the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 13 Apr 2026
Modelling the effects of microbial spatial heterogeneity on soil metabolic networks
Abstract. Bacteria and archaea with a wide variety of metabolisms are found in huge numbers in soil and are engaged in both intra- and inter-specific interactions. The exchange and transformation of resources within the metabolic networks formed by microbes are affected by the heterogeneity of soil, as well as by the diversity and abundance of microorganisms. Therefore, depending on environmental conditions and the relative abundance of species and resources present, not all theoretically possible interactions are likely to be realized in practice. Most studies that aim to reconstruct metabolic networks in soil do not account for the potential spatial separation between organisms, caused by the heterogeneous physical structure of the soil environment, and thus only represent some kind of "average network" that may not reflect reality. Here, we further developed a simple geometric model to study how bacterial spatial distributions can alter the functioning of metabolic networks and the emerging behaviours that can arise from them. We show that the spatial distribution of bacteria impacts the transformation of resources depending on the distance to which cells can alter their environment, and that it can lead to behaviours that blur the line between cooperation and competition between bacterial species when both interact with a third partner species. We found that when bacterial density is low, have short interaction ranges and are distributed independently of one another, the use of available resources is less efficient and more variable. On the other hand, when population densities are high and interactions occur over longer distances, more complex interactions emerge. For example, apparent competitors can enter into mutualistic interactions merely due to their spatial configuration around a common partner. Overall, we show that the spatial distribution of organisms may be an important regulatory factor of the functioning of microbial communities and may determine the rates at which resources are transformed in soils.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-1841', Anonymous Referee #1, 15 May 2026
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AC2: 'Reply on RC1', Xavier Raynaud, 10 Jul 2026
Reviewer 1
The authors provide a nice example of the role of spatial heterogeneity not only in resource transformation but also in the species interactions that will emerge in soils, which can be very different from the “average behavior” in which they are actually lumped. I think the contribution is clear, and the paper is well written. I have some comments that I hope can help this nice manuscript get published:Response :
We thank the reviewer for the kind remarks.
General comments
General Comment 1
Framing and scope: the term "metabolic networks" implies a level of complexity that the model doesn't deliver, and the paper should reframe its contribution more precisely. The term metabolic networks carries a strong implication of either genome-scale modelling (Flux Balance Analysis, constraint-based approaches) or large-scale cross-feeding reconstructions (as described in the introduction). However, my understanding of what SHISHAMO actually models is better described as a resource transformation graph, species passing resources through space. There seems to be a gap between what the title implies and what the paper delivers, and maybe a clarification of the terminology might be helpful. Similarly, terms like resource dynamics give a sense that we are dealing with a dynamic model, and this is not the case, so maybe the authors can revise a bit the terminology and use a more precise language that reflects the static, geometric nature of the model.Response:
Although we believe that a 3 molecules linear networks such as the one studied in the manuscript meets the definition of a metabolic network (Dräger \& Planatcher, 2013), we agree that this term is generally associated with highly complex, often experimentally unresolved, networks, which study implies complex modelling approaches. We have updated the manuscript and replaced the terms "metabolic network" by metabolic exchanges.
General Comment 2
Positioning relative to existing models. The introduction lacks engagement with spatially explicit microbial models already in the literature (e.g., DEMENT model (Allison 2012) and similar), and the paper needs to clearly articulate what SHISHAMO uniquely offers. Models like DEMENT ask how trait diversity and enzyme kinetics drive decomposition rates, and SHISHAMO works specifically on network topology and spatial arrangement. This distinction is not clear, and the authors should at least acknowledge the existing body of literature to make the unique contribution of their model clear.Response:
We agree that the modelling context around these questions was lacking in the manuscript. We have added a paragraph that describes different models and approaches that have been published to highlight the differences and the novelty of SHISHAMO compared to the existing models (eg. BACWAVE (Zelenev et al 2000), DEMENT (Allison 2012), COMETS (Harcombe et al 2014), MOSAIC (Mbé et al 2020), LBios (Vogel et al 2015) as well as other unnamed models (Kaiser et al., 2014, Nunan et al 2020, Zech et al 2022 Maestrali et al 2026).
