Microbiomes Through the Looking Glass

Reviewer #1 (Public review):

Summary:

In this manuscript, the authors develop a novel method to infer ecologically-informative parameters across healthy and diseased states of the gut microbiota, although the method is generalizable to other datasets for species abundances. The authors leverage techniques from theoretical physics of disordered systems to infer different parameters - mean and standard deviation for the strength of bacterial interspecies interactions, a bacterial immigration rate, and the strength of demographic noise - that describe the statistics of microbiota samples from two groups-one for healthy subjects and another one for subjects with chronic inflammation syndromes. To do this, the authors simulate communities with a modified version of the Generalized Lotka-Volterra model and randomly-generated interactions, and then use a moment-matching algorithm to find sets of parameters that better reproduce the data for species abundances. They find that these parameters are different for the healthy and diseased microbiota groups. The results suggest, for example, that bacterial interaction strengths, relative to noise and immigration, are more dominant for microbiota dynamics in diseased states than in healthy states.

We think that this manuscript brings an important contribution that will be of interest in the areas of statistical physics, (microbiota) ecology, and (biological) data science. The evidence of their results is solid and the work improves the state-of-the-art in terms of methods. There are a few weaknesses that, in our opinion, the authors could address to further improve the work.

Strengths:

(1) Using a fairly generic ecological model, the method can identify the change in the relative importance of different ecological forces (distribution of interspecies interactions, demographic noise, and immigration) in different sample groups. The authors focus on the case of the human gut microbiota, showing that the data are consistent with a higher influence of species interactions (relative to demographic noise and immigration) in a disease microbiota state than in healthy ones.

(2) The method is novel, original, and it improves the state-of-the-art methodology for the inference of ecologically relevant parameters. The analysis provides solid evidence for the conclusions.

Weaknesses:

In the way it is written, this work might be mostly read by physicists. We believe that, with some rewriting, the authors could better highlight the ecological implications of the results and make the method more accessible to a broader audience.

Reviewer #2 (Public review):

Summary:

This valuable work aims to infer, from microbiome data, microbial species interaction patterns associated with healthy and unhealthy human gut microbiomes. Using solid techniques from statistical physics, the authors propose that healthy and unhealthy microbiome interaction patterns substantially differ. Unhealthy microbiomes are closer to instability and single-strain dominance; whereas healthy microbiomes showcase near-neutral dynamics, mostly driven by demographic noise and immigration.

Strengths:

A well-written article, relatively easy to follow and transparent despite the high degree of technicality of the underlying theory. The authors provide a powerful inferring procedure, which bypasses the issue of having only compositional data.

Weaknesses:

(1) This sentence in the introduction seems key to me: "Focusing on single species properties as species abundance distribution (SAD), fail to characterise altered states of microbiome." Yet it is not explained what is meant by 'fail', and thus what the proposed approach 'solves'.

(2) Lack of validation, following arbitrary modelling choices made (symmetry of interactions, weak-interaction limit, uniform carrying capacity).
Inconsistent interpretation of instability. Here, instability is associated with the transition to the marginal phase, which becomes chaotic when interaction symmetry is broken. But as the authors acknowledge, the weak interaction limit does not reproduce fat-tailed abundance distributions found in data. On the other hand, strong interaction regimes, where chaos prevails, tend to do so (Mallmin et al, PNAS 2024). Thus, the nature of the instability towards which unhealthy microbiomes approach is unclear.

(3) Three technical points about the methodology and interpretation.
a) How can order parameters h and q0 can be inferred, if in the compositional data they are fixed by definition?
b) How is it possible that weaker interaction variance is associated with approach to instability, when the opposite is usually true?
c) Having an idea of what the empirical data compares to the theoretical fits would be valuable.

Implications:

As the authors say, this is a proof of concept. They point at limits and ways to go forward, in particular pointing at ways in which species abundance distributions could be better reproduced by the predicted dynamical models. One implication that is missing, in my opinion, is the interpretability of the results, and what this work achieves that was missing from other approaches (see weaknesses section above): what do we learn from the fact that changes in microbial interactions characterise healthy from unhealthy microbiota? For instance, what does this mean for medical research?

