Tree stem density and basal area increases with elevation while species richness decreases. Stem density and species richness both decrease with latitude. Subtropical forests have distinct tree species composition compared to those in the tropical region. In addition, floristic similarity of subtropical plots is between 13 to 16% while similarity between tropical forest plots is between 3% to 9%. Overall, plots ~ 0.5-ha or larger may be preferred for describing patterns at regional scales in order to avoid plot size effects. We highlight the need to promote collaboration and capacity building among researchers in the Andean region  in order to generate and synthesize information at regional scale.Our knowledge about the structure and function of Andean forests at regional scales remains limited. Current initiatives to study forests over continental or global scales still have important geographical gaps, particularly in regions such as the tropical and subtropical Andes. In this study, we assessed patterns of structure and tree species diversity along ~ 4000 km of latitude and ~ 4000 m of elevation range in Andean forests. We used the Andean Forest Network (Red de Bosques Andinos,  The Tropical Andes have been identified as one of the most important hotspots of global biodiversity , 2. Inde2 total) of their cloud forests Reviewers' comments:Reviewer's Responses to QuestionsComments to the Author1. Is the manuscript technically sound, and do the data support the conclusions?The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1: YesReviewer #2: Partly**********2. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: I Don't KnowReviewer #2: Yes**********3. Have the authors made all data underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.The Reviewer #1: NoReviewer #2: Yes**********4. Is the manuscript presented in an intelligible fashion and written in standard English?PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #1: YesReviewer #2: Yes**********5. Review Comments to the AuthorPlease use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. Reviewer #1: General remarks:This paper reports on trends in stem number, basal area and species diversity patterns for trees in a series of plots spanning ~4000 km of latitude and 4000 m of elevation range. The results are a useful addition to the analysis of trends in the physical and biological structure of Andean forests. In general, I found the manuscript clearly written and not over-reaching in its conclusions.condesan.org/) database which, at 71 present, includes 491 forest plots  representing 72 a total of 86,964 tree stems ≥ 10 cm diameter at breast height belonging to 2341 identified 73 species, 584 genera and 133 botanical families.”I believe that most last contribution of this manuscript would be the publication of the data upon which all the analyses were conducted. Unfortunately, it appears that this manuscript does not meet PLOS One standards of data availability. The authors state that “All relevant data are within the manuscript and its Supporting Information files.”, and that “We used the Andean Forest 70 Network , but that led only to plot metadata, not to the actual data.In summary, even with a diligent effort I was unable to find the data on which this manuscript is based. If somehow the stem data are in fact publicly accessible without restriction somewhere, they are not easily findable even with reasonable effort. The authors should clearly show exactly where the individual stem data can be freely accessed with no restrictions.The authors state “The plot data that support the findings of this study are available from Andean 251 Forests Network upon reasonable request”, so it appears to me that the data are not publicly available without restriction. PLoS ONE’s data availability policy states: “PLoS journals require authors to make all data necessary to replicate their study’s findings publicly available without restriction at the time of publication.” To replicate the study’s findings requires access to the individual stem data. Unless public access without restriction is provided the manuscript is not acceptable according to PLoS ONE’s standards.https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0183819#sec013. In their S1 Table those authors provide individual stem data for size, location and taxonomic identity of ~80,000 individual census measurements, which is a similar-size data set. I strongly encourage the authors to include the individual stem data as a table in Supporting Information so that the exact version of the dataset that they used to generate the paper is archived with the paper. Data in a dataset of this nature are constantly and very correctly changing as errors are detected and corrected and as taxonomic concepts evolve. It would be difficult in the future to recreate these analyses unless the version of the database at the time of these analyses is published. Such publication of the freely available base data is a PLoS ONE requirement for publication, and it is also best scientific practice.In the case of this manuscript complying with PLoS ONE’s data policy is not an onerous requirement. Stem data for 87,000 individuals is not large dataset and the data could easily be easily be included as a table in the Supporting Information. An example from PLoS One is Clark et al. 2017 My pdf copy of the manuscript lost line numbering after line 274, so after that I use the page numbers of my pdf copy to reference comments.It is unclear how many individuals were analyzed. The Abstract states 86,944 stems, but on page 26 a total of 97,054 stems is mentioned. It is not clear if the 86,944 applies only to the analyses involving taxonomic identity. I assume that the total 97,054 stems were used in the analyses of basal area and stem number, there is no reason to discard individuals for these analyses. In any case the sample size for each set of analyses must be clarified.The authors are very aware of the issues of plot size and its effects on scaling to larger spatial scales. They are clear that they omitted many very small plots (<0.1 ha) from their analyses. However the analyzed plots are located in mountainous terrain, and are likely spatially biased towards rare flat areas. In addition, most  of the plots were subjectively sited  and may be subject to the “majestic forest” bias. It would be useful for the authors to provide their opinion of the effects on non-random plot placements on these results.Other comments:I suggested deleting lines 230-241, this section is not directly relevant to the reported research.Table 1. Clarify if temperature and rainfall are annual averages. This table would be easier to read with vertical lines separating the variables, and “Min” and “Max” over each of those columns.Page 22. Spell out CHELSA. Rapid variation in environmental gradients is well known in tropical mountain area. Are there any site-specific data to check the accuracy of the predicted climate with actual climate on the ground?The whole paragraph on page 22 on climate data reads like climate was actually measured on the ground. In fact climate variables were predicted from remotely sensed data, with an unknown (or unreported) degree of uncertainty. All of these data should be labeled as “estimated” or “predicted” to make clear that actual ground-measured data are not being reported. It’s fine to report remotely sensed data, but the manuscript should be clear that is what’s being reported. Based on this manuscript there is no way to know how good these estimates are at the plot level. If the authors in fact do know the accuracy of these predictions it would be useful to report that.Figure 3 caption, B, change “climate” to “estimated annual rainfall”. What is the reason for the inverted scale on panel B? All the other scales are linear increasing, so this exception is confusing. I suggest plotting plot B like the other variables, both variables increasing from the origin.Figure 4. Move Elevation and Latitude to the top of each column rather than below .Table 2. Add units to the column headings were these are missing.Figure 4 is confusing. What is the difference between panels E and G? The text states that “Species richness decreased with latitude ” but panel E is based on elevation, not latitude. Please clarify in the text and in the figure legend.Consider replacing “hump-shaped elevational pattern of tree species richness” with “mid-elevation peak in species diversity”.Reviewer #2: I liked the manuscript and the overall approach. I also enjoy reading synthesis-based analyses that are based on field-plot data. I also think this particular plot network has an enormous potential for future work and research to support conservation and management of Andean forests. However, in its current form, this work requires more analytical thinking, especially to discuss the main findings and the causal mechanisms behind the patterns that were reported. See the attached file for detailed comments.