The role of intra-guild indirect interactions in assembling plant-pollinator networks

Understanding the assembly of plant-pollinator communities has become critical to their conservation given the rise of species invasions, extirpations, and species’ range shifts. Over the course of assembly, colonizer establishment produces core interaction patterns, called motifs, which shape the trajectory of assembling network structure. Dynamic assembly models can advance our understanding of this process by linking the transient dynamics of colonizer establishment to long-term network development. In this study, we investigate the role of intra-guild indirect interactions and adaptive foraging in shaping the structure of assembling plant-pollinator networks by developing: 1) an assembly model that includes population dynamics and adaptive foraging, and 2) a motif analysis tracking the intra-guild indirect interactions of colonizing species throughout their establishment. We find that while colonizers leverage indirect competition for shared mutualistic resources to establish, adaptive foraging maintains the persistence of inferior competitors. This produces core motifs in which specialist and generalist species coexist on shared mutualistic resources which leads to the emergence of nested networks. Further, the persistence of specialists develops richer and less connected networks which is consistent with empirical data. Our work contributes new understanding and methods to study the effects of species’ intra-guild indirect interactions on community assembly.

The authors investigate the role of intra-guild indirect interactions on plant-pollinator network assembly using motif analysis and a colonization model that incorporates adaptive foraging.They find that adaptive foraging promotes the coexistence of specialists and generalists within the same guild and that colonizers tend to form intra-guild indirect interactions with species of opposite niche breath (specialist colonizers with generalist incumbents for plants and generalist colonizers with specialist incumbents for pollinators).
The manuscript is generally well written, especially the discussion, and the core ideas---motif analysis for studying indirect interactions and the effects of adaptive foraging on community assembly---are novel and interesting.My main critique is that the study is heavily theoretical/modelling/simulationbased and would really benefit from additional analyses involving empirical networks.I also have some other suggestions for improving the manuscript.
--Tighter integration of empirical networks in analyses The authors provide some comparison of their theoretical work to empirical networks (L255, L260, etc.), but these analyses are relatively limited and appear as more of an afterthought.While I like the overall modelling approach and find the theoretical results interesting, it will be important to see whether the findings translate to empirical networks.I appreciate that it is not possible to study the assembly of these empirical networks, but can the authors do something like provide a breakdown of motif frequencies in empirical networks?Right now, the comparison centers on three broad network properties (richness, connectance, and nestedness, see Fig. 6) and the results themselves are not especially clear and convincing and, moreover, do not provide any additional support to the main findings regarding intra-guild competition and higher-level interaction patterns.