General Comment 3
The model description is quite short and lacks the explicit statement of their assumptions, such as that there is an assumed entire consumption of the resources within the disc, no uptake, etc. Figure 1 shows the model's details, but a written description would be helpful. Also, the authors should justify a bit more about the choices of the paper, for example, why a geometric snapshot of the system is sufficient to draw conclusions about the functioning of the metabolic network and resource transformation, and network functioning, especially if these imply a dynamic process. Additionally, some acknowledgment of the limitations in the interpretation of this model is needed in the discussion, especially keeping in mind how much the authors can generalize the outputs if just a couple of scenarios are presented with one parameter combination. I believe there is an attempt at this in the future work section, but more detail is needed in my opinion.Response:
Following this and another comments by the other reviewer we have updated Figure 1 to make some model parameters clearer. We also added some lines of description in the methods section to better explain our modelling choices. The section "Spatial Representation" was updated to:
"SHISHAMO represents microbes and resources in a finite 2D space. Bacterial cells and the effect they have on their environment are represented by discs, where the disc centre is the cell location and the radius r – or range – is the distance within which a cell interacts with its environment, e.g. resource acquisition or release of metabolites (see zoom in Fig. 1). Although in the soil solution, metabolites diffuse around cells, in the model, diffusion to and from the cell is simplified as an homogeneous spread over the disc. This approximation allows us to consider diffusion in a simple and rapid fashion in which the complexities of diffusion and the dependency on time are removed. This assumes that the balance between metabolite consumption and release in soil reaches an equilibrium (Raynaud et al 2008) and is in accordance with experiments (Gantner et al 2006) and modelling (Franklin and Mills, 2008) that suggest that microbial cells have only a limited effect of a few tens of micrometers on their environment. Although the units in the model are arbitrary, the values we used for the radius r in our simulations makes that 1 pixel is approximatively equivalent to 1 µm.
General Comment 4
The authors present comparisons between simulation outputs and what are referred to as 'theoretical relationships' or a 'theoretical model' (e.g., Equation 1, Figure 4a). However, it is unclear to me what these theoretical relationships represent and where they come from, as their derivation is deferred entirely to the supplementary materials. On closer reading, Equation 1 appears to be an analytical solution derived from the model's own geometric assumptions under CSR, that is, a self-consistency check confirming that the stochastic simulation converges to its analytical expectation, rather than a validation against an independent theoretical framework or empirical data. This distinction is important and should be made explicit. The authors should clarify in the main text what the theoretical relationships are, what assumptions underlie them, and what the comparison with simulation output actually demonstrates. This concern is related to the lack of explicit model equations in the methods section (see General Comment 3): without a clear statement of the model's governing assumptions, it is difficult to see what the authors are actually doing.Response:
Equation 1 is, as the reviewer noted, the analytical solution of the model when cells are randomly distributed. It has two purposes. First, as the reviewer has noted, it serves has a consistency check to confirm that, under CSR, the model converges to its analytical expectation. However, in the manuscript, we also explore other spatial distributions of organisms. The analytical expectations of the model under the other spatial distributions we have explored (LGCP and "aggregated LGCP") are much more complex, if not impossible, to derive. For these cases, Equation 1 is used as a reference to explore how the spatial distribution makes the model results diverge from the CSR expectation.
We have updated the description of how Equation 1 has been obtained in the methods and explained more clearly its use in our work:
"As the model considers that an individual cell is able to use all the available resources within its disc, the expected amount of resources for a simple 3 resource linear network with cells distributed under CSR is:
\bar{R}1 & = AT(1-c1)
\bar{R}2 & = AT c1(1 -c2)
\bar{R}3 & = AT c1 c2
where AT is the total surface of the modelled area, \bar{ Ri}, the average amount of the ith resource of the linear network and cs the expected area coverage of each species S_s.
The details about and the demonstration of how we obtained these formulas can be found in the supplementary material. In our analyses, these equations were use to confirm that, under CSR, the numerical model converges to its analytical expectation and to explore how the other cell distribution types studied, for which theoretical expectations are not available, make the numerical model diverge from its CSR results."
General Comment 5
The paper does not define the biological identity of the entities referred to throughout as 'species.' It is never made clear whether S1, S2, and S3 are meant to represent individual bacterial taxa, functional groups, broader taxonomic groups, or metabolic guilds. This ambiguity is consequential rather than merely semantic. The parameterization choices, particularly the disc radius, which encodes the spatial range of interaction, and the cell densities used in simulations, are only interpretable if the biological level of organization is known. For individual bacterial cells, diffusion-based interaction ranges on the order of 10–50 µm are plausible; for functional groups distributed across soil aggregates, the relevant spatial scales would be fundamentally different. Furthermore, the paper's two main real-world examples point implicitly in different directions: the nitrification analogy in the discussion treats AOA/AOB and NOB as species, which are in reality broad functional guilds, while the eclipse dilemma is grounded in a synthetic community of individual species (E. coli and S. enterica). The paper moves between these framings without acknowledging the difference. This lack of conceptual clarity also directly constrains the discussion of empirical validation. What data would be needed to confront the model depends entirely on what its entities represent. If species correspond to individual taxa, validation would require methods with species-level metabolic resolution, such as DNA-SIP, qSIP, or NanoSIMS combined with FISH, approaches that, while technically demanding, are increasingly available and have been used to detect taxon-specific carbon exchange interactions in soil.