Reviewer #3 (Public review):

Summary:

I found the manuscript to be well-written. I have a few questions regarding the model, though the bulk of my comments are requests to provide definitions and additional clarity. There are concepts and approaches used in this manuscript that are clear boons for understanding the ecology of microbiomes but are rarely considered by researchers approaching the manuscript from a traditional biology background. The authors have clearly considered this in their writing of S1 and S2, so addressing these comments should be straightforward. The methods section is particularly informative and well-written, with sufficient explanations of each step of the derivation that should be informative to researchers in the microbial life sciences who are not well-versed with physics-inspired approaches to ecology dynamics.

Strengths:

The modeling efforts of this study primarily rely on a disordered form of the generalized Lotka-Volterra (gLV) model. This model can be appropriate for investigating certain systems, and the authors are clear about when and how more mechanistic models (i.e., consumer-resource) can lead to gLV. Phenomenological models such as this have been found to be highly useful for investigating the ecology of microbiomes, so this modeling choice seems justified, and the limitations are laid out.

Weaknesses:

The authors use metagenomic data of diseased and healthy patients that were first processed in Pasqualini et al. (2024). The use of metagenomic data leads me to a question regarding the role of sampling effort (i.e., read counts) in shaping model parameters such as $h$. This parameter is equal to the average of 1/# species across samples because the data are compositional in nature. My understanding is that $h$ was calculated using total abundances (i.e., read counts). The number of observed species is strongly influenced by sampling effort, so it would be useful if the number of reads were plotted against the number of species for healthy and diseased subjects.

However, the role of sampling effort can depend on the type of data, and my instinct about the role that sampling effort plays in species detection is primarily based on 16S data. The dependency between these two variables may be less severe for the authors' metagenomic pipeline. This potential discrepancy raises a broader issue regarding the investigation of microbial macroecological patterns and the inference of ecological parameters. Often microbial macroecology researchers rely on 16S rRNA amplicon data because that type of data is abundant and comparatively low-cost. Some in microbiology and bioinformatics are increasingly pushing researchers to choose metagenomics over 16S. Sometimes this choice is valid (discovery of new MAGs, investigate allele frequency changes within species, etc.), sometimes it is driven by the false equivalence "more data = better". The outcome, though, is that we have a body of more-or-less established microbial macroecological patterns which rest on 16S data and are now slowly incorporating results from metagenomics. To my knowledge, there has not been a systematic evaluation of the macroecological patterns that do and do not vary by one's choice in 16S vs. metagenomics. Several of the authors in this manuscript have previously compared the MAD shape for 16S and metagenomic datasets in Pasqualini et al., but moving forward, a more comprehensive study seems necessary (2024).

References

Pasqualini, Jacopo, et al. "Emergent ecological patterns and modelling of gut microbiomes in health and in disease." PLOS Computational Biology 20.9 (2024): e1012482.

Author response:

Reviewer #1:

Strengths:

(1) Using a fairly generic ecological model, the method can identify the change in the relative importance of different ecological forces (distribution of interspecies interactions, demographic noise, and immigration) in different sample groups. The authors focus on the case of the human gut microbiota, showing that the data are consistent with a higher influence of species interactions (relative to demographic noise and immigration) in a disease microbiota state than in healthy ones. (2) The method is novel, original, and it improves the state-of-the-art methodology for the inference of ecologically relevant parameters. The analysis provides solid evidence for the conclusions.

Weaknesses:

In the way it is written, this work might be mostly read by physicists. We believe that, with some rewriting, the authors could better highlight the ecological implications of the results and make the method more accessible to a broader audience.

We thank the reviewer for their positive and constructive feedback. We particularly appreciate the recognition of the novelty and robustness of our method, as well as the insight that it sheds light on the shifting ecological forces between healthy and diseased microbiomes. In response to the concern about the manuscript’s accessibility, we aim to revise key sections – including the Introduction, Results, and Discussion – to more clearly articulate the ecological relevance of our theoretical findings. We would like to emphasize that our approach offers a novel perspective for analyzing individual species' abundances, as well as for understanding interaction patterns and stability at the community level. By placing our results within a broader context accessible to readers from diverse backgrounds, we aim for the revised version to appeal to a wider audience, including ecologists and microbiome scientists, while preserving the rigor of our underlying statistical physics framework.

Reviewer #2:

Strengths:

A well-written article, relatively easy to follow and transparent despite the high degree of technicality of the underlying theory. The authors provide a powerful inferring procedure, which bypasses the issue of having only compositional data.