--Additional temporal analyses
The authors record motif groups in sets of three subsequent time steps (L124) but then group the motif data for all colonizers, regardless of when they established in a network (L127).It would be very interesting to see an explicit breakdown of the distribution of these three-motif sequences (i.e., similar to information presented in Table 1).It would also be cool to see if/how motif distributions change during the colonization trajectory, e.g., early vs. middle vs. late stages.
--Remind the reader of the four questions I like the four research questions (L76) but found it difficult to remember each question when they were referred to simply by Q1 etc.This was especially the case when reading the section "Core motifs produced by plant species" (L142).It would be helpful if sentences could be rewritten to remind readers of each question as the answers are presented.
--Clarify what information is presented in Table 1 and Fig. 4 I did not find the information in Table 1 very easy to interpret.Is the establishment rate over all 121 simulations?Is such information worth presenting by model (W/ AF etc.) rather than broken down by plants vs. pollinators?Which rates are meant to sum to 1? The bottom line is that I did not find Table 1 very effective.Also, it wasn't clear to me if Fig. 4 (which I did find intuitive) presented the same/similar information to Table 1.
--Consider specialists as having more than one interaction I would be curious to know if it would be possible to perform the analysis with specialists defined by a diet breadth greater than one (L218)?Could it also work if specialists had a potential diet breadth greater than one but only realized one interaction at a time?In a similar vein, do the authors think results would change significantly if species were categorized into specialists, generalists, and supergeneralists (with motifs reflecting this categorization)?Such an extension would help bring the work closer to empirical systems, in which diet breaths follow distributions that are much more complicated than just specialist having 1 interaction and generalists having > 1 interactions.Also, in simulations the number of interactions of a generalist is drawn from a uniform distribution (L388)---would results change if other distributions were used, particularly ones that more closely match empirical degree distributions?--Describe how results for plant-focused motifs fit with pollinator-focused motifs Results for pollinators are by-and-large considered *separately* from results for plants.I would like to see a discussion on how the results regarding pollinators (e.g., generalist colonizers with specialist incumbents) and plants (e.g., specialist colonizers with generalist incumbents) might emerge *together* from a modelling/technical standpoint; this could go around L253.
Minor comments --Fig.1.I don't know what a "passing" interaction is?Is there a better term that can be used instead?Maybe "transient" or "temporary"?Or perhaps add a definition in the caption.
--L109.Add a short explanation of the "dynamic species pool" and how it works.
--L122.It would be helpful to have an example of how "colonizers' interactions transform from one motif group to another."I had a hard time imaging what this would look like.
--Fig. 2. I think the figure title would be clearer if it was, "...each motif group."Also, personally I would find "Spec" easier to read than "Spc".
--Fig. 3.Because most plant-pollinator networks are drawn with plants as the lower guild and pollinators as the upper guild, it would be easier for me to follow if figures reflected this convention.
--Fig.6.I did not understand what was done based on the sentence (L272) beginning, "We performed a one-sided..." Consider expanding the technical description.

General comment
Dritz et al. developed a dynamic model to describe the assembly of mutualistic network, a surprisingly overlooked aspect of mutualistic networks.By including adaptive foraging in this article, they provided an innovative theoretical approach of the question, allowing them to account for the plasticity of interactions, that is often neglected.By combining this model with a motifs approach, they could track the impact of colonization on the network over the assembly process.This article is definitely a niece piece of science that provide a new and results about the dynamics of invasion in a network context.The introduction and discussion are well written and clear.I have no major comments about that manuscript.I have two main points of discussion I would like to raise: 1) about the use of motifs and possible bias and limits; 2) for the moment big parts of the methods are quite obscure and require lot of energy from the reader to be understood because we need to read previous article about the model, and the format (methods at the end) does not help.I detail a bit these points in the following paragraphs.Otherwise figures and results could a bit clearer, but as I said above, these are no major issues and this article is really a worthy reading, thanks to the authors for that.
Authors focused on indirect effects that propagate through path of length 2 only, so the shortest indirect effects possible, but is never highlighted, while it would be nice to discuss this point.However, many studies have shown that in diverse networks like those studied by authors, an important part of indirect effects propagate through long-paths (Higashi & Nakajima 1995;Nakajima & Higashi 1995;Guimarães et al. 2017;Pires et al. 2020).The same studies using the Jacobian matrix of dynamical systems to study indirect effects over all these possible path (Nakajima & Higashi 1995), that in contrast to motif approach allow to integrate these effects and measure their strength, including abundances and interaction strengths to calculate propagation from species to species.Thus, I wonder why did authors prefer motifs approach relative to this method?About motifs analyses, also see my comment for lines 395-406, that is, I think, of importance.
The model is not understandable without referring to other papers, because parameters and variables are not described at all in the main Methods and partially in Appendix S2, which is, I think, a problem to understand the study.Some important equations are missing, for example the equation linking   to   and to species abundances.To summarise, in absence of further explanations and description the equations presented in Methods are useless.Nerveless, once the reader has done the effort to read previous paper (Valdovinos et al. 2013), this model is definitely a niece piece of work and this paper a nice piece of science.But more efforts are needed in explaining (again) the model in the present study.