**********what does this mean?). If published, this will include your full peer review and any attached files.6. PLOS authors have the option to publish the peer review history of their article  digital diagnostic tool, AttachmentPONE-D-19-30260_First_ReviewDec2019.pdfSubmitted filename: Click here for additional data file. 16 Mar 2020March 30th, 2020Dr. Joerg Heber, Editor-in-ChiefPLoS ONEDear Dr. Herber,I am writing to submit our revised manuscript (PONE-D-19-30260) entitled Elevation and latitude drives structure and tree species composition in Andean forests: results from a large-scale plot Network for consideration for publication in PLoS ONE. We are very thankful for your comments and those of the reviewers as they have allowed us to improve our manuscript. We have carefully considered each of them and addressed all of them. In this sense, we have made clear the point about data availability as well as we have improved the discussion concerning the major results. Please find below the detailed responses to each comment. Line and Page numbers referred correspond to the revised manuscript with track changes. With best regards,Dra. Agustina Malizia Instituto de Ecología Regional (IER) (CONICET-UNT)----------------------------------------------------------------------------------------------------------------------------------------Editor CommentsPlease seriously consider the concerns of the referees and make revisions according to their suggestions, especially you should pay attention to comments about data availability  and the discussions on the major results. Response: We have paid attention to all comments made by both reviewers, incorporated all of them in the manuscript, and responded to each one in detailed. Please, see below. Reviewers' comments:Reviewer's Responses to QuestionsComments to the Author1. Is the manuscript technically sound, and do the data support the conclusions?The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.Reviewer #1: YesReviewer #2: Partly ________________________________________2. Has the statistical analysis been performed appropriately and rigorously?Reviewer #1: I Don't KnowReviewer #2: Yes________________________________________3. Have the authors made all data underlying the findings in their manuscript fully available?The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.Reviewer #1: NoReviewer #2: Yes________________________________________4. Is the manuscript presented in an intelligible fashion and written in Standard English?PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #1: YesReviewer #2: Yes ________________________________________5. Review Comments to the AuthorPlease use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. Reviewer #1: General remarks:This paper reports on trends in stem number, basal area and species diversity patterns for trees in a series of plots spanning ~4000 km of latitude and 4000 m of elevation range. The results are a useful addition to the analysis of trends in the physical and biological structure of Andean forests. In general, I found the manuscript clearly written and not over-reaching in its conclusions.condesan.org/) database which, at present, includes 491 forest plots  representing a total of 86,964 tree stems ≥ 10 cm diameter at breast height belonging to 2341 identified species, 584 genera and 133 botanical families.”I believe that most last contribution of this manuscript would be the publication of the data upon which all the analyses were conducted. Unfortunately, it appears that this manuscript does not meet PLOS One standards of data availability. The authors state that “All relevant data are within the manuscript and its Supporting Information files.”, and that “We used the Andean Forest Network , but that led only to plot metadata, not to the actual data.In summary, even with a diligent effort I was unable to find the data on which this manuscript is based. If somehow the stem data are in fact publicly accessible without restriction somewhere, they are not easily findable even with reasonable effort. The authors should clearly show exactly where the individual stem data can be freely accessed with no restrictions.https://redbosques.condesan.org/) is to check general information about the Network . Response: In Table S1 we included: i) number of stems, ii) basal area (both extrapolated to 1-ha) and iii) species richness for each of the 491 plots. Additionally, in Appendix 1 we reported the abundance of tree species per country. This information constitutes the primary input used in the analyses to describe the main structural and compositional trends across the Andean forests. Thus, we included the following text in the manuscript to make explicitly clear that the information upon which replicate the analyses is available in the supporting information: “All relevant data upon which all the presented results in this manuscript are based on is included in its Supporting Information files…”. . We also clarified that the link to Red de Bosques Andinos  number of stems, ii) basal area and iii) species richness for each of the 491 plots which, and as we stated previously, it is provided in the supporting files. To avoid confusion, we have deleted the sentence: “The plot data that support the findings of this study are available from Andean Forests Network upon reasonable request”.https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0183819#sec013. In their S1 Table those authors provide individual stem data for size, location and taxonomic identity of ~80,000 individual census measurements, which is a similar-size data set. I strongly encourage the authors to include the individual stem data as a table in Supporting Information so that the exact version of the dataset that they used to generate the paper is archived with the paper. Data in a dataset of this nature are constantly and very correctly changing as errors are detected and corrected and as taxonomic concepts evolve. It would be difficult in the future to recreate these analyses unless the version of the database at the time of these analyses is published. Such publication of the freely available base data is a PLoS ONE requirement for publication, and it is also best scientific practice.In the case of this manuscript complying with PLoS ONE’s data policy is not an onerous requirement. Stem data for 87,000 individuals is not large dataset and the data could easily be included as a table in the Supporting Information. An example from PLoS One is Clark et al. 2017 Response: We understand the reviewer's request; however, as explained above, the data required to replicate this research is available in the supporting information included in the manuscript. Also, the Andean Forest Network dataset belongs to the different research groups that are part of the Network. Currently, these research groups are implementing projects and research with master's and doctoral students based in part on the same information presented here. It is not our intention to hinder research initiatives that require an embargo of the data until the different research projects are complete, making the base information available.My pdf copy of the manuscript lost line numbering after line 274, so after that I use the page numbers of my pdf copy to reference comments.Response: We added line numbers until the end of the manuscript. Apparently, lines were missing after number 274 as the reviewer stated. We apologize for the inconveniences.It is unclear how many individuals were analyzed. The Abstract states 86,964 stems, but on page 26 a total of 97,054 stems is mentioned. It is not clear if the 86,964 applies only to the analyses involving taxonomic identity. I assume that the total 97,054 stems were used in the analyses of basal area and stem number, there is no reason to discard individuals for these analyses. In any case the sample size for each set of analyses must be clarified.Response: Corrected. We added a clarifying sentence: For calculations of stem density and basal area we used all stems ≥10 cm DBH  while for species richness we used stems ≥10 cm identified to species level  . We also clarified this in the abstract: “…representing a total of 86,964 identified stems ≥ 10 cm diameter…” .The authors are very aware of the issues of plot size and its effects on scaling to larger spatial scales. They are clear that they omitted many very small plots (<0.1 ha) from their analyses. However the analyzed plots are located in mountainous terrain, and are likely spatially biased towards rare flat areas. In addition, most  of the plots were subjectively sited  and may be subject to the “majestic forest” bias. It would be useful for the authors to provide their opinion of the effects on non-random plot placements on these results.Response: Forest plots may not have been located strictly at random thus is challenging to guarantee that some of them were not subject to the majestic forest bias. However, forest plots setup were based on the combination of several factors: (1) accessibility, (2) sustainable over time to ensure long term monitoring for some plots, and (3) homogeneity in terms of forest type, topography, and disturbances in order to be representative of particular forest types. We clarified this in text . In this sense, we have stated that: “The majority of the plots are placed in mature forests, but the Network also includes several older secondary forests plots, i.e. > 30 years old as a result of human activities and the associated land-use changes” (P13 279-281).Concerning the majestic forest bias, small plots may be subjected to this effect showing higher estimated values of basal area . In this sense, in the result section we have reported that “Plot size had a significant effect on basal area, small plots of 0.1-ha tended to present higher basal area than 1-ha plots (Appendix 1) (P19 L396-397). However, taking into account the three variables combined, the variance explain is less than 10%, as we have stated: “Combined, elevation, latitude and plot size explained 9.5% of the variation in basal area” (P19 L398). Finally, in the discussion section we added: “…as well as majestic forest effect could be expected in these small plots (P24 L504-505). Phillips OL, Malhi Y, Vinceti B, Baker T, Lewis SL, Higuchi N, ... & Ferreira LV. (2002). Changes in growth of tropical forests: evaluating potential biases. Ecological Applications, 12(2), 576-587.Other comments:I suggested deleting lines 230-241, this section is not directly relevant to the reported research.Response: Agreed, we deleted it. Table 1. Clarify if temperature and rainfall are annual averages. This table would be easier to read with vertical lines separating the variables, and “Min” and “Max” over each of those columns.Response: Done. We clarify in the legend of Table 1  that we referred to total annual rainfall and mean annual temperature. Also, we added vertical lines in this table, and “min” and “max” as suggested. Additionally, in legend of Table S1 we also clarified that we referred to total annual rainfall and mean annual temperature. Page 22. Spell out CHELSA. Rapid variation in environmental gradients is well known in tropical mountain area. Are there any site-specific data to check the accuracy of the predicted climate with actual climate on the ground?Response: We spelled out CHELSA as “Climatologies at high resolution for the Earth’s land surface areas” (P16 L318). We were not able to corroborate the accuracy of