Spatial structure favors microbial coexistence except when slower mediator diffusion weakens interactions
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eLife assessment
This important study uses computational simulations to explore how spatial structure can affect the coexistence between different microbial species, ultimately helping to explain diversity in microbial communities. The evidence supporting the conclusions is solid, although the parameter values used in the simulations were deemed to be unrealistic. Further investigation on whether the conclusions would hold under more realistic assumptions would be very interesting to microbial ecologists quite broadly.
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 Microbiology and Infectious Disease (eLife)
Abstract
Microbes often exist in spatially structured environments and many of their interactions are mediated through diffusible metabolites. How does such a context affect microbial coexistence? To address this question, we use a model in which the spatial distributions of species and diffusible interaction mediators are explicitly included. We simulate the enrichment process, examining how microbial species spatially reorganize and how eventually a subset of them coexist. In our model, we find that slower motility of cells promotes coexistence by allowing species to colocalize with their facilitators and avoid their inhibitors. We additionally find that a spatially structured environment is more influential when species mostly facilitate each other, rather than when they are mostly competing. More coexistence is observed when species produce many mediators and consume some (not many or few) mediators, and when overall consumption and production rates are balanced. Interestingly, coexistence appears to be disfavored when mediators are diffusing slowly because that leads to weaker interaction strengths. Overall, our results offer new insights into how production, consumption, motility, and diffusion intersect to determine microbial coexistence in a spatially structured environment.
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eLife assessment
This important study uses computational simulations to explore how spatial structure can affect the coexistence between different microbial species, ultimately helping to explain diversity in microbial communities. The evidence supporting the conclusions is solid, although the parameter values used in the simulations were deemed to be unrealistic. Further investigation on whether the conclusions would hold under more realistic assumptions would be very interesting to microbial ecologists quite broadly.

**Reviewer #1 (Public Review):
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Lobanov et al. investigated the effects of spatial structure in microbial communities that interact via secreted metabolites. The work builds up on a previous theoretical model by the authors that considered wellmixed populations in which different bacterial species secrete and consume different sets of metabolites, and metabolites in turn modify the growth rates of species. The model considers communities that are periodically exposed to dilutions, and the authors focus on the regime in which bacterial densities do not reach saturation before the next dilution. Analyzing the stable outcome of these dynamics through comparison with wellmixed scenarios, the authors found that space can favor species richness, especially in the case of communities with prevalent facilitative interactions. This positive …**Reviewer #1 (Public Review):
**
Lobanov et al. investigated the effects of spatial structure in microbial communities that interact via secreted metabolites. The work builds up on a previous theoretical model by the authors that considered wellmixed populations in which different bacterial species secrete and consume different sets of metabolites, and metabolites in turn modify the growth rates of species. The model considers communities that are periodically exposed to dilutions, and the authors focus on the regime in which bacterial densities do not reach saturation before the next dilution. Analyzing the stable outcome of these dynamics through comparison with wellmixed scenarios, the authors found that space can favor species richness, especially in the case of communities with prevalent facilitative interactions. This positive effect on species coexistence is also more pronounced in situations in which species produce more kinds of metabolites than they consume. On the other hand, the positive effects on coexistence can be reversed when bacterial dispersal becomes relevant over the timescale of the simulations, as well as in cases in which the diffusion of metabolites is too slow  which could even result in less coexistence than in wellmixed scenarios. These results add to an ongoing discussion on the different ways in which spatial effects can impact microbial community dynamics and species richness.The conclusions of this paper are mostly well supported by the data, but some aspects of the methodology and analysis need to be clarified and extended.
 This is a model with many parameters and the manuscript should be clearer about how these parameters were used in different scenarios. It is probably a matter of rewriting the text, but I found it hard to understand which parameter values remained the same in scenarios with or without space, as well as how the strength of interactions was assigned, among a few other examples. In other cases, additional analysis (e.g. on how the spatial impact on coexistence depends on the average strength of interactions) would make the work more comprehensive.
 To assess stable coexistence and richness, the authors use a criterium in which species have to be almost equally abundant (above 90% of the abundance of the fastestgrowing species). It is not clear if the results would change significantly if potentially less abundant species would be classified as coexisting ones.
 The majority of the results consider scenarios in which bacteria cannot disperse very effectively so bacterial dynamics is mostly driven by the growth of the initial populations at each region. Expanding on the analysis of higher dispersal rates would be valuable in order to analyze additional realistic scenarios of how bacteria grow and disperse in space.

