree size distributions in

ecology. PLoS ONE, 2013; 8: e58036 (doi: 10.1371/journal.pone.0058036)



A.3Validation of forest factory

We also analyze the relationship between observed and simulated productivity including negative

values (figure 5 in manuscript). Here we show the whole data cloud as scatterplot (figure A5).

Figure A5: validation graphic fig 3b) including all points. Every point represent compares the productivity of a forest plot of the German forest inventory with the simulated productivity of that plot. Points are transparent.



Appendix B

B.1 Impact of temperature and functional diversity on the results.

To explore the sensitivity of the results in figure 4 to changes in the temperature of the used climate

time series, we reconduct the full analysis using a modified climate times series (we alter the

temperature time series by 1.5°C, resulting in a mean annual temperature of 6.8°C and 9.8°C). In general,

the observed pattern persists (figure B1, first & second rows). There is a slightly positive effect for forest

stands with low height heterogeneity but a negative effect for forests with high height heterogeneity.

Additionally, the variability of the productivity between the forest stands increases with increasing

temperatures.

To analyse the effect of functional diversity on productivity (instead of richness), we calculate Rao´s

Q (Rao 1982, Laliberte & Legendre 2010) using all of the physiological parameters that are related to the

productivity calculation (n=12). However, the effect of richness on productivity is negligible (figure B1).

The variability in productivity did not decrease with increasing Rao´s Q as it did for species number.

Figure B1: Sensitivity of forest stand productivity (above-ground wood production) against mean annual temperature (MAT).

Left column based on simulation with a MAT of 6.8°C (fig a), b), c), middle column (fig d), e), f)) based on the measured data of

Hainich and right column based on a simulation with a MAT of 9.8°C (fig g), h), i)). Mean productivity of the nine structure

classes fig( a), d), g)): low, mid and high basal area BA (5-15 m² hectare-1

; 15-25 m² hectare-1

; 25-35 m² hectare-1

) and low mid

and high tree height heterogeneity Θ (O.5-2.5 m; 2.5-4.5 m; 4.5-6.5 m ); Mean productivity depending on species number (fig b),

e), h) of forest stand. Mean productivity depending on Rao´s Q ( fig c), f), i)). Gray bars indicate the interquartile range.

Comment [CT1]: Functional diversity?

Appendix B on May 19, 2018http://rsos.royalsocietypublishing.org/Downloaded from


B.2 Analysis of the German forest inventory and comparison to results of

forest factory

We analyse the influence of structure on productivity within the 2418 selected plots of the German

forest inventory in the same manner as the forest factory and calculate AWPandAWP (see method

section). Because forest stands with large tree height heterogeneities were rare (2 % show height

heterogeneity larger 4 m), we calculated results for four new height heterogeneity classes (0-1, 1-2, 2-3,

3-4 m) and add one basal area class (35-45 m²). We analyse the forest stands of the forest factory using

the same structure classes and the climate measurements from Hainich for the year 2000. The

productivity in the field data increases with basal area, whereas it decreases with increasing tree height

heterogeneity in a manner similar to that observed in the analysis of the forest factory dataset (figure

B2, compare with figure 4). Additionally, the increment of productivity of 250 % between forest stands of

low and high basal areas is similar to the productivity increment of forest stands generated by the forest

factory. Finally, the almost constant productivity of forest stands in the highest tree height heterogeneity

class is also found in the forest stands of the forest factory.

Figure B2: Analysis of mean forest stand productivity (above-ground wood production) of the German forest inventory (a)

and forest stands of the forest factory (b) for 16 structure classes. Basal area classes were 5-15; 15-25; 25-35 and 35-45 m²

hectare-1

. Tree height heterogeneity (Θ) classes were 0-1; 1-2; 2-3 and 3-4 m.

We also analyse the relationship between diversity and productivity by using two different methods.

First, we calculate theAWP for the plots of the German forest inventory, which consists only of beech,

spruce or pine trees or their mixtures. This selection was made because other mixtures do not cover a

Comment [CT2]: This is an oversimplification!

Actually, only the highest heterogeneity level

appears to have an important effect with German

forest inventory while the sensitivity is higher with

the model.



sufficient number of forest structure classes for the analysis. Second, we calculate the mean productivity

of all plots containing the same number of species (as conducted, for example, by Vila et al 2007). With

the second analysis, we find an increase in productivity of 10 % between one and two species mixtures,

which corresponds to the findings of other studies (e.g., Vila et al 2007). The calculated AWP instead

shows no effect of diversity, which corresponds to the analysis of the forest factory (fig B1, and figure 4).