If species correspond to functional groups, broader approaches such as PLFA-SIP may suffice. The authors should commit to a level of biological organization, justify their parameterization choices accordingly, and use this as the basis for a more concrete and realistic discussion of how the model might eventually be confronted with empirical data.Response:
Thank you for pointing this out. Our not defining the entities was an oversight. The discs in the model represent individual bacterial cells and the 'species' are thus bacterial taxa. We believe that fine-scale, high resolution methods are necessary for full parameterization/validation approach of the model. It is true that we treated AOA/AOB and NOB as species rather than broad functional guilds. This example was mostly for illustrative purposes but was evidently misleading with regard to the scale at which the model operates. While updating the introduction, we have removed this example and replaced it by other examples of species specific degradation of organic products, more in line with our work (albeit not necessarily in soils due to the scarcity of examples).
General Comment 6
The discussion makes several claims that go beyond what the model actually demonstrates. For example, lines 310-311 suggest that the model integrates pore variability and could help improve larger-scale models, but SHISHAMO represents spatial heterogeneity only through the positions and clustering of bacterial discs. It does not model pore geometry, water films, or any physical soil structure, so the connection to pore variability is not justified and needs either a clearer argument or to be toned down. More broadly, the discussion tends to present future possibilities rather than clearly stating what has actually been shown. The core contribution of the model, that spatial arrangement affects how metabolic networks function, is potentially valuable, but it is not new on its own. What SHISHAMO could add is a formal way to quantify how much spatial arrangement matters and under what network conditions. However, the current results only explore one parameter combination for the eclipse dilemma, so the broader claims in the discussion, such as lines 300-301 about making soil compartments in larger models
more realistic, are not yet supported by the results. The authors should be more explicit about what has been demonstrated, what is plausible based on the results, and what remains speculative. Related to this, the paper would benefit from at least a few sentences on the biological and ecosystem-level implications of its findings. For instance, if spatial arrangement can shift a metabolic network from competitive to mutualistic functioning, what does that mean for nutrient cycling, carbon storage, or greenhouse gas production in soils? Processes like aggregate disruption, tillage, or rewetting after drought all redistribute microorganisms in space, and the model suggests this could have consequences for how microbial networks function. Making this connection explicit would help clarify why quantifying spatial effects on metabolic networks matters beyond a mathematical exercise, and would strengthen the justification for the model in both the introduction and the discussion.Response:
The reviewer is perfectly correct. The discussion was overly optimistic and excessively enthusiastic. We have rewritten large parts of the discussion to better frame our results.
Specific comments
Line 36The example of Kundu et al. (2019), and the motivation for part of the work, is quite off for a soil paper. The example highlights the complexity in the termite’s gut. I wonder if there are not sufficient complex networks in soil systems that the authors can add that can be more fitting for a soil paper.
Response:
Due to the complex structure and opaque nature of soil, examples of metabolic interaction in soil microbial communities are relatively rare. Nevertheless, metabolic exchanges is considered to be ubiquitous in microbial ecosystems (Kost et al 2023) and there has been simple interaction networks that have been described in microbial communities extracted from soil (McInerney et al., 2009; Jiang et al., 2018; Sun et al., 2023).
The initial choice of citing the Kundu et al. (2019) paper was to illustrate the complexity that can exist in metabolic exchange networks. The introduction has been entirely rewritten to take this, and other points into account. We have kept the Kundu et al example as an illustration of how complex metabolic networks can be.
Line 159-162
For the eclipse dilemma, the authors mentioned the following example: "Such metabolic interaction network has been described for interactions between populations of E. Coli and S. enterica". I just wonder how relevant this dilemma is then for soils if they provide this example only. Would it be possible to add a soil analog to anchor the eclipse dilemma in their system of interest?Response:
We agree that the eclipse dilemma example is rather theoretical, despite the fact that both E. coli and S. enterica can live in soils. Our aim with this example is to show how a simple network with two species and two resources in interactions can lead to a complex behaviour, that depend on the spatial distribution of the organisms. Following this comment and another one from the other reviewer, we took care, while rewriting the introduction to better introduce the eclipse dilemma and the consequences for soil functioning of such interactions that can lead to complex emergent behaviour.
