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: open (until 03 Jun 2026)
- RC1: 'Comment on egusphere-2026-1841', Anonymous Referee #1, 15 May 2026 reply
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RC2: 'Comment on egusphere-2026-1841', Pierre Quévreux, 25 May 2026
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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
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).