the predicted climate with actual climate on the ground. In this sense, Andean precipitation patterns are currently not yet well described, due to the high spatio-temporal variability and low density of rain gauges, thus we expect some underestimations and overestimations in precipitation values . Nevertheless, we believe we have used the best available climatic information to describe general climatic patterns across Andean forest plots. Buytaert, W., Vuille, M., Dewulf, A., Urrutia, R., Karmalkar, A. & Célleri, R. (2010) Uncertainties in climate change projections and regional downscaling in the tropical Andes: implications for water resources management. Hydrol. Earth Syst. Sci., 14, 1247-1258The whole paragraph on page 22 on climate data reads like climate was actually measured on the ground. In fact climate variables were predicted from remotely sensed data, with an unknown (or unreported) degree of uncertainty. All of these data should be labeled as “estimated” or “predicted” to make clear that actual ground-measured data are not being reported. It’s fine to report remotely sensed data, but the manuscript should be clear that is what’s being reported. Based on this manuscript there is no way to know how good these estimates are at the plot level. If the authors in fact do know the accuracy of these predictions it would be useful to report that.Response: We rephrased the information within this paragraph adding the word estimated and predicted in order to make clear that it was remotely sensed data information . Figure 3 caption, B, change “climate” to “estimated annual rainfall”. What is the reason for the inverted scale on panel B? All the other scales are linear increasing, so this exception is confusing. I suggest plotting plot B like the other variables, both variables increasing from the origin. Response: We showed the inverted scale on Fig 3B (y axis = temperature) to emphasize illustratively the location of plots associated with elevation and temperature, i.e. higher plots are also the colder ones and are graphed in similar position in both panels . We also clarified it  in the legend of Fig 3 .Figure 4. Move Elevation and Latitude to the top of each column rather than below . Response: Done. We moved Axis X (Elevation and Latitude) above to the top of each columnTable 2. Add units to the column headings were these are missing. Response: Done. We added the symbol “#” (number) in two of the columns. Figure 4 is confusing. What is the difference between panels E and G? The text states that “Species richness decreased with latitude ” but panel E is based on elevation, not latitude. Please clarify in the text and in the figure legend.Response: Done. We clarified that Fig 4F is the one that refers to latitude . Fig 4E does not distinguish between tropical and subtropical sections, while Fig 4G does distinguish between tropics and subtropics taking into account only 1ha-plots (n = 109). This is stated in text .Consider replacing “hump-shaped elevational pattern of tree species richness” with “mid-elevation peak in species diversity”. Response: Done. We replaced as suggested.________________________________________6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.If you choose “no”, your identity will remain anonymous but your review may still be made public.Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.Reviewer #1: Yes: David B. ClarkReviewer #2: Nohttps://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org. Please note that Supporting Information files do not need this step.While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, Reviewer #2: I liked the manuscript and the overall approach. I also enjoy reading synthesis-based analyses that are based on field-plot data. I also think this particular plot network has an enormous potential for future work and research to support conservation and management of Andean forests. However, in its current form, this work requires more analytical thinking, especially to discuss the main findings and the causal mechanisms behind the patterns that were reported. See the attached file for detailed comments.Manuscript Review PLOS ONE (PONE-D-19-30260)Structural and compositional trends along elevation and latitude gradients of Andean forests By Malizia et al…General comments:This study is based on data collected from an impressive number of research sites, between temporary and permanent forest plots, located in different parts of the Andes in South America, an important biological hotspot that has received less attention compared to lowland forests. Broadly, this paper takes advantage of the wide and complex environmental range covered by the dataset to address the questions of the combined effects of elevation and latitude on the structure and tree species composition of Andean forests. By means of generalized models, the authors found that forest density (i.e. number of trees or stems per unit of area) increased with elevation with an opposite effect from latitude. The differences in species richness found between tropical and subtropical Andes are not surprising and are aligned with previous studies. However, the degree of similarity (or dissimilarity) in terms of species diversity in these two broad regions within the Andes was an interesting finding. The authors very well highlight the immense value that this Andean plot-network (i.e. Red de Bosques Andinos) has for strengthening scientific research in the region and promote collaboration. These are not ‘novel’ questions but given the amount of data used, especially compared to an earlier study from the same group , I find the paper of high interest for many scientists and forest ecologists, and readers of PLoS ONE. However, in its current form this manuscript remains largely descriptive and a better explanation of the causal mechanisms behind how elevation and/or latitude drives structure and composition is missing. The implications of the results to other aspects of forest structure (e.g. carbon) or dynamics (e.g. stem turnover) could be added too. I think the paper should be improved, especially in the discussion section, before being considered for publication. I am pointing out several comments, questions, and occasionally, a few suggestions, that could help moving this paper forward. Response: We appreciate the reviewer effort for improving the manuscript. We have incorporated all comments and addressed each one in detail below. Typesetting and formatting:I don’t normally pay too much attention to these aspects at this stage. However, I strongly recommend the paper by checked for type setting errors, and the written structure of some paragraphs is reviewed to help the reader. Details are offered below indicating page and line numbers. Yet, as a direct note to the authors, in the pdf version I had access to there was no line number after page 13 of the document (after Table 1), and at line 275 (Table 1), the page number starts again with 1. For this section then I will be referring my comments using these numbers while trying to point out the paragraph number and a few words in the sentence to facilitate the review process.Response: Done. We added continuous line numbers after line 274, until the end of the manuscript.Title:I suggest the title to be more directly linked with the results (e.g. Elevation and latitude drives structure and tree species composition in Andean forests). As I will mention later, the manuscript includes in the discussion a long portion about the value of the plot network that I am not sure if is relevant. However, if the authors decide to keep it, maybe a change in the title should also reflect this .Response: We have changed the title as suggested. Abstract:This section needs to be modified a bit. In particular, the reader will benefit from having more specific results being mentioned in the abstract. For example, there is an important aspect of the study related to plot size and its effects on the results that is not mentioned here. Response: Agreed. We added a sentence to refer to plot size effect: Overall, plots ~ 0.5-ha or larger may be preferred for describing patterns at regional scales in order to avoid plot size effects . Page 4, Lines 68 - 69: “…Here, we assessed patterns of Andean forest tree structure and diversity along ~ 4000 km of latitude and ~ 4000 m of elevation range…”. Consider changing to: “…In this study, we assessed patterns of structure and tree species diversity across a wide altitudinal and latitudinal range in Andean forests…” Response: We changed it as suggested. Page 4, Line 75: “…Subtropical forests have distinct composition from tropical forests...” Consider changing to: “…Subtropical forests have distinct tree species composition compared to those in the tropical region…”Response: We changed it as suggested.Introduction:Page 4, L83: “Indeed, the Tropical Andes…”. The region is already mentioned in the first sentence. Just start the line with something like “…Indeed, this region is one of the most diverse terrestrial hotspots on earth [1]…”Response: We changed it as suggested.Page 5, L86: “…that have not been described yet…” Change to: “…that have not yet been described…”.Response: We changed it as suggested.P5 L87-90: There are two different sentences, with different citations too, that mention “climate regulation”. Unify or combined these statements avoiding repetition. Response: We combined both sentences.P5 L92-95: Again, two sentences discuss similar aspects, specifically about social aspects . Consider simplifying this paragraph. Also, is not clear what “contrasting patterns of human population growth” means? Please clarify. Response: We combined both sentences.P5 L96: “Changes to Andean forests…” Changes in what? Forest cover? Structure? I don’t think the word “patterns” fits here. Consider something like: “…Changes in Andean forest cover includes both forest expansion, mostly frequent above 2000 masl) and deforestation that often dominates at lower elevations [12]…”Response: We changed it as suggested.P5 L102: “…are already undergoing…” Change to: “…experiencing an apparent shift in species composition (i.e…)” Response: We changed as suggested. P5 L104: Are these predicted shifts for plant species, animal