Equation 3
It seems that the area of the square is missing in the equation in order to actually get a percentage loss relative to the resource available. Maybe this is just a typo in the equation.Response:
The equation is for a single cell, and is independent of the area modelled. We emphasised the fact that the equation applies to only one cell in the text and corrected a typo in the explanation. The paragraph has been rewritten as follow:
"The maximal loss one bacterium can suffer from the intersection with another single bacterium of the same radius r is -50%, i.e. they share resource every single pixel. The theoretical % loss L of one single cell can be calculated from the area of the intersection between the two discs. As we assumed that all cell discs had the same radius, L can be calculated as a function of distance between cells d as in Schnell et al (2021)".
Line 253
“so” I believe it is a typo.Response:
This was indeed a typo and has been corrected.Citation: https://doi.org/10.5194/egusphere-2026-1841-AC2
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AC2: 'Reply on RC1', Xavier Raynaud, 10 Jul 2026
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RC2: 'Comment on egusphere-2026-1841', Pierre Quévreux, 25 May 2026
This paper proposes a model to explore the functioning of metabolic networks in soil microbial communities depending on the spatial distribution of microbe species. Instead of modelling the community with ODE, the authors proposed a kind of instantaneous model of reaction-diffusion in which microbial cells consume resources and release by-products in a disc of influence. Several species of microbes and resources/by-products form metabolic networks with diverse structures (linear, loop…) characterised by competition and mutualism through cross-feeding. The authors manipulated the structure of the network, the radius of the influence zone of bacterial cells and the spatial distribution of cells and species. They found that the clustering of cells and species was critical to enable cross-feeding, which was modulated by the radius of the influence zone. In particular, competition between two species could be turned into apparent mutualism by the presence of a third specie closing a loop of cross-feeding.
Being more used to classic models based on ODE, I was happy to see something original to address in an elegant way the complexity of soil microbial communities. The proposed individual-based model enables to explore the functioning of diverse microbial communities at large scale while sparing computation power. Although the model greatly simplifies the system (e.g. population dynamics is not implemented), it is able to capture competitive and mutualistic direct and indirect interactions. In particular, the authors were able to fully explain the observed patterns when parameters were varied.
I agree with the authors on their results and conclusions but I think they can significantly improve the manuscript. In particular, I found that the introduction only provides a few elements of soil context before rushing to the technical aspects. Some elements of fundamental community ecology are missing to propose more detailed questions and predictions. In the same vein, the discussion focuses on technical aspects (limitations of the models and future developments) and does not respond to specific questions. In addition, the authors could improve the fluidity of the reading of the introduction by rephrasing several sentences to better articulate their ideas. Please find some propositions in my point by point comments:Introduction
1 - l.53 “Allison (2005)” instead of “(Allison, 2005)”
2 - l.53 delete “Networks are convenient for modelling.” and rephrase the following sentences (l.53-55) that are not efficiently written: “Metabolic network can be modelled through network theory, which represents the system formed by a set of potentially interacting entities as a collection of nodes connected by edges (Biggs et al., 2015).”
3 - Predictions on the effects of indirect interactions must be developed.
4 - “We supposed that increased spatial heterogeneity leads to clusters of microbes where metabolism is increased as well.” (l.62) some explanations with support of existing literature is needed.
5 - The introduction misses to present the role of indirect interactions and the subsequent eclipse dilemma mentioned later in the manuscript. The hypotheses presented at the end of the introduction are vague and should be more tightly linked to the methods and the results. The questions rased for this soil system have been addressed in a similar way in the context of general community ecology (and plant communities in particular). Liautaud et al. 2019 (10.1111/ele.13289) would be interesting for instance. Therefore, I encourage you to include this broader link with community ecology in your introduction. This is my first major comment.
Methods
6 - l.75 rephrase: “Units in the model are arbitrary but in the version presented in this study 1 pixel is equivalent to 1 µm”.
7 - “1 µm” (l.75) To properly write units in LaTeX you can use the siunitx package with command \qty{1}{\micro\meter}
8 - “The products of cell metabolism are spread homogeneously across the disc.” (l.79) this sentence is redundant with sentence l.74-75. In the same vein, “This approach allows us to represent diffusion in a simple and rapid fashion in which the complexities of diffusion and the dependency on time are removed.” (l.80-81) should be moved to the “Spatial representation” subsection.
9 - Figure 1: please write “2 species (S1 and S2)” in the caption for consistency with the presentation of resources. In addition, a zoom on a circle with a dot at its centre representing a bacterial cell and a legend for the disc would be welcome to illustrate the general description of the model.