Figure B3: Mean productivity of forest stands (above-ground wood production) depending on species number for stands of the

German forest inventory, which includes only beech, spruce and pine and their mixtures. Grey bars represent the mean

productivity over all plots with the corresponding species number. Blue bars represent mean productivity ( of the

Manuscript), where we build the mean over all , while keeping the species number constant. Lines represent the

interquartile range.

B.3 Forest stands with only one or two species

The relationship between forest structure and productivity (fig B1) can be analyzed for stands with

only one species. Thereby the general pattern (productivity increases with increasing basal area and

decreasing height heterogeneity) can be found in all monocultures and mixtures (fig B4, B5, B6).

However, monocultures vary in their absolute productivity values (fig B4), but AWPN for all monocultures

shows the general pattern quite well. In case of two species mixture with beech (fig B5) the differences

of the productivity-structure-relationships between the mixtures are much lower and vanish almost

completely for species mixtures with more than two species

Comment [CT3]: B4 deals with monocultures!

Comment [CT4]: There is no B6



Figure B4: Analysis of the structure-productivity relationship of monocultures (a-h); every dot represent one forest stand.

Darker grays indicate higher height heterogeneity classes. AWPN values over all eight monocultures (i) with IQR as gray stripes.



Figure B5: Analysis of the structure-productivity relationship of two-species-mixtures with beech (a-g) and beech monoculture

(h); every dot represent one forest stand. Darker grays indicate higher height heterogeneity classes. (i) AWPN over all seven

two-species mixtures with IQR as gray stripes.

B.4 additive Partitioning analysis

Based on the coneptconcept of Loreau & Hector (2001) we perform and additional

parititioningpartitioning analysis. As the forest factory does not include information about age we use as

monocultures the average of those monocultures which show a similar forest structure. The structure

indices (BA, Ɵ) are z-transformed so that both have a mean of 0 and a standard deviation of 1. We select

the 10 nearest monocultures using Euclidian distance ( 95% of the structural distances between

monoculutresmonocultures and the mixtures are below 0.22 in the z-transformed structure and the

average distance is 0.08).

The overall analysis of the forest stands shows that both complementarity/ selection mechanisms

hasmechanisms have low potential to explain the variance of the forest productivity (fig B6). This finding



does not change if we use relative abundances (in terms of biomass or basal area) for the calculation of

the expected yield.

Figure B8: additional partitioning. a) complementarity; b) selection; c) net biodiversity effect. Line is a linear model with a as

slope. Stars indicate significance of the model: *** indicates a p-value <0.001. Every dot represents one forest stand.

The analysis of the nine different forest structure classes shows also hardly any correlation between

selection/complementarity and forest productivity.

B.5 example of the application of structure-optimality-mechanism

We analyse the relationship between diversity and the three indices of the structure-optimality-

mechanism (fig B1) by calculating the coefficient of determination for all structure classes.

The correlation between species number and optimality or forest structure indices are on average

much higher than the correlation found in the additive partitioning analysis (fig B12) and reach an R² of

up to 0.25. Please note, that a high correlation between species number and one index does not

automatically result in a strong correlation of that indixindex with the productivity . For instance, in the

forest structure class with high basal areas and low tree height heterogeneity species number correlates

quite well with structure indices (fig 13 a & b) but only week correlation with optimality (fig 13 c)).

However, optimality is the main driver of productivity in this structure class (fig 13 f).

Comment [CT5]: B11?

Comment [CT6]: Check the sentence



Figure B12: Coefficient of determination (R²) between number of species and the indices of the structure-optimality-

mechanism for the nine structure classes.



Figure B13: Relationship between number of species and forest structure indices (Ɵ and BA) as well as optimality (Ω) for

forest stands with high basal area and low tree height heterogeneity (a, b, c)). Relationship between forest structure indices (Ɵ

and BA) and optimality (Ω) with forest productivity (AWP) (d, e, f). Every dot represents one forest stand. Black line shows a

fitted linear model.



B.6 Diversity-productivity relationships covering only one forest structure

class.

Beside the comparison between the forest stands of the forest factory with analysis of large data set,

which based on forest inventories and cover several forest structure classes, subsamples of the forest

factory can be compared with small datasets which belong only to one forest structure class.