Point-by-point comments
Line 38: I do not know this paper but by quickly reading through I do not see how ref. 20 (Bogdziewicz et al. 2018) is linked to this point.I might have missed something, but good to check if it is the right reference.
Lines 75-79: here and in the following parts, I started to have a problem of terminology to fully understand.In question 1 a colonizer is a species that attempt to colonize the system, regardless the success of the colonization.But in following questions, a colonizer becomes a successful colonizer.I think it is important to distinguish both.When authors study motifs, do they present the result sonly for successful colonizer or all colonizers?Edit: answer to that question is present lines 407-413, but since Methods are at the end might be good to find a way to clarify it in the main text.
Lines 78-79: at this point, it is not intuitive what is behind question 3 for me.I struggle to see where this question goes, which kind of mechanism it aims to explore (competitive exclusion?niche partitioning?) and what are the assumptions of authors.
Lines 111-113: without further explanation, this sentence is very enigmatic.It could be either developed here, or removed from here and developed in Methods.
Line 116: before entering in motif description, I really missed basic information on network size at the end of the process.So, it starts by 3X3 networks, and could end with 150X150 networks if all colonizing species survived and there is no extinction.Knowing the average network size at the end of simulation would be helpful to understand motifs analyses.
Edit: After continuing reading I found richness and connectance plots latter, but I really think it misses some description of the dynamics and end point of the simulation before describing the motifs part, otherwise it is really abstract.Authors could have a first plot at this stage that describe the dynamics of simulations and number of successful colonization and extinctions.Something in the spirit of what is below.
Lines 124-127: I should admit that for me it was not clear all long the article I had the feeling I had to guess when authors used the motifs count calculated at the moment of the colonization, after the extinctions, or after the subsequent colonization event.I think it could be labelled more clearly.Each motif characterizes the niche breadth (specialist or generalist) of the focal colonizing species (specie highlighted by the box) and the niche breadth of species that share its mutualistic partner(s), as follows: 1) "Spc -Spc", specialist colonizer (blue) that interacts indirectly with at least one specialist in its guild (orange): … Fig. 3: in C, it took me time to guess that authors mean "No subsequent specialist establishment", as subsequent is missing.
It is a just a convention that can be changed but having the plants as the top guild of the bipartite network is not intuitive (they are often represented as the bottom guild, with pollinators as top guild).
Since the paper is complex, I would stick to classic norms as much as possible to keep the readers focusing on important complexity.
Table 1: so this table correspond to motifs account at the moment of colonizer's arrival?Could be good to be very clear about that.
Lines 285-288: Isn't table 1 instead of Figure 4 that shows this result?
Lines 293-297: I find the wording "mutualisms mediate species coexistence" a bit weird.I would have said "adaptive foraging mediates species coexistence", as without adaptive foraging mutualism does not maintain high coexistence.
Lines 346-350: About the emergence of nestedness through indirectly connected species it could be worthy to link this result to similar results found when introduced a phenological structure in mutualistic networks (Duchenne et al. 2021).Like adaptive foraging, phenological structure also protects specialist from extinctions through indirect effects, and thus promote nestedness and stable coexistence of a higher diversity (Duchenne et al. 2021).
Lines 376 -380: I could not find the meaning and units of   ,   ,   .
Variable names are not described.Often for readability variables are represented with capital letters, while parameters with lowercase letters, I think following this convention would help to understand quickly the equations, that are here really hard to understand, especially without description.
Basic assumptions of the model (e.g.linear functional response) have to be guessed from the equation but are not explicitly mentioned.
Finally, I have the feeling that there are too many important information that have to be checked in appendix.In my opinion the model, which is the core of the article, should be described in the Methods not in supplementary.Showing the equations without parameters description is almost useless as readers do not have any idea of what they represent.The paper should be roughly understandable without the appendix I would say, here without the model description, it is not the case.
Equation 2 & 3: I spent a long time trying to understand why authors divided   by   in the functional response.This was not clear for me, even after reading Valdovinos et al. (2013).I guess it is because   is already included in   .This kind of stuffs could be explained explicitly to the readers, to avoid them to get headache :) Equation 3: Why do not use a classical functional response of type 2 for saturating the production of resources?As model behaviour is already described with this formulation, I understand that authors sticked t this choice, but I wonder if there is specific argument behind this choice.
Line 385: Why 121?where is that from?what are the parameter combination that is tested?
Lines 395-406: Authors performed motifs counts that are not corrected by richness, while they show that species richness is different between cases with or without adaptive foraging.I guess the number of different motifs in each categories (Spc-Gen, Gen-Spc, etc.) increases with network size, isn't it?
Richer is the network, more we expect motifs 1 and 3, because they are based on logical condition "at least", while we expect less motifs 1 and 4, because they are base on logical condition "only".This is exactly the pattern we observe between simulations with adaptive foraging (more motifs 1 and 3) and simulations without adaptive foraging (less motifs 1 and 3, more motifs 2 and 4), that could be explained completely by difference in species richness.
Thus, I wonder what do authors think about the possibility that difference sin motifs count is driven by difference in species richness mainly?
Lines 414-424: I realized at the end that what authors called network is not obvious.Do they mean the interaction matrix defined by   (then including species abundance), or something independent from species abundance?Could be good to clarify it from the beginning.
Discussion: limits of the model are never highlighted or discussed, while I think it is always a good exercise and having the potential limits clearly written in the discussion helps the reader to link this work with previous one.
Table S1: last column of Table S1 is called "Motif frequency after establishments" where I guess after establishments is synonym of "after the subsequent colonization event" (line 127).I would suggest being very constant in the terminology used to help the readers, especially to maintain the word "subsequent" everywhere it is needed, to distinguish first colonization events than subsequent ones.
Appendix S2: if mortality is per capita, then it should be time -1 individuals -1 , isn't it?
Moreover, if parameters are drawn in gaussian distribution (that is not indicated), that means that negative values are possible, while it does not seem rational.How do authors deal with that?