Weaknesses:

(1) This sentence in the introduction seems key to me: "Focusing on single species properties as species abundance distribution (SAD), it fails to characterise altered states of microbiome." Yet it is not explained what is meant by 'fail', and thus what the proposed approach 'solves'. (2) Lack of validation, following arbitrary modelling choices made (symmetry of interactions, weak-interaction limit, uniform carrying capacity). Inconsistent interpretation of instability. Here, instability is associated with the transition to the marginal phase, which becomes chaotic when interaction symmetry is broken. But as the authors acknowledge, the weak interaction limit does not reproduce fat-tailed abundance distributions found in data. On the other hand, strong interaction regimes, where chaos prevails, tend to do so (Mallmin et al, PNAS 2024). Thus, the nature of the instability towards which unhealthy microbiomes approach is unclear. (3) Three technical points about the methodology and interpretation. a) How can order parameters ℎ and 𝑞0 can be inferred, if in the compositional data they are fixed by definition? b) How is it possible that weaker interaction variance is associated with an approach to instability, when the opposite is usually true? c) Having an idea of what the empirical data compares to the theoretical fits would be valuable. Implications: As the authors say, this is a proof of concept. They point at limits and ways to go forward, in particular pointing at ways in which species abundance distributions could be better reproduced by the predicted dynamical models. One implication that is missing, in my opinion, is the interpretability of the results, and what this work achieves that was missing from other approaches (see weaknesses section above): what do we learn from the fact that changes in microbial interactions characterise healthy from unhealthy microbiota? For instance, what does this mean for medical research?

We greatly appreciate the reviewer’s thoughtful analysis highlighting both the strengths and areas of ambiguity in our work.

(1) To clarify the sentence on the limitations of species abundance distributions (SADs), we aim to explain in the revised version that while SADs summarize the relative abundance of individual species, they fail to capture the species-species correlations that we have shown (Seppi et al., Biomolecules 2023) to be more susceptible to the healthy state of the host. Our method thus focused on the interaction statistics among species, providing insights into underlying dynamics and stability of the microbiomes and their differences between healthy and unhealthy hosts.

(2) Regarding model assumptions, we acknowledge that the weak interaction regime and symmetry hypotheses simplify the analysis and may not capture all empirical richness, such as fat-tailed distributions of species abundance. However, we interpret instability not as a path to chaos per se, but as a transition toward a multi-attractor phase, where each microbiome reaches a different fixed point. This is consistent with prior empirical findings invoking the “Anna Karenina principle”, where healthy microbiomes resemble one another, but disease states tend to deviate from this picture (see Pasqualini et al., PLOS Comp. Bio. 2024). We consider our framework as a starting point and agree that further extensions incorporating strong interaction regimes (as suggested by Mallmin et al., PNAS 2024) or relaxing other model assumptions could reveal even richer dynamical patterns. The computational pipeline we present can be, in fact, easily generalizable to include different population dynamics models.

On the technical questions: (a) While compositional data constrain relative abundances, we can still estimate diversity-dependent parameters (h and q0) using alpha-diversity statistics across samples, which show meaningful variation; (b) The counter-intuitive instability that the reviewer pointed out arises from the interplay between demographic stochasticity and quenched disorder. It is the combined contribution of these two factors in phase space – not either one alone – that drives the transition. For clarity, see Figure 1 in Altieri et al., Phys. Rev. Lett. 2021; (c) We plan to include plots that compare empirical data to theoretical model fits. This will help visualize how well the model captures observed microbial community properties demographic noise (𝑇), healthy communities are more stable (i.e., distantσ from the and how even with larger species interaction heterogeneity (σ) and larger critical line), as measured, by the replicon eigenvalue. Finally, regarding interpretability and implications: by showing that ecological interaction networks – not just species identities – differ between healthy and unhealthy states, our work suggests a conceptual shift. This could inform medical strategies aimed at restoring community-level stability rather than targeting individual microbes. In the revised Discussion section, we will elaborate on this point to better highlight its practical implications and outline potential directions for future research.