Positive diversity-productivity relationship:

Many studies have analysed forest productivity in two or three species mixture experiments (e.g. Edgar

et al. 2001, Chen et al 2003, Amoroso et al 2007, Pretzsch et al 2010). For instance, Edgar et al. 2001

analysed pure aspen stands and stands with admixtures of other species. The analysed forest stands are

described by a top canopy height of ~ 25 m, a high basal area and a mediumΘ. For the analysed forest

stands an increase of basal area with diversity was found (basal area increase of 30%). Beside a positive

structure mechanism (see manuscript fig 4), the optimality-mechanism might also support the positive

effect: In the monocultures larger aspen trees shade some smaller ones. In the mixture, smaller trees



belong mostly to more shade-tolerant species and aspen only occur in the top layer which should result in

an increase in optimality. Thus, the positive effect of diversity on productivity results from positive

correlation between diversity and structure as well as optimality. This change in both forest properties

(structure and optimality) is then responsible for the increase in productivity (figure B10). In other studies

sometimes a separation over height of the species is described (e.g Pretsch et al. 2010) or a change in

forest structure can be related to the observed productivity (e.g Amoroso et al 2007, Chen et al 2003).

Negative diversity-productivity relationship:

A decreasing relationship between diversity and productivity was found by Jacob et al. 2010 in the

Hainich forest (Germany). They analysed nine forest plots which all show high basal areas, high tree

height heterogeneity and cover an area of 50x50 meter. The plots contain only deciduous tree species

(more than six) whereby the monocultures are dominated by beech (abundance = 96%). For the

corresponding forest stands of the forest factory (same structure class only deciduous trees) (n =16) a

negative relationship between Shannon-diversity and productivity can be observed which fits to the field

observations. Our analysis of the structure-optimality-mechanisms reveals a strong effect of optimality (R²

= 0.91) and no effect of structure (R²=0.01). Thus, the negative relationship can be explained by the fact

that beech is the most productive species for all sizes of trees in such a forest (figure 6, area A). The low

diverse forests in the study are dominated by beech resulting in the maximal productivity (high Ω). If beech

trees are replaced by trees of other species (due to an increase in diversity) the productivity have to

decrease. In this example diversity has a negative effect on optimality, while structural effects can be

neglected (see manuscribtmanuscript figure 7). The result is a negative diversity-productivity-relationship.

This negative effect also occurs if we include also evergreen species (spruce and pine).



Figure B11: Concept of the structure-optimality-mechanism, which convert a change in diversity into a change of

productivity. A change in tree diversity between two forests result in a change of forest structure and/or optimality Ω. The

change in forest structure splits into a change of the vertical structure Θ (e.g. trees of different heights) and/or in a change of

horizontal structure (e.g basal area). Optimality describes how large is the productivity compared to the maximal possible

productivity of the current forest structure.

Literature

• Jacob M, Leuschner C, Thomas FM, Productivity of temperate broad-leaved forest stands

differing in tree species diversity. Ann. for. Sci. 2010; 67: 503 (doi: 10.1051/forest/2010005)

• Edgar CB, Burk TE. Productivity of aspen forests in northeastern Minnesota, U.S.A., as related to

stand composition and canopy structure. Can. J. Forest Res. 2001 31: 1019–1029

(doi:10.1139/x01-029

• Pretzsch H, Block J, Dieler J, Dong PH, Kohnle U, Nagel J, Spellmann H, Zingg A. Comparison

between the productivity of pure and mixed stands of Norway spruce and European beech along

an ecological gradient, Ann. for. sci. 2010; 67: 712 (doi: 10.1051/forest/2010037 )

Comment [CT7]: Not as the right place



• Rao, C. R. Diversity and dissimilarity coefficients—a unified approach. Theoretical Population

Biology. 1982 21:24–43.

• Vilà M. Vayreda J, Comas L, Ibáñez JJ, Mata T, Obón B. Species richness and wood production:

a positive association in Mediterranean forests. Ecol. Lett. 2007; 10: 241–250 (doi:

10.1111/j.1461-0248.2007.01016.x)

• Morin X, Fahse L, Scherer-Lorenzen M, Bugmann H. Tree species richness promotes

productivity in temperate forests through strong complementarity between species. Ecol. Lett.