REVIEWER COMMENTS
Reviewer #1 (Remarks to the Author): Review of "The role of intra-guild indirect interactions in assembling plant-pollinator networks," by Dritz et al.
The authors investigate the role of intra-guild indirect interactions on plant-pollinator network assembly using motif analysis and a colonization model that incorporates adaptive foraging.They find that adaptive foraging promotes the coexistence of specialists and generalists within the same guild and that colonizers tend to form intra-guild indirect interactions with species of opposite niche breath (specialist colonizers with generalist incumbents for plants and generalist colonizers with specialist incumbents for pollinators).
The manuscript is generally well written, especially the discussion, and the core ideas---motif analysis for studying indirect interactions and the effects of adaptive foraging on community assembly---are novel and interesting.My main critique is that the study is heavily theoretical/modelling/simulation-based and would really benefit from additional analyses involving empirical networks.I also have some other suggestions for improving the manuscript.
Response: We thank the reviewer for the constructive criticism and useful suggestions that have greatly improved the quality of our manuscript.We have incorporated them all in the new version of our manuscript except for the additional analysis involving empirical plant-pollinator networks.Our next response explains why our motif analysis cannot be applied to static networks, and why current temporal plantpollinator networks data are not well-suited for our analysis.We connect our results with empirical findings in the discussion section, which is the best we can do in terms of data-theory integration given the limitations of current empirical data.After all, one main reason we use theoretical approaches to investigate important questions in ecology is that empirical research has temporal, spatial, and other scale-related limitations.We elaborate on this in the discussion section (L450-461).
--Tighter integration of empirical networks in analyses The authors provide some comparison of their theoretical work to empirical networks (L255, L260, etc.), but these analyses are relatively limited and appear as more of an afterthought.While I like the overall modelling approach and find the theoretical results interesting, it will be important to see whether the findings translate to empirical networks.I appreciate that it is not possible to study the assembly of these empirical networks, but can the authors do something like provide a breakdown of motif frequencies in empirical networks?Right now, the comparison centers on three broad network properties (richness, connectance, and nestedness, see Fig. 6) and the results themselves are not especially clear and convincing and, moreover, do not provide any additional support to the main findings regarding intra-guild competition and higher-level interaction patterns.
Response: We agree with the reviewer that the comparison with empirical networks based on broad properties (richness, connectance, and nestedness) does not provide strong support for our main findings of how intra-guild indirect interactions of colonizers contribute to higher-level interaction patterns in assembling pollination networks.For this reason, that figure was moved to the Supplementary Information (see new Figure S1).
However, to the best of our knowledge, there is no empirical data on assembly of plant-pollinator networks both at the scale of 150 years and at a fine enough temporal resolution (i.e., sampled at least every 3 years) to make a fair comparison with our motif results.Moreover, the motifs developed in this study are not meant to be a metric to characterize the structure of a static pollination networks.Rather, they are meant as a tool to investigate the transient dynamics of colonizer establishment via intra-guild indirect effects (L154-157).Specifically, our motifs focus on a focal species that is followed from its colonization to subsequent extinctions and colonizations.Therefore, providing a breakdown of motif frequencies in empirical networks (shown below for all 121 empirical networks used for new Figure S1) would be an erroneous way to use our motif analysis as there is no assembly information that can be tracked for each focal species.Therefore, we cannot include this analysis in the new version of our manuscript.We explain this limitation of current empirical data, which is also the strength of our study -as we can unveil an understanding of network assembly that is not possible to obtain via empirical research, at least with current data -in L450-461.