species? Please clarify.Response: Predicted shifts are for vascular plant species. We clarified it.P6 L109-114: I am not sure if this whole paragraph fits here. Are those “knowledge gaps” related to the study? I understand the importance of collaborative research networks but the next paragraph (L116) immediately start discussing the effects of elevation on tree density. Consider removing this paragraph or in any case a connecting sentence is needed before you jump to the density portion.Response: Knowledge gaps are related to the study. We clarified this, and rephrase the sentence adding connection to next paragraph (P6 L121-125). P6 L121 “…subtropical section of the Andes…” Just say” “subtropical Andes…” Response: We changed as suggested. P6 L128: “Species richness…” All species? Plants? Response: We referred to plant species. We clarified it.Clarify. P7 L134: “…also showed…” -- > “…also shows the…” Response: We changed as suggested. P7 L135: “…being maximum…” -- > “…reaching a maximum at…”. Response: We changed as suggested. P7 L136: “…Argentina [38], decreasing…” -- > “…Argentina [38], while decreasing above…”. Response: We changed as suggested. P7 L138-140: I agree that long-term monitoring is needed, but the study do not use or report temporal trends so how is this relevant here? Consider moving to the conclusions. Response: We deleted as suggested.P7 L142: “…the main structural and diversity patterns…” -- > “…the main patterns of structure and tree species diversity in Andean forest communities…”Response: We changed as suggested. P7 L144: Why consider species richness as a structural component? Response: Actually, we consider species richness within diversity patterns. We clarified this. P7 L148-150: “…This study…” This paragraph would fit better perhaps at the beginning of this section in L142. Also, is not clear what do you mean about “…at regional scales in global context...”? Perhaps just say “…This study is one of the first attempts to describe and characterize regional patterns of forest structure and diversity in the Andes across (go to L143)…” Response: We moved the sentence to the beginning of the paragraph and changed as suggested. Two major points here: 1) I think is important to highlight how is this study different from the Baez et al study? I understand that in the 2015 paper there was no consideration about diversity and here you use a much higher number of plots. Thus, I see the need for making this point clear; 2) I think at the end of the introduction some general hypotheses would be useful. What were the patterns expected considered earlier evidences? Response: We added a sentence highlighting the progress of this analysis in relation to Baez et al 2015, as suggested . Also, we added a general hypothesis and two specific ones at the end of introduction section .Materials and Methods:P8 L155: “…Paleogene . Subsequent…” Change to “…Paleogene , and subsequent collisions…”. Response: We changed as suggested. P8 L156: The reference of Hoorn et al, 2010 does not follow PLoS guidelines (i.e. ). P8 L157: “…late middle…” -- > “…late mid Miocene…” Response: We changed as suggested. P8 L160: A citation is needed for this paragraph after “…Amazon ecosystems…”. We added citation. P8 L164: “…biodiversity and distribution…” -- > “…biodiversity and species distributions…” Response: We changed as suggested. P8 L169: “…vary gradually…” how? What does the word gradually means? I think the paragraph that starts later in L180 of page 9 with “...The mountain forest ecosystem…” should be moved here in support of this initial statement. In relation to this, I liked Figure 1, but I also thinks it deserves a better explanation, either in the main text or at least as an expanded figure caption. Why these variations in forest architecture? Some lines on temperature and radiation effects would be useful. Response: We reorganized the paragraph, including suggestions for a better understanding (P9 L191-206). Also the paragraph includes lines on temperature and radiation. P9 L194: Consider using “is” instead of “has been” when referring to the objective of the network. Response: We changed as suggested. P9 L196-197: Delete “the” before exchange, development, strengthening. Response: We deleted as suggested.P10 L205-212. This whole section and the next (L215 to 212) about the protocols can be combined, simplified and shortened. Response: We simplified, combined and shorten both sections as suggested. P11 L226: “…events and recorded and the DBH of marked trees are…” -- > “…events arerecorded and the DBH of marked trees is remeasured…” Response: We changed as suggested.P11 L230-241: I understand the importance of this section and I hugely support collaboration and networking. I am trying to find sections that could be simplified to allow for more space for discussion and I think this is definitely one of those parts. This paragraph here seems out of place. It could be shortened and added to the background section, used in a new appendix to fully describe the work of the Andean network or simply removed. As mentioned earlier when reviewing the title of the paper, if the goal is to highlight the value of the network a different approach would be useful, where a more in-depth discussion about research collaboration and networking is part of the manuscript. Response: We deleted this section as suggested by Reviewer 1.P12 L247: Are these values in precipitation 1901 ± 903 refers to the mean and SD? Clarify. Response: We clarified as suggested. P12 L248: “…mature forest but the Network also includes a few older…” -- > “…mature forests but the network also includes several older… Response: We changed as suggested.P12 L250-252: This statement about the data being available is out of place. This should be part of the data availability statement that is one of the specific sections asked by PLoS. Also, with regards to this there are three different statements: In Data availability the authors express: Yes - all data are fully available without restriction Later, when answering the questions on where this data could be found the authors expressed “All relevant data are within the manuscript and its Supporting Information files…”. Delete the portion in the main text and unify these statements clearly. Response: We deleted the incorrect statement in text as suggested and clarified that: “All relevant data upon which all the presented results in this manuscript are based on is included in its Supporting Information files…” . In this sense, as mentioned before in Table S1 we included: i) number of stems, ii) basal area (both extrapolated to 1-ha) and iii) species richness for the 491 plots. Additionally, in Appendix 1 we reported the abundance of tree species per country. As stated before, this information constitutes the primary input used in the analyses to describe the main structural and compositional trends across the Andean forests. We clarified this in text .P12 L254: Again, the values in plot size refers to mean and SD? I don’t understand 0.32 ± 0.47 ha? How is this possible?. The same observation applies to the subsequent parts where plot size is mentioned. Also, I don’t think is necessary to put ± 0 whenever the plot size remains constant in some regions/countries. Response: We clarified that values in plot size refers to mean ± SD, and deleted ± 0.P12 L261: “…being the longest subset…” -- > “…being the longest known subset…” ChangedP13 L270 or caption in Figure 2: Please clarify what do you mean when you say “…One (1) census refers to the establishment of a permanent plot”? I understand a one census plot as that with only one measurement, whether temporal or permanent.Response: We deleted the phrase as it was confusing. Exactly, one census refer to one measurement, whether temporal or permanent. L275 Table 1 (No page number! We added page number): It is not clear to me that if the range shown for plot area also corresponds to the range in basal area. That is for example: Row 1 in the table (AR). A 0.16 ha plot accounts for 78 stems and 5 m2 in BA, while the 6-ha plot is linked to 1834 stems and 189.4 m2? Why not just simply express everything in 1 ha scale? I understand the issues of extrapolation, especially from really small plots, but yet you still perform the analysis later. Please clarify. Response: The range shown for plot area not necessary corresponds to the range in stems or basal area. In this table we prefer to show plot values, and not extrapolate to 1-ha in order to avoid the very large variability and dispersion when scaled to 1-ha . We discarded small plot for the analyses. We clarified this in text: “To analyze patterns in stem density, basal area and species richness, we considered those plots ≥ 0.1-ha (n = 236) where stems ≥10 cm DBH were measured. Due to high variability and dispersion when extrapolating basal area and stem density at a larger spatial scale we discarded plots of 0.01-ha, 0.04-ha, 0.05-ha and 0.08-ha ” . This was also stated in the discussion section . *** Starting here there is no line number, and page number is 2 for the section where “Data analyses” subtitle is included. I’m using these numbers and will add the “p” for paragraph.Response: We added line and page numbers. P2 paragraph 1: “…resolution that represents the…” -- > “…resolution covering the average…” Response: We changed as suggested.P2 p1: “…from 1 C for Ecuador…” -- > “from 1 C in Ecuador…” Same for the rest of the sentences where a similar text is used (i.e. change “for” to “in”). Response: We changed as suggested.Data Analyses P2 p2: Delete “In order to…” Just simply say “To analyze…” Changed“…(n = 236) and stems…” -- > “…(n = 236) where stems ≥ 10 cm DBH were measured. Due to high variability and dispersion when extrapolating basal area and stem density…we discarded plots of 0.01 to 0.08 ha in size ...”Response: We changed as suggested.. Related to this part of the analytical approach, I am wondering how different are the extrapolations when you compare a 0.08 ha plot and a 0.1 one? You have discarded quite a lot of plots using this cut-off (which I am ok with) but I asked myself if maybe just 0.05 ha would have been enough?Response: In addition to the high variability and dispersion of data when extrapolating