(2011); 14: 1211–1219 (doi: 10.1111/j.1461-0248.2011.01691.x)

• Chen HYH, Klinka K. Aboveground productivity of western hemlock and western red cedar mixed-

species stands in southern coastal British Colombia. Forest Ecol. Manag.2003 184: 55–64 (doi:

10.1016/S0378-1127(03)00148-8 )

• Amoroso M.M. and Turnblom E.C. Comparing productivity of pure and mixed Douglas-fir and

western hemlock plantations in the Pacific Northwest. Can. J. For. Res. 2006. 36: 1484–1496

• Laliberte E. and Legendre P. A distance-based framework for measuring functional diversity from

multiple traits. Ecology. 2010; 299–305

Appendix D

The RWorkspace

The Workspace strucDivProd.RData contains the following three objects:

forests contains the forest stand characteristics (BA, Theta, Omega), the productivity, the species

richness and a column called mixture. The number in this column refers to the line in mixtureSpecies

where the mixtures are described. The numbers in these strings refers to the rows of species, which also

contains the parameters of the species.



Comments to Author:

Reviewers' Comments to Author:

Reviewer: 1

Comments to the Author(s)

The manuscript deals with the effect of forest structure on the relationship between tree species

diversity and stand productivity. It relies on the use of a gap model (FORMIND3.0) and a specific

procedure for stand initialization called “Forest Factory”. The main message is that density and height

heterogeneity have a large influence on productivity (in their case study, greater than the effect of

species richness and functional diversity) and that the relationship between diversity and productivity

depends on stand structure. This topic is highly interesting and highly relevant. Although based on a

static perspective, the fact that population or community size structure modifies significantly the effect

of diversity on productivity is of major interest for plant ecologists. This is also a complex issue and the

authors tackled it quite well. Moreover, the authors brought important modifications to comply with

reviewers’ comments. I have however several concerns about the analysis itself, the structure of the

paper and the way the topic is presented.

R1.1: Thank you for your motivating and helpful comments and the inspiring literature. Please note,

major changes in the manuscript are marked in blue and page and line information refer to the pages of

the manuscript.

First, the structure of the paper is quite unusual and could be a bit clarified. The analysis of underlying

mechanisms (see pages 8-9) should be introduced in the method as the interest of this analysis does not

really depend on the results obtained for the effect of species diversity on productivity. Of course, such a

modification would imply to better integrate mechanisms in the introduction and the results sections.

R1.2:Thanks for this comment. We added a section to the Methods (3.e.). The results of this analysis are

now presented in the results section (Section 4.b). In addition, we added some sentences in the

introduction regarding the mechanisms (Page 2 line 7: This approach…) and revised the corresponding

sections in the discussion (section 5.b & 5.c).

The introduction is quite general and doesn’t provide any clear hypotheses about the potential effects of

structural attributes on productivity. For instance, the important positive effect of basal area on

productivity is well-known. That is why many authors consider density (Zeide 2005) as different from

forest structure (see for instance Pommerening 2002). In the same vein, several recent articles found

negative effects of size heterogeneity in monospecific stands (e.g. Bourdier et al. 2016) and one recent

study (Dănescu et al. 2016) revealed positive effects of size heterogeneity (and species diversity) in

mixed stands (in Germany). These studies already indicate that the effect of size heterogeneity on

productivity can be significant in both monocultures and mixed stands. I think the authors could thus

better inform the reader about these effects and try to be more specific when presenting their

hypotheses. This would also help the authors to clarify their discussion. For instance, the authors don’t

discuss thoroughly the mechanisms that could explain the negative effect of size heterogeneity on

Appendix C on May 19, 2018http://rsos.royalsocietypublishing.org/Downloaded from


productivity. Finally, the idea of comparing mechanisms (see Bauhus and Forrester 2016 for a review of

processes) is interesting. Unfortunately, it is not mentioned in the questions of the introduction.

R1.3: Thank you for mentioning these interesting papers. We added a new paragraph to the introduction

to present previous studies regarding forest structure to motivate our hypothesis (page 1 line 24-30) and

revised the three questions in the introduction (page 2 line 9-14). Furthermore, we revised the text in

the discussion and in more detail discuss the effect of the mechanisms, especially the effect of size

heterogeneity on productivity. (p 10 line 5:6 & section 5.b )

I have two concerns about the analysis. First, the authors don’t consider mean size or succession stage to

control for the diversity and the size heterogeneity effects. The authors justified this choice by the fact

that basal area and mean height are correlated in their data. I think this is a problem and not a

justification. It means that the effect of basal area and mean size are confounded and that the author

cannot separate them with their constructed data set. This is a pity as, according to figure 1, tree height

has a major effect on tree growth efficiency (see next paragraph). I think it should be at least discussed

(see Lasky et al. 2013, Zhang et al. 2012).