--Additional temporal analyses
The authors record motif groups in sets of three subsequent time steps (L124) but then group the motif data for all colonizers, regardless of when they established in a network (L127).It would be very interesting to see an explicit breakdown of the distribution of these three-motif sequences (i.e., similar to information presented in Table 1).It would also be cool to see if/how motif distributions change during the colonization trajectory, e.g., early vs. middle vs. late stages.S2).We found that the distribution of motifs among attempted colonizers does not vary significantly between these groups.However, the establishment rate across all motif groups decreased over time, meaning that early colonizers established at a higher rate than later colonizers which is consistent with the empirical evidence we referred to in the discussion.We also expanded new Table S3 (prior Table S1) to more explicitly show the cumulative distribution of motifs (across all colonizers in each assembly model) at each of the three subsequent timesteps, that is: Motif frequency after establishment, motif frequency after extinctions, and motif frequency after subsequent establishment.

Response: Following the reviewer's suggestion, we extended our theoretical analysis to investigate whether motif distributions among attempted and established colonizers varied among early, mid, and late state colonizers by adding Fig S2, which more intuitively illustrates the information previously presented in old Table 1 (now new Table
--Remind the reader of the four questions I like the four research questions (L76) but found it difficult to remember each question when they were referred to simply by Q1 etc.This was especially the case when reading the section "Core motifs produced by plant species" (L142).It would be helpful if sentences could be rewritten to remind readers of each question as the answers are presented.
Response: Agreed.Sentences were rewritten throughout the results to clarify which question each result addresses.For example, for the section "Core motifs produced by plant species with adaptive foraging" these questions can be found in L193, L196, L200, and L204.
--Clarify what information is presented in Table 1 and Fig. 4 I did not find the information in Table 1 very easy to interpret.Is the establishment rate over all 121 simulations?Is such information worth presenting by model (W/ AF etc.) rather than broken down by plants vs. pollinators?Which rates are meant to sum to 1? The bottom line is that I did not find Table 1 very effective.Also, it wasn't clear to me if Fig. 4 (which I did find intuitive) presented the same/similar information to Table 1.S2 in  --Consider specialists as having more than one interaction I would be curious to know if it would be possible to perform the analysis with specialists defined by a diet breadth greater than one (L218)?Could it also work if specialists had a potential diet breadth greater than one but only realized one interaction at a time?In a similar vein, do the authors think results would change significantly if species were categorized into specialists, generalists, and super-generalists (with motifs reflecting this categorization)?Such an extension would help bring the work closer to empirical systems, in which diet breaths follow distributions that are much more complicated than just specialist having 1 interaction and generalists having > 1 interactions.Also, in simulations the number of interactions of a generalist is drawn from a uniform distribution (L388)---would results change if other distributions were used, particularly ones that more closely match empirical degree distributions?