10 - Figure 3: A few annotations to highlight competitive and mutualistic interactions would be welcome to improve the pedagogy of the figure.
11 - The eclipse dilemma should be presented in the introduction in which the sentence l.160 should be for instance.
12 - Equation 2: please write \bar{R}_{2,\dot} instead of \bar{R_{2,\dot}} to place the bar correctly. The same problem is present in the supporting information.
Results
13 - Figure 4: Please writhe “csr” and “lgcp” in capital letters to be consistent with the text. In addition, the legend for the right panel representing the distribution of cells is missing and the text presenting these drawing is missing in the caption.
14 - “When these parameters are high, S1 covers a large area and produces a lot of R2 but then S1 and S2 are more likely to intersect, increasing R3 at the expense of R2. This is expected because if all species were present everywhere then only R3 would remain at the end.” (l.193-195) This more than expected, this is actually predicted by equation 1 when c1 and c2 get close to 1. Please rephrase to include these predictions.
15 - “The deviations from CSR are similar for the two distributions.” (l.198) An explanation is needed here.
16 - More generally the paragraph l.197-205 does not explain efficiently the observed patterns. You should first explain the effects of the distributions and how their alterations of resource transformations ripple from one resource to another. Then, you explain the effect of cell number and disc radius which are consistent for all resources and distributions. Some elements are given in paragraph l.206-215 but is can be done in a much integrated way.
17 - l.224 It would be good to remind that the results presented in this section are at the scale of the cell. Please remind it in the caption of figures 5 and 6 as well.
18 - Figure 5: Although you explain in the text that cases 4 and 6 are not exhaustive, it would be better to draw different configuration between the two cases because it is confusing to see the same configuration leading to opposite results.
Discussion
19 - “The review from Warrier et al. (2026) shows a good overview of the multiple impacts that spatial structure, biotic or abiotic, can have on microbe communities in all sorts of environments.” (l.268-270) This reference should be better integrated in the rest text. Concluding a paragraph with such a sentence weakens the discussion.
20 - The paragraph l.272-277 is very technical for a discussion. The idea must be developed with examples of other distributions and the expected changes in the results. As it is it does not contain valuable information for the reader.
21 - A comparison with ODE models (Allison 2005 and Kaiser et al 2014 10.1111/ele.12269) would be welcome to highlight the value of the model.
22 - A more general paragraph on indirect effects echoing my comment for the introduction would be welcome to provide more depth to the discussion. This is my second major comment.
Supplementary information
23 - typo l.3 “an n-dimensions”
24 - A table containing the values of parameters used in simulations is needed.
25 - typo l.23 “Quantities”
26 - typo eq.3 “for”
I hope that my comments will help the authors to improve the manuscript.
Sincerely yours
Pierre QuévreuxCitation: https://doi.org/10.5194/egusphere-2026-1841-RC2 -
AC1: 'Reply on RC2', Xavier Raynaud, 10 Jul 2026
Reviewer 2 - Pierre Quévreux
This paper proposes a model to explore the functioning of metabolic networks in soil microbial communities depending on the spatial distribution of microbe species. Instead of modelling the community with ODE, the authors proposed a kind of instantaneous model of reaction-diffusion in which microbial cells consume resources and release by-products in a disc of influence. Several species of microbes and resources/by-products form metabolic networks with diverse structures (linear, loop…) characterised by competition and mutualism through cross-feeding. The authors manipulated the structure of the network, the radius of the influence zone of bacterial cells and the spatial distribution of cells and species. They found that the clustering of cells and species was critical to enable cross-feeding, which was modulated by the radius of the influence zone. In particular, competition between two species could be turned into apparent mutualism by the presence of a third specie closing a loop of cross-feeding.
Response:
We thank the reviewer for the positive comments.Being more used to classic models based on ODE, I was happy to see something original to address in an elegant way the complexity of soil microbial communities. The proposed individual-based model enables to explore the functioning of diverse microbial communities at large scale while sparing computation power. Although the model greatly simplifies the system (e.g. population dynamics is not implemented), it is able to capture competitive and mutualistic direct and indirect interactions. In particular, the authors were able to fully explain the observed patterns when parameters were varied.
I agree with the authors on their results and conclusions but I think they can significantly improve the manuscript. In particular, I found that the introduction only provides a few elements of soil context before rushing to the technical aspects. Some elements of fundamental community ecology are missing to propose more detailed questions and predictions. In the same vein, the discussion focuses on technical aspects (limitations of the models and future developments) and does not respond to specific questions. In addition, the authors could improve the fluidity of the reading of the introduction by rephrasing several sentences to better articulate their ideas.