R1.4: Thanks for mentioning this important issue. We made an additional analysis replacing basal area by

mean tree height of the forest stands and estimated the influence of forest structure and species

diversity on forest productivity (Appendix Figure B13). The analysis reveals a similar pattern compared to

the analysis in the manuscript (Figure 5), which results from the correlation between basal area and

mean tree height (R²=0.52). We also tried an analysis using only subsamples of different mean height

classes (Figure R1 shows the analysis using only the forest stands which are smaller or larger than a mean

height of 25m). In this analysis the pattern changes slightly regarding the diversity-productivity-

relationship. Hence, it would be worthwhile to analyze forest structure based on three variables

(including a forest height index) in future research. We mentioned this aspect in Discussion: Page 12

Lines 16:22

Second, and most importantly, the fact that the Factory Model selects species according to their ability

to have positive growth under shade means that relative abundances of species within a mixture can

vary with density and size heterogeneity. I think it is important that the author try to control for this

effect.

R1.5: Thanks for raising this interesting point. We made an additional analysis to quantify how strong the

mentioned effect might influence our results. We did an additional analysis, but include only those forest

stands with an more or less equal species abundance (FEve higher than 0.9, Laliberte & Legendre 2011).

The pattern stays quite the same for the diversity analysis and structure classes, except for forest stands

with high basal area and high tree height heterogeneity (figure B10; Appendix B.6). We add several lines

in the discussion, regarding this point: Page 10 Lines 25:33

I was not convinced by the validation section. The fact that climate data used for simulations is different

from climate experienced by inventory plots appears problematic. However, I think that the comparisons

of results obtained for simulations and empirical data is more interesting and more relevant. It shows

that results are coherent using different approaches (empirical data, simulations). I suggest the authors

focus more on this comparison.



R1.6: We follow your suggestions and move the former validation section into the appendix. Instead we

add two new sections (3.c and 4.c), which present results of the analysis based on the German forest

inventory (which was in the appendix before).

In the main text, we lack some justifications for several important choices made by the authors (the

reader has to read appendix files very carefully to understand these choices). Why do the authors

standardise (normalise?) tree productivity according to tree crown area (page 4 line 10)? Why do you

sum these values at the stand scale?

R1.7: Thanks for mentioning this point. We do not standardize tree productivity before we calculated

forest productivity. We sum up the total AWP of each tree to get the AWP for the whole forest stand.

We applied crown-size-standardization only for Figure 2 and for Figure A3 in the Appendix A to compare

the productivity of species per area. To make this point more clear, we renamed the standardized tree

productivity into productivity efficiency (AWPtree per unit crown area) in the captions of the figures. See

also page 4, lines 27:29.

Why is the maximum diameter value set to 50cm (a low value for a temperate forest)?

R1.8: Thanks for raising this point. We agree that a dbh of 50 cm is low compared to the maximal stem

diameters temperate trees could reach. We limit the dbh to reduce the technical complexity. However, it

is technically possible to increase the maximal dbh within the forest factory and we plan to revise this

aspect of the current forest factory. In case of the German forest inventory, 66% of the plots consist of

trees which all are smaller than a dbh of 50 cm. Thus, we include a sufficient part of the German forest

inventory for the first version of the forest factory approach. We discuss these aspects in the Appendix

A.2. “We selected[…]are possible”

I have read carefully the Appendix files. There are too many language mistakes (see corrections in the

attached files). It is important that the authors explain on which basis they define their 15 stand

structures (empirical data?) as some diameter distributions appear highly unrealistic (e.g. stand 15).

R1.9: Thanks a lot for your efforts regarding the Appendix. The aim of this study was to represent various

theoretically possible forest structures systematically (by changing max and the 95 %-quantile) with

equal frequencies. We heuristically choose these 15 (due to computation time), whereby a finer

resolution between the different types would be possible. Case 15 of the stem size distribution

represented an old even-aged forest within the model (where all trees get full light). We agree that such

a forest has a much broader stem size distribution in the field, whereby the tree height variability would

be also relative low (as in the simulation) due to tree-specific alometies.