Response: We agree with the reviewer that Table 1 in the previous version of our manuscript was not easy to interpret so we moved it to the supplementary information (Table
Response: We thank the reviewer for making these comments, which helped us see that we needed to clarify that our assembly model actually reproduces all the attributes of empirical networks the reviewer points out.We address this set of comments by adding more panels to new Figure S1.We explain how the new panels of Fig. S1 answer each comment in the last paragraph of this response. The definition of specialist plant and pollinator species having only one interaction while generalist species having more than one, directly connects with qualitatively different behaviors of the Valdovinos et al's (2013) model.On the one hand, specialist plant species offer the most exclusive floral rewards to the pollinator species that visits them and specialist pollinator species offer the highest quality of visits to the one plant species they visit but cannot adaptively re-arrange their foraging efforts because they only interact with one plant species.On the other hand, the rewards offered by the generalist plant species are shared by several pollinator species (causing exploitative competition) and generalist pollinator species visit several plant species, diluting their conspecific pollen.Given these very distinct differences in model behavior between species having one interaction versus having more than one interaction, our motif analysis based in such a distinction is very effective in capturing the effect of intraguild indirect interactions on community assembly.
There is only a quantitative difference in model behavior between generalist and super-generalist pollinator species (e.g., between 3 and 20 interactions), that is, supergeneralist pollinators have the greatest niche flexibility and as a result become the most quantitatively specialized.However, distinguishing between generalists and supergeneralists does not increase our ability to detect intra-guild indirect interactions.
In summary, the distinction between specialists and generalists in our analysis is the most effective way to detect intra-guild indirect interactions in a very complex set up (assembly + population dynamics + adaptive foraging), which is a strength of our work.That is, it is a smart distinction to conduct an analysis that disentangles simple dynamic patterns from a very complex dynamical process.Our assembly model still produces degree distributions (including the full array of specialist to super-generalist species) observed in empirical networks that the reviewer is referring to (see new Fig S1A,B).Moreover, the species that colonize with only one interaction usually end up with more than one interaction throughout the assembly process.Thus, in essence we are already modeling species that have "a potential diet breadth greater than one but only realized one interaction at a time" rather than "true specialists" as the reviewer suggests.Finally, to the best of our knowledge, there is no empirical data on the distribution colonizers' degrees when they enter a network.Therefore, we believe that the uniform distribution is the most parsimonious.
--Describe how results for plant-focused motifs fit with pollinator-focused motifs Results for pollinators are by-and-large considered *separately* from results for plants.I would like to see a discussion on how the results regarding pollinators (e.g., generalist colonizers with specialist incumbents) and plants (e.g., specialist colonizers with generalist incumbents) might emerge *together* from a modelling/technical standpoint; this could go around L253.
Response: We followed the reviewer's suggestion by discussing in L406-414 how the core "Spec-Gen" and "Gen-Spec" motifs for plants and pollinators, respectively, can emerge together.That is, the specialist plant colonizers in motif group "Spec-Gen" can provide exclusive resources to generalist pollinator colonizers in motif group "Gen-Spec" who can in turn perform high quality visits by quantitatively specializing on those plants.This advantageous "mega-motif" combining plants' "Spec-Gen" and pollinators' "Gen-Spec" motifs is the most likely to emerge from assembly given its positive, direct effects on species of the opposite guild.Moreover, this "mega-motif" would lead to even more nested networks.
--Fig. 1.I don't know what a "passing" interaction is?Is there a better term that can be used instead?Maybe "transient" or "temporary"?Or perhaps add a definition in the caption.
Response: Changed "passing" to "extinct".The dashed line is meant to indicate which interactions disappear as a result of a species becoming extinct.
--L109.Add a short explanation of the "dynamic species pool" and how it works.
Response: This phrase was deleted.The intention was to say that colonizing species (identified by characteristics such as their foraging efficiency or nectar production rate) are randomly generated rather than originating from a finite regional species pool.However, on further investigation, the phrase "dynamic species pool" indicates in prior literature that eco-evolutionary feedbacks are influencing species' characteristics which is not the case in this model.Thus, we deleted the phrase to avoid any confusion with prior uses of this phrase.
one motif group to another."I had a hard time imaging what this would look like.
Response: An example was added to L165-167.That is "For instance, if a specialist colonizer belonging to motif group "Spec-Spec" transformed to motif group "Spec-Gen", this would indicate that all intra-guild indirect specialists went extinct".
--Fig. 2. I think the figure title would be clearer if it was, "...each motif group."Also, personally I would find "Spec" easier to read than "Spc".Response: We added an Appendix S3 to explain which structural metrics we used in our analysis and which statistical tests were performed.We performed Welch tests to statistically evaluate the hypothesis that networks assembled from the model with adaptive foraging are richer, less connected, have a higher pollinator:plant ratio, and are more nested than networks assembled from the model without adaptive foraging.The Welch tests were paired to compare networks populated by specialist plants and specialist pollinators at the same probability.Additionally, we performed Welch test to statistically evaluate the hypothesis that the connectance, plant:pollinator ratio, and richness of empirical networks is significantly different from simulated networks produced from our assembly model with adaptive foraging.