basal area and stem density of small plots at a larger spatial scale, we chose the 0.1 cut-off point as it is a standard minimum size for plots in forestry, thus for comparisons. Citation [55] should be placed after the (GLM) portion as this work refers to this modeling approach. Response: We changed as suggested. “Considering the nature of the response variables…” what is that nature? Statistical distribution? Did you perform a distribution test ahead of the GLMs? Please clarify. Response: We referred that: “We used a Quasi-Poisson distribution for stem density and species richness …, and a Gaussian distribution with log-link function for basal área”. This is clarified in text  with stems ≥ 10 cm DBH. To describe species composition, we applied a Non-Metric Multidimensional Scaling approach…” Response: We changed it as suggested. […[61] using latitudinal bands as random factor…” -- > “…as a random factor…” Response: We changed it as suggested. P4: Include citations for all R packages used.Response: R package used are cited in text: “All analyses were performed in R 3.4.3 [63], using AER to test overdispersion in GLM, vegan for ordination analysis, and lme4 for LMM” (P18 L372-373).Results:P4 p2: “… Mean annual air temperature and rainfall were positively correlated  …” I trust the numbers but the correlation in the figure seems to be driven by a few really wet points. Can you clarify this? Adding a trend line would be useful too. Using green and red dots here makes difficult to tease apart the countries. I suggest using an alternate color palette and perhaps different symbols for each country. Response: We have checked the correlation and it is correct. There are some plots that have between 2000 and 3000 mm of rainfall which also have around 25 degrees of temperature, but also some other plots with 4000 and 5000 mm of rainfall that also have around 23-24 degrees. We did not include a trend line as this is a correlation and no cause-effect is expected. P5 p1: Delete “Considering plots…” since is already mentioned in the methods. Just start with“we found that stem density…” Response: We changed as suggested.With regards to this section and Figure 4, the small-sized plots seem to be creating a lot of noise in the trends. Why not testing stem density and basal area for only 1-ha plots as shown for species richness in Fig 4G? Also discussed later, are the plots with higher stem density also showing high basal area? There is a brief mention in the discussion about this relationship, but a simple bivariate plot would help. Response: We tested stem density and basal area for only 1-ha plots and found that results and tendencies were very similar. Thus we kept small plots in order to have higher number of plots. Plots with higher stem density not necessary have higher basal area. P6 p2: “…we registered a total of 97,054 tree stems’…” The abstract mentions 86,964 individuals (?). Also, are these all tree species? When authors say stems it might imply other life forms as palms or tree-ferns. Please clarify.Response: The number 97,054 referred to all stems ≥10 cm while 86,964 referred to identified stems ≥ 10 cm diameter to species level. We clarified this in abstract . We addressed the entire manuscript to trees but actually we included palms and ferns. P6 p2: “…was shared among all data sets…” -- > “…was shared among all plots…” Response: We changed as suggested. P6 p3: “The study plots tended to segregate along…” Use a different word for segregate:cluster, group. Response: We used the word “group” as suggested (P20 L426-438).P6 p3: “…Elevation and latitude correlated with both…” -- > “…correlated well with…”. Also, in Figure 5 could you explain what does each axis in the NMDS represent? Response: We changed as suggested. Discussion and conclusions: See in bold edits and suggestions.An overall recommendation here is that for every sentence/statement where the authors are highlighting a specific result, having a direct reference to the particular figure or table where the reader can refer to again would be quite useful. Also, I think authors can separate the conclusions here. P9 p1: “…it was less expected for rainfall as [5]…” Change the structure of the sentence and citation format to “…it was less expected for rainfall as Urrutia et al [5] reported for the Andes where rainfall did not covaried linearly with elevation…”. Also, this statement relates to an earlier observation about the need for some hypothesis statements. If you say “it was less expected”, what were your initial expectations? Response: Changed as suggested. Actually, we were referring that our findings were different from those of Urrutia et al. We rephrased the statement to avoid confusion . P9 p2: “Both stem density and basal area were related with the gradients addressed…” -- >“Both stem density and basal area were related to the gradients covered by our dataset…”Response: Changed as suggested. “…patterns of stem density were more consistent with elevation and latitude than for basal area…”Response: Changed as suggested. Here, authors repeat some sentences from the results section. “Stem density peaked at 10-15 latitude”. Response: We rephrased the statement and differentiate it from the result section. “The observed increase in the mean values of the structural variables with elevation hasnot…”Response: Changed as suggested. P10 p1: “…or maybe some local climate and topographic conditions…” This sounds vague. What other climate or topographic conditions might have influenced these results? Explain. Response: We refer to some slopes orientation which may imply wetter or drier conditions, for example. We explained it in text as suggested (P24 L495-496). Land-use history is briefly mentioned as a potential driver of stem density. Yet, the authors have some (limited) information on the time since disturbance for some of the plots. Why not discuss this better? Can you filter some of the results based on different disturbance periods? Very dense plots might be a reflection of recent (or not that recent) events. At least in the form of an Appendix this would add some support when contrasting such a wide range of sites and conditions. Response: We do not have this information that is why we did not reported it. Nevertheless, we discussed that for the secondary plots considered, it may have had some influence on stem density (P24 L497-498). P10 p1: Change “border effect” for “edge effect”. Response: Changed as suggested.Also, briefly explain why these effects are more pronounced for small plots?. Why plots ~0.5 ha or larger might be preferred? This section discussing potential effects of plot size also needs some citations. See for example: Wagner et al. 2010 Biotropica, Volume 42 (6): 664-671 and some references therein.Response: We added the citation as suggested.P10 p2: I think only mentioning the main hypotheses (e.g. Janzen & Connel) is not enough here. How these hypotheses are related to the results found? Response: We explained in text as suggested. P11 p2: “…plots associated with low diversity of tree species…”Response: We changed as suggested. P11 p2: Change the reference format for Kattan et al. 2004 accordingly. P11 p3: Delete “As well…” Response: We deleted as suggested. P12 p1: “…are unknown…” change to -- > “ are not clear [36]”Response: We changed as suggested. There is quite an abrupt change from this last paragraph to the next that discuss the importance of the Andean forest plot network. What are some of the potential implications of the findings? What does it mean that some forests in the Andes have higher density than others? More carbon? Less carbon? What about diversity? Are these forests well protected? I am not asking for a detailed analysis but just a brief consideration to potential links of the results to management or conservation aspects.Response: We added a brief consideration as suggested .P12 p2: The enumeration used in this long paragraph is confusing. There are two sections discussing different aspects, yet, some are redundant (e.g. #4 and #8 about models). Consider rewriting.Response: We re-wrote as suggested. P12 p2: “…improving the number of hectares per country…” -- > “…increasing the area covered per country…”Response: We changed as suggested.AttachmentResponse to Reviewers. Malizia et al. FINAL.docxSubmitted filename: Click here for additional data file. 26 Mar 2020Elevation and latitude drives structure and tree species composition in Andean forests: results from a large-scale plot NetworkPONE-D-19-30260R1Dear Dr. Malizia,We are pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it complies with all outstanding technical requirements.Within one week, you will receive an e-mail containing information on the amendments required prior to publication. When all required modifications have been addressed, you will receive a formal acceptance letter and your manuscript will proceed to our production department and be scheduled for publication.https://www.editorialmanager.com/pone/, click the "Update My Information" link at the top of the page, and update your user information. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.Shortly after the formal acceptance letter is sent, an invoice for payment will follow. To ensure an efficient production and billing process, please log into Editorial Manager at onepress@plos.org.If your institution or institutions have a press office, please notify them about your upcoming paper to enable them to help maximize its impact. If they will be preparing press materials for this manuscript, you must inform our press team as soon as possible and no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact With kind regards,RunGuo ZangAcademic EditorPLOS ONEAdditional Editor Comments :Reviewers' comments: 30 Mar 2020PONE-D-19-30260R1 Elevation and latitude drives structure and tree species composition in Andean forests: results from a large-scale plot Network Dear Dr. Malizia:I am pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department. onepress@plos.org.If your institution or institutions have a press office, please notify them about your upcoming paper at this point, to enable them to help maximize its impact. If they will be preparing press materials for this manuscript, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact plosone@plos.org. 