Response:
We thank the reviewer for these comments. Please see our responses to the individual comments made below.Please find some propositions in my point by point comments:
1. Introduction
1. l.53 “Allison (2005)” instead of “(Allison, 2005)”
Response:
This was corrected.2. l.53 delete “Networks are convenient for modelling.” and rephrase the following sentences (l.53-55) that are not efficiently written: “Metabolic network can be modelled through network theory, which represents the system formed by a set of potentially interacting entities as a collection of nodes connected by edges (Biggs et al., 2015).”
Response:
We thank the reviewer for rewriting the sentence.3. Predictions on the effects of indirect interactions must be developed.
Response:
While rewriting parts of the discussion, we added a short section on indirect interactions in soils. The updated text is as follows:
"Beyond the mere direct interactions between individuals belonging two species as described above, networks of interactions can lead to complex, indirect effects that can have profound impact on the the abundance of species and the functioning of ecosystems (Wooton, 1994). These indirect interactions can arise from interaction chains (i.e. a set of linked direct interactions) or from interaction modification (i.e. the presence of one species alters the direct interaction between two other species). For example, enzyme excretion by some bacteria can enhance the overall resource availability of the community and thus alter the interactions between members of the community. Moreover, cross-feeding interactions between multiple partners can lead to unexpected indirect effects. Harcombe et al (2014) studied the cross feeding interactions between Escherichia coli and two strains of Salmonella enterica and found that, depending on the spatial arrangement of the bacterial colonies, the presence of a competitor could enhance the growth of the colony it is competing with."4. “We supposed that increased spatial heterogeneity leads to clusters of microbes where metabolism is increased as well.” (l.62) some explanations with support of existing literature is needed.
Response:
We have rewritten the section to :
"Here, we propose to implement a spatially explicit network of metabolic interactions in order to determine how the spatial organisation of cells in bacterial communities affects the metabolic flows. We used the model SHISHAMO (Spatial Heterogeneity In Soils, Hotspots And Micro Organisms), a spatially explicit, individual-based model, which was first introduced in Nunan et al 2020. in order to study the impact of soil heterogeneity on two simple networks : a 2 species linear network, and a 3 species network with 2 loops . Our goal was to study the outputs of SHISHAMO on these simple cases, that are also patterns that can be found in larger metabolic networks. We expected that an increased spatial heterogeneity in microbial spatial distributions would impact the metabolism of the community (Harcombe et al 2014). In places where cells belonging to different taxa involved in cross-feeding exchanges are aggregated, the production of metabolites was predicted to increase, as was the spatial variability of metabolite concentrations}".5. The introduction misses to present the role of indirect interactions and the subsequent eclipse dilemma mentioned later in the manuscript. The hypotheses presented at the end of the introduction are vague and should be more tightly linked to the methods and the results. The questions rased for this soil system have been addressed in a similar way in the context of general community ecology (and plant communities in particular). Liautaud et al. 2019 (10.1111/ele.13289) would be interesting for instance. Therefore, I encourage you to include this broader link with community ecology in your introduction. This is my first major comment.
Response:
We agree that several aspects were missing from the introduction (better framing on soil functioning, importance of indirect interactions, more context on soil modelling, etc). Following this comments and comments from the other reviewer, we have rewritten parts of the introduction to improve the context of our work around these questions.Methods
6. l.75 rephrase: “Units in the model are arbitrary but in the version presented in this study 1 pixel is equivalent to 1 µm”.
Response:
The sentence was rephrased to :
"Although the units in the model are arbitrary, the values we used for the radius r in our simulations mean that 1 pixel is equivalent to approximatively 1 µm".7. “1 µm” (l.75) To properly write units in LaTeX you can use the siunitx package with command \micro\meter.
Response:
The siunitx package does not seem to be compatible with the Copernicus LaTeX class. We used the \textmu command instead.8. “The products of cell metabolism are spread homogeneously across the disc.” (l.79) this sentence is redundant with sentence l.74-75. In the same vein, “This approach allows us to represent diffusion in a simple and rapid fashion in which the complexities of diffusion and the dependency on time are removed.” (l.80-81) should be moved to the “Spatial representation” subsection.
Response:
We removed the repetition that was on line 79 and moved the lines that were on l.80-81 to the “Spatial representation” subsection.
9. Figure 1: please write “2 species (S1 and S2)” in the caption for consistency with the presentation of resources. In addition, a zoom on a circle with a dot at its centre representing a bacterial cell and a legend for the disc would be welcome to illustrate the general description of the model.Response:
We have changed the figure and also updated the text to:
"Bacterial cells and the effect they have on their environment are represented by discs, where the disc centre is the cell location and the radius r – or range – is the distance within which a cell interacts with its environment, e.g. resource acquisition or release (see zoom in Fig. 1)".10. Figure 3: A few annotations to highlight competitive and mutualistic interactions would be welcome to improve the pedagogy of the figure.