We add some sentences regarding this issue in the Appendix A.2. “We select […] calculation time”.

I didn’t get what rule 1 consists of (how does it work?).

R1.10: The initial stem size distribution contains no information regarding the total tree number. We

therefore pack the forests in the first iteration as densely as possible by only considering tree crowns.

Later, the number of trees will be reduced due to rule 3. We add several sentences in the Appendix A.2

to clarify this point. A.2. “The input stem […] distribution (see figure 1)”.



Figure A4 (Appendix A): these graphs are of major importance for your results. They indicate that height

of the trees impact tree growth efficiency (growth per unit of crown area). If I understand correctly,

small and large trees are less efficient for all species (for Hainich environmental conditions). Is this

pattern (which is important for your study) really supported by empirical studies? I was surprised by

some values: for instance, your model predicts that small beech trees (a shade tolerant species) cannot

grow when they receive less than 80% of available light at the top of their crown. Such a value appears

very high.

R1.11: Thanks for mentioning this point. We revised figure A4 to clarify it. Now the graphic starts with

the height related to a dbh of 5 cm to show only those height-light-productivity-relationships, which are

relevant for the manuscript and which lay within the range of the data used for fitting. For the

parameterization of this relationship we use yield tables to estimate the productivity efficiency of the

different species under full light. These yield tables show this bell-shaped relationship for all

parameterized species (Schober 1996, Bohn et al. 2014). Additionally, we used typical light response

curves for the different species (Sonntag 1996 ; we add some sentences regarding this point in the

Methods). We assume the light response curve does not change between trees of different heights. The

combination of these two approaches results in the relationships of figure A4.

Figure 2 is difficult to read (even with subsamples). I suggest the authors provide the distribution of plots

for each number of species in separate graphs (in a supplementary material).

R1.12: Done, see Appendix A.3 figure A5

The number of inventory plots varies in your text: 2418 page 6 and 2415 page 7.

R1.13: Both numbers are wrong and we apologize (they originate from an older version of the

manuscript). It should be: 5,060 forest plots of the German forest inventory are used for the analysis in

the manuscript. In case of the comparison between simulated and field AWP now 13,136 forest plots are

used (Figure A6)

References

-Bourdier T, Cordonnier T, Kunstler G, Piedallu C, Lagarrigues G, Courbaud B. 2016. Tree size inequality

reduces forest productivity: An analysis combining inventory data for ten European species and a light

competition model. PLoS ONE 11.

-Dănescu A, Albrecht AT, Bauhus J. 2016. Structural diversity promotes productivity of mixed, uneven-

aged forests in southwestern Germany. Oecologia: 1-15.

-Forrester, D.I., Bauhus. J. 2016. A review of processes behind diversity—productivity relationships in

forests. Current Forestry Reports 2: 45-61.

-Lasky JR, Uriarte M, Boukili VK, Erickson DL, John Kress W, Chazdon RL. 2014. The relationship between

tree biodiversity and biomass dynamics changes with tropical forest succession. Ecology Letters 17:

1158-1167.

-Pommerening A. 2002. Approaches to quantifying forest structures. Forestry 75: 305-324.

-Zhang Y, Chen HYH, Reich PB. 2012. Forest productivity increases with evenness, species richness and



trait variation: A global meta-analysis. Journal of Ecology 100: 742-749.

-Zeide B. 2005. How to measure stand density. Trees 19: 1-14.

Reviewer: 2

Comments to the Author(s)

The authors explore the relationship between tree biodiversity and productivity of forests using a

simulation modelling approach. They create a large number of forest stands in silico, each of which has a

realistic stem-size distribution and is comprised of randomly generated mixtures of species. They then

use a well-known spatially-explicit size-structured forest model within which trees compete with one

another for light depending on the relative size, position and foliar density of their crowns. This model is

used to calculate the annual aboveground woody growth of each constituent stem, and thence the

above-ground wood production (AWP) of the whole stand. The authors repeat this exercise for almost

400,000 stands, and then explore the covariance between species richness and AWP estimates in these

simulations. They find that forest structure (i.e. basal area and height heterogeneity) have a very strong

influence on AWP, and that the productivity-biodiversity effect is small and contingent upon forest

structure.