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SA, SB and SC of the three species, the spin-structures of the ground state can be classified into two types. In Type-I the three spins are either parallel or anti-parallel to each other, while in Type-II they point to different directions but remain to be coplanar. Moreover, according to the magnitudes of SA, SB and SC, the spin-structures can be further classified into four kinds, namely, p + p + p , one species in f (fully polarized) and two species in q (a mixture of polarized atoms and singlet-pairs), two in f and one in q, and f + f + f. Other combinations are not allowed. The scopes of the parameters that supports a specific spin-structure have been specified. A number of spin-structure-transitions have been found. For Type-I, the critical values at which a transition takes place are given by simple analytical formulae, therefore these values can be predict.We have performed a quantum mechanic calculation  together with an analytical analysis based on a classical model. Then, according to the relative orientations of the spins  For these systems, when the temperature is extremely low , the spatial degrees of freedom are nearly frozen and the spin degrees of freedom play essential roles3. Various spin-structures will emerge, and they are found to be sensitive to the very weak spin-dependent forces. Therefore, these systems might be ideal for realizing exquisite control.The study of the multi-species Bose-Einstein condensates (BEC) with atoms having nonzero spin is an attractive topicN spin-1 atoms, the polar phase (p-phase) and the ferromagnetic phase (f-phase) have been found in the ground state (g.s.)10. In the p-phase, the spins of atom are two-by-two coupled to zero to form the singlet pairs (s-pair), and the total spin of the condensate S = 0. In the f-phase, all the spins are fully polarized, i.e., lying along a common direction, and S = N. For 2-species BEC, it was found in23 that there are three types of spin-structures, namely, (i) the p + p spin-structure where both species are in p-phase; (ii) the f//f structure where both species are in f-phase, and the two total spins (each for a species) are lying either parallel or antiparallel to each other; and (iii) the f//q structure where one in f-phase and one in quasi-ferromagnetic phase .When the BEC contains only one kind of The above message from 2-species BEC attracts the exploration on the spin-structures of multi-species BEC. Note that, for 3-species BEC, the three intra-species and three inter-species spin-dependent interactions can be repulsive or attractive. Thus, the spin-structures are expected to be very rich. However, this interesting topic is scarcely studied before. This paper is a primary study on this topic. The aim is to clarify the variety of the spin-structures and the related critical phenomena, and the effects of the intra- and inter-species interactions. We believe that the knowledge extracted from 3-species BEC would be in general useful for understanding the spin-structures of many-body systems with multi-species.J = A, B, C) and N, while the interaction energy increases with N2, the relative importance of the kinetic terms is very weak when N is very large. Therefore, the TFA is applicable when the particle numbers are huge as usually in the experiments of BEC .From the experience of 2-species BEC, the spin-structures are seriously affected by the compactness of the spatial wave functions  calculation, a corresponding classical model has been proposed and solved analytically. The results from the model are checked via a comparison with those from QM calculation. This model helps greatly to understand the complicated 3-species spin-structures.We proceed in the following way:i-th atom of the J-species. The inter-species interaction is m and ω, and use Let the mixture of three kinds of spin-1 atoms be trapped by isotropic and harmonic species-dependent potentials J-species where the spins are coupled to Z-component MJ. According to the theory given in27, SJ and MJ are fixed), and the set A- and B-species, in which SA and SB are coupled to Note that, in the ground state (g.s.), every particles of a kind will condense to a spatial state , as a reasonable approximation, the contribution of the former can be neglected. Then, we have Since the spin-dependent forces are in general two order weaker than the spin-independent forces  will occur at J to III) will occur at If a wave function . An example is given in Fig. 1, Form I3, and empty, respectively.The spin-structures in multi-species BEC is caused by the inter-species interactions. Obviously, they would act more effectively when the three species are distributed closer to each other. Therefore, in the following examples, we take the miscible states into account, in which all the three species have nonzero distribution at the center , \docummentclasspt{minima/γC (Eq. ). They g via Eq. . Then, tA at A can link with a Form IC at Nonetheless, the realization of the miscible state is based on a number of assumptions. First, it is assumed that all the wave functions are nonzero at the center, thus mentclass2pt{minimM can be neglected. Accordingly, a candidate of the g.s. can be expanded asMaking use of the spin basis-state, we define a set of basis-states for the g.s. asCarrying out the diagonalization of J-species. Similarly, we haveTo extract information on spin-structure from Examples are given below.Neglecting all spin-independent terms, the spin-dependent energy of the g.s. can be written asBased on Eq. , we propThe effect of the inter-species force is embodied by There are two types of spin-structures. When all pg.s. be the point where For Type-IJ. At the minimum the three equations pg.s. cannot locate inside the cuboid. It implies that the three species cannot all be in the q-phase.In this case P1 belong to the first kind, the other three containing Let a rectangle on the surface of the cuboid be denoted as pg.s. were located on pg.s. cannot be located on P1. It implies that the case with one or two species in P-phase is prohibited, while all species in P is possible. This fact coincides with the finding found in 2-species condensates, in which the P-phase is extremely fragile when it is accompanied by an f or a q. Therefore, the P + f or P + q structures do not exist, but the P + P structure is allowed23.If this case is realistic, the g.s. would have at least one species in pg.s. can only access P1 and the three rectangles of the second kind, but those edges each being a common edge of two rectangles belonging to two kinds should be excluded.With the prohibition of the above two cases, f//f//f. . The three inequalities f//f//f-structure. The energy of this structure f//f//f structure is the only choice for the g.s. When some species  is polar in nature , whereas QA and QB can be negative or weakly positive. If they are positive and large, the inter-species interaction should be even stronger to ensure that the inequalities hold. The equality for C-atoms arrive at a balance. The energy f//q//f (B-species in q) and q//f//f (A-species in q) can be similarly discussed. These three together are called the double-f-structure (double-f-str).When mentclass2pt{minimpg.s. is in the interior of f//q//q. The inequality C) are required. This leads to the constraint listed in the third row of Table C-species are polar in nature, whereas f//q//q structure. The structures q//f//q and q//q//f can be similarly discussed. The three together are called the single-f-str.When mentclass2pt{minimp and the structure is therefore denoted as p + p + p. When f-str will be lower than p + p + p → single-f-str will occur.When all the three species are polar in nature  if f-phase. Starting from p + p + p to a single-f-str as mentioned above. Recall that the single-f-str must have p + p + p has f-strs  cannot both be satisfied Otherwise, two contradicting inequalities f-strs can survive. Therefore, p + p + p can only transit to a specific single-f-str depending on the parameters. Besides, the transitions among the three single-f-strs  are prohibited.We aim at the effect caused by the variation of the inter-species forces. Note that q-phase can be changed to a f-phase. Therefore, the single-f-str → double-f-str transition will occur (as shown below). One can prove that the three sets of constraints for the three double-f-strs do not compromise with each other as before. Thus, a single-f-str can only transit to a specific double-f-str depending on the parameters, and the transitions among the three double-f-strs are prohibited. When f//f//f structure.When p + p + p → single-f-str → double-f-str → f//f//f.With these in mind the increase of Two numerical examples of Type I are shown in Figs. According to the model, when 23. Obviously, Eq.  is helpful to the transition \documentThe two angles obtained in this way should ensure that the two second order derivatives given in Eqs.  and 47)47) are prom Eqs.  and (47)f + f + q. The constraints appear as (refer to the second row of Table When mentclass2pt{minimf + q + f and q + f + f can be similarly discussed.The angles are subjected to the two coupled equations (refer to Eqs.  and 49)49))40\dof + q + q. The constraint imposed on this structure is listed in the third row of Table When mentclass2pt{minimp + p + p.When all A comparison of the results from the model and from the diagonalization of π. This supports the assumption of coplanar structure.Table The structures can be described by the norms of the three spins The spin-structures not in entclass1pt{minimaThe spin-structures can be further classified according to the norms of the spin. In addition to Starting from the e-I Fig.  the equae-I Fig. , 34) an an\docume-I Fig. ). Thus, e-I Fig. , analytiK-species BEC  and is believed to hold also for K-species cannot all be in K-species BEC remain to be checked.Recall that, for 2-species BEC, the phases  to Eqs.  and 30)\documentFeatures of the spin-structures of 3-species condensates with spin-1 atoms have been extracted from a model and have been checked via a QM calculation. Note that the effect of the spatial wave function is embodied in the factors