Response:
We have modified the figure as well as the caption that is now:
"Graphic representation of the eclipse dilemma and the way it is implemented in SHISHAMO. Mutualistic partners S1 and S2 (resp. S1 and S3) feed each other by exchanging R1 and R2 (resp. R1 and R3) resources). Mutualistic competitors (S2 and S3) compete over the same resource R1 but feed their shared partner S1.
11. The eclipse dilemma should be presented in the introduction in which the sentence l.160 should be for instance.
Response:
A reference was added in the section on indirect interactions.12. Equation 2: please write $\bar{R}_{2,\dot}$ instead of $\bar{R_{2,\dot}}$ to place the bar correctly. The same problem is present in the supporting information.
Response:
We thank the reviewer for providing the correction. This has been changed in the manuscript.2. Results
13. Figure 4: Please writhe “csr” and “lgcp” in capital letters to be consistent with the text. In addition, the legend for the right panel representing the distribution of cells is missing and the text presenting these drawing is missing in the caption.
Response:
CSR and LGCP have been written in capital letters and the legend has been updated.14. “When these parameters are high, S1 covers a large area and produces a lot of R2 but then S1 and S2 are more likely to intersect, increasing R3 at the expense of R2. This is expected because if all species were present everywhere then only R3 would remain at the end.” (l.193-195) This more than expected, this is actually predicted by equation 1 when c1 and c2 get close to 1. Please rephrase to include these predictions.
Response:
The text was modified to include the reviewer's remark:
"This is due to the balance between the production of R2 by species S1 and consumption of R2 by species S2. When these parameters are high, S1 covers a large area and produces a lot of R2 but then S1 and S2 are more likely to intersect, increasing R3 at the expense of R2 as expected from Eq. 1 when c1 and c2 tend to 1.15. “The deviations from CSR are similar for the two distributions.” (l.198) An explanation is needed here.
Response:
See next answer.16. More generally the paragraph l.197-205 does not explain efficiently the observed patterns. You should first explain the effects of the distributions and how their alterations of resource transformations ripple from one resource to another. Then, you explain the effect of cell number and disc radius which are consistent for all resources and distributions. Some elements are given in paragraph l.206-215 but is can be done in a much integrated way.
Response:
We thank the reviewer for this relevant recommendation. We modified the whole subsection as follows:
"Figure 4 shows the quantity of resources at the end of simulations in the case of a simple linear network with 2 species and 3 resources. If we compare spatial distributions, we see that Figure 4a. shows that for CSR, Figures 4b. and 4c. show differences in resource amounts between the theoretical CSR model and LGCP, and aggregated LGCP, respectively. LGCP
favours intersections by grouping cells of a same species with each their own probability field; aggregated LGCP favours intersections by distributing cells according to the same probability field. Still, the variations R1 for both distributions compared to CSR remain under -1 %, following similar trends. The amount of R2 decreases by a few tenths of percent relative to CSR, with a stronger variation for aggregated LGCP compared to LGCP. Finally, the behaviours of LGCP and aggregated LGCP are more distinct for the end resource R3. In the case of LGCP, the variation remained very close to 0 and within one percent most of the time. However, the deviations are much larger for aggregated LGCP. This situation leads to more R3 being produced compared to CSR. This can be explained by the fact that in aggregated LGCP, all bacteria from the two species tend to be aggregated, which is not the case for the other distributions where species are independently distributed (Section 2.3.1). Therefore, more compact distributions like aggregated LGCP favour interactions between species.
The effect of spatial distributions is impacted by the number of cells and the radii of their discs. For CSR (Fig. 4a. ), the higher the number of cells per species and the bigger the disc radius, the less R1 is left. It should be noted that doubling the radius does not multiply the consumption by 4, which can be explained by the increased probability of disc overlap among bacteria from S1. In the case of R2 and R3, the more cells there are and the bigger their disc radii, the higher R2 and R3 concentrations are at the end. However, the quantity of R2 reaches a maximum at about 200 cells when the range is 30 pixels. With lower ranges the shape of the curve suggests that a plateau would be reached at cell values greater than 300. This is due to the balance between the production of R2 by species S1 and consumption of R2 by species S2. When these parameters are high, S1 covers a large area and produces a lot of R2 but then S1 and S2 are more likely to intersect, increasing R3 at the expense of R2 as expected form Eq. 1 when c1 and c2 tend to 1.