This is an exciting piece of research, underpinned by very substantial computational work, that elegantly

complements (and to some extent challenges) observational studies based on repeated measurements

made in inventory plots. The journal has provided me with responses to previous reviews. I see that the

authors have added new sections exploring “underlying mechanism” and “validation” of the simulations.

I found the new mechanistic section of particular interest.

R2.1: Thank you for your helping comments. We revised the manuscript based on your points and

revised the explanation of the model description within the manuscript. Please note, major changes in

the manuscript are marked in blue and page and line information refer to the pages of the manuscript.

I found the science compelling, but I would encourage the authors to focus on restructuring the text, in

order that the paper gets the positive attention that it deserves. My comments below are aimed at

improving the flow and wording of the manuscript. I have just two scientific points to raise:

(a) Assumption iii included in the new section on page 9 got me thinking! The authors simulate stands in

which the species identity of stems is initially random, but it light demanding trees (e.g. birch) have been

placed beneath a dense canopy then the simulator will calculate that they have negative growth rates.

Instead of using these negative growth rates when calculating AWP, the authors have instead replaced

the offending stems by species that are more shade tolerant. Whilst this make sense in terms of re-

creating realistic forests, this step is in effect replicating successional processes inside the simulator: it’s

increasing the likelihood of complementarity effects in old-growth forests (i.e. those with high BA and

low height heterogeneity). I haven’t thought through the consequence of this, but I suggest that it’s

considered more explicitly in the discussion

R2.2: This is a good point. Please see also reply R1.5 to the first reviewer. We added some further

description regarding this issue in the Discussion. Page 10 Lines 25:33



(b) Please would the authors provide a slightly longer explanation of the inner workings of FORMIND in

the text (for those unwilling wade through lengthy SI sections) and particularly its main assumptions. I

think it assumes that all plant “traits” including light-response curves for photosynthesis and respiration,

allocation and allometry are invariant of the competitive environment a tree is found in. I’m not unhappy

about these assumptions – a line must be drawn somewhere! – but feel that readers would benefit from

having all this information in one place.

R2.3: Thanks for this comment. We explained in the revised version the algorithms in more detail.

Section 3.b.

“Minor” comments.

The summary contains numerous grammatical errors. Please check this particularly carefully, as many

readers never get beyond the summary!

We revised the summary.

Page 7 Line 26. Might I suggest replacing “horizontal tree density measures (basal area)” with “basal

area”? In my view, basal area isn’t a good measure of tree density!

Done. Page 1 Line 31

Page 7 Line 21 “We compiled a large set of forest stands by using a new forest modelling approach,

which we refer to as the forest factory approach”. I think “simulated a large set of forest stands by

randomising species identities” would be a better word than “compiled” here.

Done. Page 2 Line 2

Page 7 Line 32. “For every forest stand, we measure productivity as above ground wood production per

hectare for one year (AWP) using a process-based forest gap model”. Consider writing “we estimate the

wood production of every tree in the stand using physiological relationships encoded in a process-based

forest gap model (FORMIND) and then estimate instantaneous aboveground wood production by

summing the wood production of all trees in the simulated stands”. I’ve included “instantaneous” here

because your model isn’t accounting for mortality, so will give a high AWP than measured in permanent

plots ( see papers by Coomes et al http://onlinelibrary.wiley.com/doi/10.1111/gcb.12622/abstract and

Jucker et al. 2016 http://onlinelibrary.wiley.com/doi/10.1002/ece3.2175/pdf for similar approach being

used in permanent plots, with some discussion on the subject)

Thanks, we changed the formulation according to your suggestion. Page 2 Lines 4:7

Page 7 Line 36. Please define “canopy structure” at this point or even before.

There is no “canopy structure” in this line. We assume that you refer to the term forest structure which

is now described in more detail before. Page 2 Line 2

Page 8: Consider including a nice explanatory figure here.

Done. The new Figure 1.



Line 11: “These species vary by allometry parameterisation, productivity and responses to

climatic patterns”…. Suggest… “These species vary markedly in SHADE TOLERANCE (key to you finding

any effect of biodiversity using your modelling approach), allometry, productivity and responses to

climate”

Done. Page 3 Lines 22:24 and Page 4 Lines 2:3

Page 8 Line 20: Again I suggest “estimate” instead of “measure” as you’re not going out and measuring

things, you’re estimating them from a complex model.