It has been suggested that scale-free networks may provide an explanation for the robustness observed in certain physical and biological phenomena, since the presence of a few highly connected hub nodes and a large number of small-degree nodes may provide alternate paths between any two nodes on average—such robustness has been suggested in studies of metabolic networks, gene interaction networks and protein folding. A theoretical justification for why many networks appear to be scale-free has been provided by Barabási and Albert, who argue that expanding networks, in which new nodes are preferentially attached to highly connected nodes, tend to be scale-free. In this paper, we provide the first efficient algorithm to compute the connectivity density function for the ensemble of all homopolymer secondary structures of a user-specified length—a highly nontrivial result, since the exponential size of such networks precludes their enumeration. Since existent power-law fitting software, such as powerlaw, cannot be used to determine a power-law fit for our exponentially large RNA connectivity data, we also implement efficient code to compute the maximum likelihood estimate for the power-law scaling factor and associated Kolmogorov–Smirnov p value. Hypothesis tests strongly indicate that homopolymer RNA secondary structure networks are not scale-free; moreover, this appears to be the case for real (non-homopolymer) RNA networks.A network is  A network is said to be scale-free if its connectivity function N(k), which represents the number of nodes having degree k, satisfies the property that power-law distribution, which by definition satisfies The 1 Newman . Scale-fpreferential attachment. In Barabasi and Albert (N(k) with which a node in the network interacts with k other nodes decays as a power-law, following Barabasi and Albert  analyzedd Albert , it was How scale-free are biological networks?not to be fit by a power-law distribution, despite published claims to the contrary. Estimating an optimal power-law scaling factor by maximum likelihood and using truncated power-law distribution. The data analyzed by the authors included data from protein–protein interaction networks  [resp. p(k)] for secondary structure connectivity of a given homopolymer, which allows non-canonical base pairs. Section The plan of the remaining paper is as follows. Section K in the ensemble of all secondary structures with run time Section nhomopolymer is a set s of base pairs , such that (1) there exist at least free energy of a homopolymer secondary structure s is defined to be s| of base pairs in s , computed the following simple recurrence relation from Stein and Waterman (O(n) space, hence is more efficient by a factor of n. In a similar fashion, the recurrence relations  is a base pair, then Z denote the number of secondary structures on the interval , for k neighbors, and for which there are exactly h unpaired positions (or holes) in either(i)i, j] are all unpaired, or(ii) that (i), in which the rightmost (i)(i)Suppose that every hairpin loop is required to have at least the Eqs. –12 for Bi, j] that have exactly k neighbors with respect to the k), so thatZ and n to indicate a length n homopolymer.Let mentclass2pt{minimi, j] where i, j] where i, j] can be partitioned into structures having exactly degree k (i.e. kk structures that can be obtained by either adding or removing a single base pair). To support an inductive argument, in proceeding from interval  to k, which have a certain number h of positions that are visible , which can be paired with the last position not be base-paired with j in ; however, can be base-paired with j in h of holes (positions in j), we introduce the variable v to keep track of the number of visible positions in Z as defined in the Eqs.  denotes the number of secondary structures on the interval , for k neighbors, and for which there are exactly h unpaired positions (or holes) in i, j]. When i, j] are all unpaired.Let N denote the number of secondary structures on  for the homopolymer model, as computed by Eq. , since other potential base pairs would contain fewer than i, j] is external to the base pair , so visibility parameters i, j).Base Case B considers all structures on  where i, j). The arrow is meant to indicate that the structure on the right is the only neighbor of that on the left, as depicted in Fig. i, j] is i, j] is visible , Base Case C considers the converse situation, consisting of the empty structure on  where i, j) many base pairs can be added to the empty structure. In Fig. j.Base Case D considers the empty structure on  is visible , so visibility parameters Inductive Case A considers the case where left and right extremities Inductive Case A: For i, j) base-paired in ,see Fig. .Fig. 5Sj base-pairs with the r, where j, since the corresponding hairpin loop would constain less than h holes  base-paired in  for some C(v) considers the case where position s of the format has k neighbors, provided the restriction of s to s to vh is due to the fact that since base pair holes are located in visible positions in s can be obtained by adding a base pair from any hole to any visible suffix position—there are vh many such possible base pairs that can be added. Finally, the last term s can obtained by removing base pair C(v).For each value s in Eq. . Figure Inductive Case C(v), fori, j], for some i, j],D considers the case where there are h holes, and positions D includes the addition requirement that position s satisfying Case D can be partitioned into subcases where the restriction of s to h holes in structure s in Case s to j, but not with s to j and j, s produced in this fashion is thus s to The term s be a structure that satisfies conditions of Case D with h holes and s to w visible positions. Then s has k neighbors provided that the restriction of s to The argument just given shows the following. Let mentclasspt{minimaInductive Case D: For i, j], and v), when implemented, this requires a test that As in Case C, we describe the function m corresponds to the length i, j].The algorithm described in Sect. Base Case A: For Base Case B: For Base Case C: For Base Case D: For all Inductive Case A: For Inductive Case B: For Inductive Case C(v): For Inductive Case D: For h is strictly less than p value for Kolmogorov–Smirnov goodness-of-fit, as described in Clauset et al.  of secondary structures having degree k, for all k within a certain range. It follows that the likelihood Recall the definition of the function , as wellfunction , definedt et al. 27\documep value, following  p value for goodness-of-fit follows Sect. 4.1 of Clauset et al.  power-law distribution with scaling factor M synthetic data sets, each containing N sampled values, in time O(mNM); however, since N is the  number of all secondary structures having degrees in sequential method would require prohibitive run time. Instead, we implemented the much faster conditional method  is the proportion of structures having degree k. However, Table p values for optimal power-law fis of connectivity data for homopolymers of lengths from 30 to 150.Since powerlaw requires input files of  connectivity degrees, when creating Table entclass1pt{minimacut-off values n homopolymer has degree greater that dg(s) is redefined to be the number of structures t that can be obtained from s by adding, removing, or shifting a base pair in s. The so-called p value of 0.248. Since RNApowerlaw determined p value of 0.219, we can not reject the null hypothesis that a power-law distribution fits the tail of Figure H. sapiens, M. musculus, D. melanogaster, C. elegans) those genes, which are enriched in exon shuffling events, displayed a higher connectivity degree on average in protein–protein interaction (PPI) networks; i.e. such genes had a larger number of interacting partners. On similar grounds that nature should reuse and amplify successful metabolic networks, one might argue that metabolic networks should exhibit scale-free properties. However, rigorous statistical analysis has shown that metabolic networks fail a goodness-of-fit test for scale-free distribution, while PPI satisfy a goodness-of-fit test for scale-free distributions over a certain range of connectivity (Khanin and Wit Since the pioneering work of Zipf on the scale-free nature of natural languages Zipf , variousIndex of Complex Networks exhibit the “strongest level of direct evidence for scale-free structure”. In a response to a preprint of Broido and Clauset (https://www.barabasilab.com/post/love-is-all-you-need, A.L. Barabási argued against the conclusions of Broido and Clauset (Information and Control. For details, references, and a history of the power-law distribution, see Mitzenmacher (There appears to be a current polemic whether certain naturally occurring networks are scale-free. Broido and Clauset  provide  Clauset  dated Ma Clauset . Here, ienmacher .Fig. 13aK is a user-specified degree bound fruA. Figure Klebsiella pneumoniae subsp. pneumoniae with EMBL accession code CP000647.1/1773227-1773291 and the 76 nt alanine transfer RNA from Mycoplasma mycoides with accession code tdbR00000006 from tRNAdb Juhling et al. (fruA, Figure Given the current interest in whether certain naturally occurring networks are scale-free, we have introduced a novel algorithm to compute the connectivity density function for a given RNA homopolymer. Our algorithm requires mentclasspt{minimag et al.  (accessimentclasspt{minimahttp://bioinformatics.bc.edu/clotelab/RNAnetworks.Since (Day et al. As an afternote, our personal opinion is that it doesn’t much matter whether a naturally occurring network arising from physical phenomena is precisely scale-free or not. If network connectivity appears to follow a power-law distribution, even approximately, then by results of Barabasi and Albert , this su


Scientific Reports 10.1038/s41598-019-56662-x, published online 27 December 2019Correction to: The original version of this Article contained an error in the title of the paper, where the word “Extracellular” was incorrectly given as “Extracellur”. This has now been corrected in the PDF and HTML versions of the Article and in the accompanying Supplementary Information file.