For the other distributions, the influence of the cell number and radius is apparent too, with some differences between LGCP and aggregated LGCP (Fig. 4b. and c.). The quantity of R1 left increases by less than a percent compared with CSR with a similar trend where the more cells there is and the larger they are, the higher the deviation gets. For R2, the deviations vary slightly depending on the disc radii although the variations are small and overlap. For R3, the differences between aggregated LGCP and the other distributions is especially strong when there are fewer cells and the disc radii are smaller. Indeed, when there are a lot of bacteria with a large radius, the probability of disc overlap is high, even under CSR, reducing effectively the deviation between the distributions. This also explains why the variability is higher for low ranges and cell densities, as this intersection is less probable (e.g. in aggregated LGCP, the values range between -1% and +8% for a 10 pixel range with 20 bacteria per species versus no differencefor a 30 pixel range with 300 bacteria per species). In that case, the distribution is predominant.
Overall, these results indicate that resource transformation are affected by three distinct properties: their spatial distributions, the number of cells, and the range over which they interact with their environment (cell radii). The first is predominant when the two latter are low, and conversely, the number of cells and their radii becomes more important than the compacity of spatial distributions to explain the final amount of resources."17. l.224 It would be good to remind that the results presented in this section are at the scale of the cell. Please remind it in the caption of figures 5 and 6 as well.
Response:
The requested changes have been made. Figure 5 legend now reads: "Impact of active mutualistic competitor species S3 on each S2 cell versus the distance to the closest S3 cell (aggregated LGCP, r = 50 pixels, 47 cells per species, compilation of 10 simulations)"
and Fig 6:
"Impact of mutualistic competitor species S3 on every S1 (left) and S2 (right) cells (aggregated LGCP, r = 50 pixels, 47 cells per species, compilation of 10 simulations)".
We added a few words at the beginning of section 3.2 and 3.2.2 accordingly to emphasis this point.18. Figure 5: Although you explain in the text that cases 4 and 6 are not exhaustive, it would be better to draw different configuration between the two cases because it is confusing to see the same configuration leading to opposite results.
Response:
We have changed the figure accordingly.Discussion
19. “The review from Warrier et al. (2026) shows a good overview of the multiple impacts that spatial structure, biotic or abiotic, can have on microbe communities in all sorts of environments.” (l.268-270) This reference should be better integrated in the rest text. Concluding a paragraph with such a sentence weakens the discussion.
Response:
In our rewriting of the discussion following comments by both reviewers, we took care to better integrate the Warrier et al 2026 review.20. The paragraph l.272-277 is very technical for a discussion. The idea must be developed with examples of other distributions and the expected changes in the results. As it is it does not contain valuable information for the reader.
Response:
This paragraph was more a perspective on this spatial distribution issue. LGCP has been used to adequately model microbial spatial distribution, but did not account for the solid phase of soil. Considering the solid phase could change could change the model that most adequately describes the distributions. We have updated this part of the discussion to be clearer.21.
A comparison with ODE models (Allison 2005 and Kaiser et al 2014 10.1111/ele.12269) would be welcome to highlight the value of the model.Response:
We added a new section in the introduction that compares SHISHAMO with the existing modelling literature on soil microbial functioning and we also reworked the discussion on these aspects.22. A more general paragraph on indirect effects echoing my comment for the introduction would be welcome to provide more depth to the discussion. This is my second major comment.
Response:
Following this comment and the other reviewer comments, we have reorganized the discussion to provide a more in-depth discussion on the role of indirect effects on soil functioning.Supplementary information
23. typo l.3 “an n-dimensions”
Response:
We replaced it with "a n-dimensional".24. A table containing the values of parameters used in simulations is needed.
Response:
We added in the main document l.139: "All parameters used for simulations throughout this paper can be found in Table S1 in the Supplementary materials."25. typo l.23 “Quantities”
Response:
This has been changed in the manuscript.26. typo eq.3 “for”
Response:
This has been changed in the manuscript.Citation: https://doi.org/10.5194/egusphere-2026-1841-AC1
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AC1: 'Reply on RC2', Xavier Raynaud, 10 Jul 2026
Model code and software
SHISHAMO Raynaud and Paris https://github.com/xraynaud/SHISHAMO
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The authors provide a nice example of the role of spatial heterogeneity not only in resource transformation but also in the species interactions that will emerge in soils, which can be very different from the “average behavior” in which they are actually lumped. I think the contribution is clear, and the paper is well written. I have some comments that I hope can help this nice manuscript get published (detailed comments are provided in the attached PDF).