Done. Page 4 Line 10

Page 8 Line 23: “The model considers establishment, mortality, competition and growth processes.” I

suggest “The model simulates the establishment, mortality, growth processes of trees that are

competing for light”

Done. Page 4 Line 1

Page 8 Line 34 “as a proxy year for a typical climate regime of the temperate zone” suggest “which has a

temperate climate” [ i.e. no need to assert this study necessarily applies elsewhere ]

We reformulate the sentence. Page 4 Line 16 We used a climate…

Page 9 Line 12: is it really “per area” for AGBtree ?

We revised this paragraph. We sum up the total AWP of each tree to get the AWP for the whole forest

stand. See also reply R1.7 and Page 4 Lines 27:29.

Page 10 “Only the structure class with a high BA and high Θ contains forest stands with a maximum of

seven species” … please follow this line through by stating why.

We reformulate the paragraph. Page 6 Lines 4:8.

Page 11 The authors should be praised for their efforts to compare modelling predictions with field

measurements, but I don’t think that comparisons with inventory datasets should be described as

“validation”. My suggestion would be that the eddy flux measurements are left where they are – simply

mentioned in the methods as “validation” of the ecophysiological modelling approach. In my mind

they’re contributing very little to the biodiversity issues that are central to the paper.

The corresponding paragraph has been now shifted to the Appendix A.4 and we removed the term

validation.

I would suggest that comparisons with inventory datasets are given more prominence throughout the

paper, as it’s now a selling point. Ps. it’s a great pity that the figures pertaining to the inventory results

are tucked away in appendices. I’d love to see them in the main body of the text.

We placed the comparison with inventory now into the Result section. Section 4.c



Up to you, but I suggest “Comparisons with field datasets” rather than “validation” here.

Done. It is section 5.b now

Page 12 Line 10 “Second”…. Please make clearer what “First” is in the previous paragraph

We replaced this with “further”. Page 7 Line 29

Page 12 Line 20 … There’s a tremendous amount of fascinating stuff summarised in this one paragraph! I

suggest you describe your findings in a little more detail

We added more detail to the paragraph. Page 6 Lines 17:26.

Page 12 Line 32… isn’t it 379,000 stands? That’s quite a lot more than 300,000.

We generated ~ 379,000 stands, but in the analysis based on the forest stands, which are inside the 9

structure classes (in total ~300,000 forest stands). We added a sentence to make this more clear. Page 8

Lines 8:9

Page 13 Line 26. Again, do you need to use basal area as a proxy for stem density? Why not just stick

with basal area as a measure of “forest structure”? In self thinning stands, the two variables are strongly

negatively correlated!

We followed your suggestion and avoided the term stem density in the whole manuscript.

Page 13: Underlying mechanisms. There are several really neat ideas in this new section. To my mind, it’s

this section that really lifts the paper to a high standard. But it’s not very tightly written at present, and it

feels “tacked on” to the original manuscript rather than being integrated into it. I’d encourage the

authors to include reference to this section in the summary, introduction and methods.

We split this section as proposed by the first reviewer and integrated this analysis into parts of the

Methods and Results. In addition, we added a few sentences to the Introduction (see also reply R1.3 to

reviewer 1).

Page 14: “The forest factory approach”. This section makes many good points, but it needs consolidating

into paragraphs (currently it has too many one sentence paragraphs) and perhaps shortening.

We revised this section. Section 5.b

Page 16: “Comparison with other studies”. I think this section is all about inventory analyses. Thus might

you consider moving the “a. Comparison with the German forest inventory” section down here? There

are several other inventory studies you could mention here, including the two I mentioned above.

Several have included basal area alongside biodiversity in their regression or path analyses. I’m not

aware of any that have also included height heterogeneity, so that’s a neat addition to the literature.

Thanks for this suggestion. We move the section into the section 5.b.



References

Laliberté, E., & Legendre, P. (2010). A distance-based framework for measuring functional diversity from

multiple traits. Ecology, 91(1), 299-305.

Schober, R., 1995. Ertragstafeln wichtiger Baumarten bei verschiedener Durchforstung. Sauerländer,

Frankfurt am Main. 4 edition.

Sonntag, M., 1998. Klimaveränderung und Waldwachstum: TREEDYN3-Simulationen mit einer Analyse

modellstruktureller Unsicherheiten. Ph.D. thesis. Universität Gesamthochschule Kassel.



the importance of forest structure to biodiversity...

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