Response
--L327.I found the argument involving A. mellifera and Bombus spp.confusing since the example with Bombus spp.doesn't seem to support the general thesis of the paragraph.
Response: Agreed, thank you for pointing this out.We edited the text to acknowledge that A. mellifera follows the trend in our model but Bombus spp.do not (L386-389).

General comment
Dritz et al. developed a dynamic model to describe the assembly of mutualistic network, a surprisingly overlooked aspect of mutualistic networks.By including adaptive foraging in this article, they provided an innovative theoretical approach of the question, allowing them to account for the plasticity of interactions, that is often neglected.By combining this model with a motifs approach, they could track the impact of colonization on the network over the assembly process.This article is definitely a niece piece of science that provide a new and results about the dynamics of invasion in a network context.The introduction and discussion are well written and clear.I have no major comments about that manuscript.I have two main points of discussion I would like to raise: 1) about the use of motifs and possible bias and limits; 2) for the moment big parts of the methods are quite obscure and require lot of energy from the reader to be understood because we need to read previous article about the model, and the format (methods at the end) does not help.I detail a bit these points in the following paragraphs.Otherwise figures and results could a bit clearer, but as I said above, these are no major issues and this article is really a worthy reading, thanks to the authors for that.
Response: We thank the reviewer for the constructive criticism and useful suggestions that have greatly improved the quality of our work.We have addressed them all in the new version of our manuscript.We paid special attention to making the Methods much easier to follow, and provided all the information needed to understand them.Specifically, we brought all the methods from previous papers and our supplementary material to the new version of our Methods section.
Authors focused on indirect effects that propagate through path of length 2 only, so the shortest indirect effects possible, but is never highlighted, while it would be nice to discuss this point.However, many studies have shown that in diverse networks like those studied by authors, an important part of indirect effects propagate through long-paths (Higashi & Nakajima 1995;Nakajima & Higashi 1995;Guimarães et al. 2017;Pires et al. 2020).The same studies using the Jacobian matrix of dynamical systems to study indirect effects over all these possible path (Nakajima & Higashi 1995), that in contrast to motif approach allow to integrate these effects and measure their strength, including abundances and interaction strengths to calculate propagation from species to species.Thus, I wonder why did authors prefer motifs approach relative to this method?About motifs analyses, also see my comment for lines 395-406, that is, I think, of importance.
Response: Thank you for the suggestion as well as the great references.We added a discussion comparing the relative strengths of each method in L42-49.Previous studies have used mathematical methods to determine the strength of indirect effects through short and long paths by accounting for positive and negative feedbacks.Network motifs function as a complimentary tool to those methods by establishing a connection between indirect effects and network structure.The trade-off is that considering indirect effects through longer paths requires larger and more complex motifs which are more difficult to interpret.We chose to only consider indirect effects among species sharing a direct mutualistic partner (a path of length 2) to detect clear dynamic patters in a relatively complex set up (assembly + population dynamics + adaptive foraging).However, defining more complex motifs to capture indirect effects through longer paths is an avenue for future research.
The model is not understandable without referring to other papers, because parameters and variables are not described at all in the main Methods and partially in Appendix S2, which is, I think, a problem to understand the study.Some important equations are missing, for example the equation linking  to  and to species abundances.To summarise, in absence of further explanations and description the equations presented in Methods are useless.Nerveless, once the reader has done the effort to read previous paper (Valdovinos et al. 2013), this model is definitely a niece piece of work and this paper a nice piece of science.But more efforts are needed in explaining (again) the model in the present study.
Response: Thank you for pointing this out, we brought all the methods from previous papers and our supplementary material to the new version of our Methods section, which greatly improves the readability of our manuscript.We added descriptions of each parameter to the text of the methods.Additionally, we added equations for V_ij (Eq.5), sigma_ij (Eq.6), and gamma_i (Eq.7).Lastly, we expressed each equation in relation to the functional response to ease model interpretation.The functional response is defined in Eq. 8.