We further clarify the relation between detailed-balanced and complex-balanced equilibria of reversible chemical reaction networks. Our results hold for arbitrary kinetics and also for boundary equilibria. Detailed balance, complex balance, “formal balance,” and the new notion of “cycle balance” are all defined in terms of the underlying graph. This fact allows elementary graph-theoretic  proofs of a previous result , our main result , and a corresponding result in the setting of continuous-time Markov chains. Detailed balance and complex balance are important concepts in chemical reaction network theory (CRNT). Both principles have been proposed already in the 1870s and 1880s by Ludwig Boltzmann in the kinetic theory of gases   mass-action systems display remarkably robust dynamics. If one positive equilibrium is CB, then so is every other equilibrium, which justifies calling the entire system CB. Moreover, there is exactly one positive equilibrium in every stoichiometric class (invariant set), and this equilibrium is asymptotically stable (implied by a strict Lyapunov function) (Horn and Jackson r is the number of reversible reactions (pairs of edges), m is the number of complexes (vertices), s is the rank of the stoichiometric matrix. Schuster and Schuster consider “generalized mass-action kinetics” in the sense that the net reaction rate contains a mass-action factor (as for enzyme kinetics). They provide “generalized Wegscheider’s conditions” on the equilibrium constants; in fact, they obtain For mass-action kinetics, complex balance has been characterized by Horn , and expFeinberg , and \doph Berge . That isIn this work, we provide new conditions on a complex-balanced equilibrium of a reversible chemical reaction network to be detailed-balanced. As just stated, a characterization has already been obtained in Dickenstein and Pérez Millán . On the The work is organized as follows. First, we present the elementary argument  that is common to all types of networks. Then, we apply it to different types of networks .mixed graph contains undirected and directed edges, in general, and that a simple mixed graph does not contain multiple edges (connecting two vertices) or loops (connecting a vertex to itself).The object of the study in this section is a simple mixed graph. Recall that a V, undirected edges U, and directed edges D). Explicitly, if two vertices Let path is a (finite or infinite) sequence of edges which connect a sequence of distinct vertices. For finite paths, the first and last vertex may be identical, in which case the path is a cycle. A path is called directed if it contains only directed edges and all edges have the same direction . In other words, a path connecting the vertices weakly directed if it contains a directed edge and all directed edges have the same direction.A balanced if it is undirected. A vertex is called balanced if the set of incident edges contains either only undirected edges or a pair of oppositely directed edges (with respect to the vertex). In other words, a vertex v is balanced if the existence of An edge is called G is called edge-balanced/vertex-balanced if every edge/vertex is balanced.An edge-balanced graph has only undirected edges and therefore is vertex-balanced and contains no directed cycle. In the following, we show the converse.G is vertex-balanced, but not edge-balanced, then it contains a directed cycle.Let G is vertex-balanced and that there exists a directed edge Assume that The main result used in the following section is the contrapositive of Proposition G is vertex-balanced and contains no directed cycle, then it is edge-balanced.Let bi-infinite if it connects a bi-infinite sequence of vertices. Bi-infinite directed paths can be viewed as a “directed cycles of infinite length.”A directed path is called G is vertex-balanced, but not edge-balanced, then it contains a directed cycle or a bi-infinite directed path.Let Analogous to the proof of Proposition Again, as a main result, we state its contrapositive.G is vertex-balanced and contains no directed cycle or bi-infinite directed path, then it is edge-balanced.Let G is vertex-balanced and contains no directed cycle, then it cannot have a finite number of directed edges.As a consequence, if In the following, we denote the positive real numbers by chemical reaction network  is given by a finite, simple directed graph (complex)n chemical species which are the left- and right-hand sides of chemical reactions.A As an example, consider the “network” consisting of the single reaction kinetic system  is given by a chemical reaction network , where (kinetics)A n chemical species) is defined asThe resulting dynamical system for the concentrations For “general kinetics,” it is often assumed that reversible reaction networks, where the underlying graph G is symmetric, that is, ij for In the following, we consider detailed-balanced (DB) if, for every An equilibrium mentclass2pt{minimcomplex-balanced (CB) if, for every An equilibrium mentclass2pt{minimObviously, we have the implicationdirected cycle A formally balanced (FB) if, for every directed cycle A state mentclass2pt{minimUnder quite weak assumptions on the kinetics, formal balance is independent of the state: With every vertex Formal balance is defined by equations for directed cycles. We introduce two other variants of cycle balance which are defined by inequalities and which are weaker than formal balance.strongly cycle-balanced (sCycB) if, for every directed cycle cycle-balanced (CycB) if, for every directed cycle A state mentclass2pt{minimmentclass2pt{minimx is FB x is CycB” is obvious if x is FB” implies x is CycB.” All other implications are obvious.The implication “For “general kinetics,” where t}(∗) in  holds foi only. If j with To see this, first note that the sign of C), then also x is FB” and “x is sCycB.” Otherwise, x is FB” and “x is sCycB.”Obviously, implication t}(∗) in  holds foAs stated above, the two new variants of cycle balance are weaker than formal balance, in general. They allow elementary graph-theoretic proofs of a previous result and of a new result which holds for arbitrary kinetics and boundary equilibria; see Theorem Algorithmically, all variants of cycle balance  are equally costly: the most expensive step is the identification of all cycles in the underlying graph. For mass action  defined asGiven a reversible reaction network, defined by a finite, simple directed graph Let mentclass2pt{minimmentclass2pt{minimAs stated in the introduction, it was shown in Dickenstein and Pérez Millán  that detx is CB and CycB, then it is DB.Let mentclass2pt{minimBy the implications  and TheoThe above result is new and stronger than the existing result: first, it holds for nce, see . HoweverTo summarize, given complex balance, detailed balance is equivalent to all variants of cycle balance. The result holds for x is detailed-balanced (DB).x is formally balanced (FB).x is strongly cycle-balanced (sCycB).x is cycle-balanced (CycB).Let mentclass2pt{minimBy the implications  and Propweakly complex-balanced (wCB) if x is wCB Only the second implication in  is not aG, which contains two independent cycles; see the left diagram. Consider the reversible cyclic network G, have deficiency zero: Both networks, x, does not contain a (weakly) directed cycle, and the same holds when G; see below.For the isolated network G, there exists a complex-balanced equilibrium x is not detailed-balanced, in particular, that the mixed graph G and x, does not have x is not cycle-balanced, that is, there exists a directed cycle in not a (weakly) directed cycle.  The only feasible subgraph For the full network Remarkably, all edges of the induced graph  can be determined without computing the complex-balanced equilibrium.The argument in Sect. A continuous-time MC is a random process on a countable state space, where a measure  on the set of states is determined by the initial measure and the transition rates (via the Kolmogorov forward equations). For a formal definition, see, e.g., Norris . In a naV and the transition rate from state q. Further, we introduce the set of transitions (edges) We denote the set of states (vertices) by V assigns a nonnegative real or infinity to each subset of V. Here, we consider only stationary if, for all reversible  if, for all A measure induced graphGiven a MC with associated symmetric, simple, directed graph entclass1pt{minimaentclass1pt{minimaG be the graph associated with a continuous-time Markov chain, where Let Its contrapositive is useful to state. If a stationary measure is not reversible, then the induced graph contains a directed cycle or a bi-infinite directed path. See Examples stochastic mass-action kinetics. The corresponding rate constants are specified as edge labels in the graph below.  The (infinite) graph Consider again the reversible cyclic network For the deterministic system, n et al. . Since tG, except for the trivial two cycles. A stationary distribution on Let Since Since there exist two different stationary distributions Finally, we summarize similarities and dissimilarities in the settings of RNs and MCs in a table.


Correction to: Inj Epidemiol 7, 29 (2020)https://doi.org/10.1186/s40621-020-00248-zAfter publication of this supplement article Lee , it was The sentence currently reads:Because our goal is not the “moon,” but for our children to leave in a world that is Injury Free.The sentence should read:Because our goal is not the “moon,” but for our children to live in a world that is Injury Free.This has now been included in this correction article.


Scientific Reports 10.1038/s41598-019-51286-7, published online 30 October 2019Correction to: A supplementary file containing a ‘dive bomb sound’ was omitted from the original version of this Article. This has been corrected in the HTML version of the Article; the PDF version was correct at time of publication.