Reviewer #3:

Strengths:

The modeling efforts of this study primarily rely on a disordered form of the generalized Lotka-Volterra (gLV) model. This model can be appropriate for investigating certain systems, and the authors are clear about when and how more mechanistic models (i.e., consumer-resource) can lead to gLV. Phenomenological models such as this have been found to be highly useful for investigating the ecology of microbiomes, so this modeling choice seems justified, and the limitations are laid out.

Weaknesses:

The authors use metagenomic data of diseased and healthy patients that were first processed in Pasqualini et al. (2024). The use of metagenomic data leads me to a question regarding the role of sampling effort (i.e., read counts) in shaping model parameters such as h. This parameter is equal to the average of 1/# species across samples because the data are compositional in nature. My understanding is that it was calculated using total abundances (i.e., read counts). The number of observed species is strongly influenced by sampling effort, so it would be useful if the number of reads were plotted against the number of species for healthy and diseased subjects. However, the role of sampling effort can depend on the type of data, and my instinct about the role that sampling effort plays in species detection is primarily based on 16S data. The dependency between these two variables may be less severe for the authors' metagenomic pipeline. This potential discrepancy raises a broader issue regarding the investigation of microbial macroecological patterns and the inference of ecological parameters. Often microbial macroecology researchers rely on 16S rRNA amplicon data because that type of data is abundant and comparatively low-cost. Some in microbiology and bioinformatics are increasingly pushing researchers to choose metagenomics over 16S. Sometimes this choice is valid (discovery of new MAGs, investigate allele frequency changes within species, etc.), sometimes it is driven by the false equivalence "more data = better". The outcome, though, is that we have a body of more-or-less established microbial macroecological patterns which rest on 16S data and are now slowly incorporating results from metagenomics. To my knowledge, there has not been a systematic evaluation of the macroecological patterns that do and do not vary by one's choice in 16S vs. metagenomics. Several of the authors in this manuscript have previously compared the MAD shape for 16S and metagenomic datasets in Pasqualini et al., but moving forward, a more comprehensive study seems necessary.

We thank the reviewer for this insightful and nuanced comment, which particularly highlights the broader methodological context of our data sources. Indeed, metagenomic sequencing introduces different biases with respect to 16S data. First, we would like to emphasize that we estimated the order parameters from the data by using relative abundances. Second, while the concern regarding the influence of sequencing depth and species diversity on the estimation of the order parameters is valid, we refer to a previous publication by some of the authors (Pasqualini et al., 2024; see Figure 4, panels g and h). There, we pointed out that the observed outcome is weakly influenced by sequencing depth in our dataset, while the main impact on the order parameters estimate comes from the species diversity of the two groups. In the same publication, we showed that other well-known patterns (species abundance distribution, mean abundance distribution) are also observed. Also, to mitigate the effect of the number of samples and sequencing depth, we estimated the order parameters by a bootstrap procedure (90% of samples for healthy and diseased groups, 5000 resamples), which resulted in the error bars in Figure 2.

We also fully agree with the broader call for a systematic comparison of macroecological patterns derived from 16S and metagenomic data. While some of us have already begun exploring this direction (e.g., Pasqualini et al., 2024), the reviewer’s comment highlights its significance and motivates us to pursue a more comprehensive, integrative analysis across data types. While we found qualitative agreement of these patterns with previous publications (e.g., Grilli, Nature Comm. 2020), we will acknowledge this as an important future direction in the Discussion section.

References

(1) Seppi, M., Pasqualini, J., Facchin, S., Savarino, E.V. and Suweis, S., 2023. Emergent functional organization of gut microbiomes in health and diseases. Biomolecules, 14(1), p.5.

(2) Pasqualini, J., Facchin, S., Rinaldo, A., Maritan, A., Savarino, E. and Suweis, S., 2024. Emergent ecological patterns and modelling of gut microbiomes in health and in disease. PLOS Computational Biology, 20(9), p.e1012482.

(3) Mallmin, E., Traulsen, A. and De Monte, S., 2024. Chaotic turnover of rare and abundant species in a strongly interacting model community. Proceedings of the National Academy of Sciences, 121(11), p.e2312822121.

(4) Altieri, A., Roy, F., Cammarota, C., & Biroli, G. (2021). Properties of equilibria and glassy phases of the random Lotka-Volterra model with demographic noise. Physical Review Letters, 126(25), 258301.

(5) Grilli, J. (2020). Macroecological laws describe variation and diversity in microbial communities. Nature communications, 11(1), 4743.