Point-by-point comments
Line 38: I do not know this paper but by quickly reading through I do not see how ref. 20 (Bogdziewicz et al. 2018) is linked to this point.I might have missed something, but good to check if it is the right reference.
Response: Agreed, this reference is related to the reproductive benefits of indirect effects but not assembly so this citation was moved to the last line in the paragraph.
Lines 75-79: here and in the following parts, I started to have a problem of terminology to fully Reviewer #1: Remarks to the Author: Review of revised "The role of intra-guild indirect interactions in assembling plant-pollinator networks," by Dritz et al.
I am Reviewer 1 from the first round of reviews.I have read the revised manuscript and the authors' response to reviews.I appreciate the thoughtful replies to my comments and understand the rationale when changes were made and when when they were not.I believe the work to be technically sound and I like the theoretical ideas and methods presented in the manuscript.However, I still would have liked to have seen greater integration with empirical data, although I understand how this is challenging.Perhaps the authors could provide more details on how their ideas could be tested with empirical data that could be collected on time scales of years rather than decades, beyond just the text added in the closing paragraph.In conclusion, while I cannot offer wholehearted support for publication, I would not stand in the way.

Fig. 2 :
Fig. 2: I think that a bit of colours could help to understand better the figure.

Fig. 2 |
Fig. 2 | Schematic representations of each motif.Each motif characterizes the niche breadth (specialist or generalist) of the focal colonizing species (specie highlighted by the box) and the niche breadth of species that share its mutualistic partner(s), as follows: 1) "Spc -Spc", specialist colonizer (blue) that interacts indirectly with at least one specialist in its guild (orange): … the revised manuscript) and replaced it with a new figure (Fig. 4 in the revised manuscript) which more intuitively shows the same information.To clarify, Fig. 4 in the previous manuscript showed the distribution of motifs following extinctions and subsequent establishment while Table 1 in the previous manuscript showed the distribution of motifs prior to extinctions and subsequent establishment.Captions of new Table S2, new Figure 4, and new Figure 7 clarify this difference.

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Both suggestions were incorporated in what is now Figure 3 (old Fig 2).--Fig.3.Because most plant-pollinator networks are drawn with plants as the lower guild and pollinators as the upper guild, it would be easier for me to follow if figures reflected this convention.Response: Thank you for the suggestion, we flipped the motifs in the figure to conform with the convention of plants as the lower guild.--Fig.6.I did not understand what was done based on the sentence (L272) beginning, "We performed a one-sided..." Consider expanding the technical description.