Reviewer #2 (Public Review):
In this work, the authors extend a mathematical model that they previously developed. Their original paper (Niehaus..Momeni, Nature Comm., 2019) models species interactions using mediators (i.e. metabolites) that species produce and that can affect other species' growth rates. Here, they extend the original model, which was wellmixed, to study communities in space. To do this, here they assume that species grow on a 1D grid, that species can possibly overlap in the same grid spot, and that species and mediators can diffuse in space. They find that spatial structure promotes the coexistence of species when interactions are more facilitating than inhibiting, and when species dispersal is low. Both of these features separately allow for species to selforganize in a way that allows them to be closer in space …
Reviewer #2 (Public Review):
In this work, the authors extend a mathematical model that they previously developed. Their original paper (Niehaus..Momeni, Nature Comm., 2019) models species interactions using mediators (i.e. metabolites) that species produce and that can affect other species' growth rates. Here, they extend the original model, which was wellmixed, to study communities in space. To do this, here they assume that species grow on a 1D grid, that species can possibly overlap in the same grid spot, and that species and mediators can diffuse in space. They find that spatial structure promotes the coexistence of species when interactions are more facilitating than inhibiting, and when species dispersal is low. Both of these features separately allow for species to selforganize in a way that allows them to be closer in space to partners that facilitate their growth. Properties of the metabolic interactions, such as the amount of metabolites produced and consumed, consumption and production rates, and metabolite diffusion also have effects on species coexistence.
Strengths: The authors extend their previously published model (Niehaus..Momeni, Nature Comm., 2019) to study the role of space in maintaining species diversity. The authors have the goal of modeling realistic bacterial communities; they in fact claim that the model's motivation is to "capture situations in which microbes can disperse inside a matrix", such as the mucosal layer of the digestive or intestinal tract, yogurt or cheese. To do this, the authors add relevant spatial aspects to their previous wellmixed model: species grow on a grid (even though 1D), where they can possibly overlap in the same grid spot, and species and mediators can diffuse in space. The advantage of the model they develop here is that it is simple enough for it to be used to explore general features of systems for which the assumptions of the model are justified. The authors perform a thorough investigation of the effect of spatial structure on the diversity that is maintained in the system. Their investigation includes the role of different types of interactions (facilitation and inhibition), species dispersal, and a range of properties of the metabolic interactions (number of mediators consumed and produced, consumption and production rates, mediator diffusion). Every scenario is compared to the wellmixed scenario to highlight the role of space.
Weaknesses: We are not convinced about some assumptions the authors make when extending their model from wellmixed (Niehaus..Momeni, Nature Comm., 2019) to spatial (this manuscript). The authors want to model a spatially structured system, with a framework that resembles the metacommunity framework, to which they add specific biophysical processes, such as the diffusion of metabolites. However, when adding these specific biophysical processes, the authors use parameters that seem to be unrealistic. One example is the packing of cells: 10^9, which implies a ratio between cells and the environment of 1:1000 volumewise. Another example is the diffusion of molecules, which is 10 times slower than stated in the literature. With these parameters, the authors aim at describing physical processes in their model, but overall the parameters seem to be far from real values. Thus we suggest either changing these parameters to realistic values, discussing why the chosen parameters are meaningful or reframing the model as an heuristic model.
Overall, we think that the contribution of the paper is to extend a previously published work (Niehaus..Momeni, Nature Comm., 2019) to model spatial communities. It is thus fundamental that the assumptions made by the authors to model the spatial dynamics are well justified. Several physical parameters are chosen to values that do not represent realistic values for spatially structured communities. The authors should discuss if the results hold also for more realistic values.

Reviewer #3 (Public Review):
The authors develop and analyze a novel model of microbial communities that considers both space and chemical mediator dynamics explicitly, with the goal of understanding the impact of spatial structure on coexistence. The authors' primary method for assessing the impact of space is to compare numerical simulations of their spatial model to simulations of an equivalent wellmixed model. They explore how spatial structure changes coexistence over a wide range of parameter space, varying parameters such as the ratio of facilitative to inhibitory interactions and the degree of mediator diffusion. They find that spatial structure can have variable effects on richness (the number of cell types within a community), in contrast to existing intuition in the field that spatial structure increases diversity.
Overall, …
Reviewer #3 (Public Review):
The authors develop and analyze a novel model of microbial communities that considers both space and chemical mediator dynamics explicitly, with the goal of understanding the impact of spatial structure on coexistence. The authors' primary method for assessing the impact of space is to compare numerical simulations of their spatial model to simulations of an equivalent wellmixed model. They explore how spatial structure changes coexistence over a wide range of parameter space, varying parameters such as the ratio of facilitative to inhibitory interactions and the degree of mediator diffusion. They find that spatial structure can have variable effects on richness (the number of cell types within a community), in contrast to existing intuition in the field that spatial structure increases diversity.
Overall, I think the approach that the authors have taken is sound. A very interesting aspect of this model is that the diffusion of mediators and microbes can occur at different rates. In other spatial systems, such as the classic Turing model of pattern formation, differences in diffusion timescales are the key ingredient needed for interesting spatial dynamics. However, while the authors have thoroughly characterized the impact of model parameters on ecological richness, their focus on this single metric provides a somewhat limited view of coexistence in their models. For example, richness considers neither the population composition nor the spatial patterns of coexistence emerging from the model. I also have some concerns about the implementation of the carrying capacity in the model, which in its current form may lead to nonphysical outcomes in a small part of the phase space.
