Benefit Transfer Loops Turn Cheating into a Scaffold for Microbial Diversity

Reviewer #1 (Public review):

In this work, Jiqi Shao and colleagues evaluate the microbial iron competition and siderophore-mediated interactions combining (a) a dynamic modeling framework based on the consumer-resource model, including multiple siderophore and siderophore-receptor types, and (b) a graph-theory framework based on directed graphs to quantify the ecological dependencies of the community (referred to as Benefit Transfer Graph). Through a plethora of simulation experiments, by changing the number of species in the community, the ratio of pure-cheaters, and the number of foreign siderophores a partial-producers can utilize (referred to in this study as 'Cheating Breadth'), the authors found:

(1) Using simulations of small communities of 5 or fewer members, they observe that closed benefit-transfer loops (commensalism/mutualism loops) serve as the structural scaffold for diversity, observing coexistence, dominance, or dynamic fluctuations in function of the fraction of receptors in species and the number of community members.

(2) Using simulations of large communities of 50 members, they observed a paradox on the capacity of partial producers to utilize different foreign siderophores (referred to in this study as 'The Paradox of Cheating'). They observed that broad 'Cheating Breadth' of partial-producer members increases the probability of community-wide extinction and can act as destabilizing forces. However, at the same time, 'Cheating Breath' of partial-producer members promotes species richness and community biodiversity.

(3) The application of graph-theory framework helps to unveil ecological complexities of small and large microbial communities, explaining the aforementioned Paradox of Cheating.

As major strengths of this work, the authors present a novel modeling framework considering the ecological complexity of siderophore-mediated interactions by differentiating types of community members (pure-producers, partial-producers, and pure-cheaters), siderophore/receptor pairs, and exploring a wide range of situations (such as the number of community members, the ratio of pure-cheaters, or the siderophore breadth of partial-producers). Moreover, the discussion and conclusions of this study are mechanistically well-founded with a graph-theory framework (Benefit Transfer Graph). All computer code and scripts to replicate the simulations, analysis, and figure generation are public in the Zenodo repository.

However, this study still has some work to do before it meets the expected standards, presenting some weaknesses to be addressed. Please regard the following paragraph as constructive feedback aimed at improving your work. The main weakness of the actual version is the Abstract, the missing Methods section, the structure of the Results section, and the results displaying (i.e., Figures), and how partial-producers are considered as cheaters (including how they referred to the capacity of partial-producers to use different siderophores as 'Cheating Breath'). The Abstract could be significantly improved with a better introduction of the system (cooperators and cheaters, and the concept of the 'Tragedy of Commons'), a better description of the modeling framework, and other details included in 'Recommendations for the authors'. The current version of the manuscript misses a proper 'Methods' section.

Moreover, the authors could include (1) a section with the simulated systems and parameter choices of simulation experiments, (2) the key model assumptions, and (3) a separate (and more detailed) section explaining the graph-theory framework applied in this study (Benefit Transfer Graph). Most of this information is included in Supporting Information, but including it in the main text will facilitate the comprehension of the work. The structure of the results displayed (i.e., Figures) is quite confusing, especially in the section 'Closed Benefit Loops Drive Transitions from Exclusion to Coexistence and Chaos'. Moreover, important results are included in Supportive Information when they should be in the main text. Also, the lack of a proper Method section makes it harder to follow the Results sections. I have included some recommendations/suggestions to improve the Results structure. This study reveals an interesting ecological dynamic in siderophore-mediated interactions. The authors suggest the existence (and further explanation) of the 'Paradox of Cheating'. However, this paradox (and their discussion) may come from a misunderstanding of concepts and/or terminologies used by the authors applied here (and maybe widely applied in cooperator-cheaters systems). The authors refer to the capacity of 'partial-producers' to utilize foreign siderophores (i.e., siderophores of other species) as cheating. Also, they refer to the number of foreign siderophores that a 'partial-producer' can utilize as 'Cheating Breadth'. A microbial cheater is one that has receptors for siderophore uptake but does not pay the cost of producing siderophore themselves. Because 'partial-producers' are generating at least one type of siderophore, these are not technically cheaters (although they may act as 'pure-cheaters', changing their gene expression and do not synthesize any siderophore for the community). All this may entail a misleading of the results and a potentially overstated title and conclusions of this work. Community members 'pure-producers', 'partial-producers' cheaters may be called in a different way, e.g., 'single-receptor producer', 'multiple-receptor producers' and 'nonproducers', respectively [Gu. et al. (2025), doi: 10.1126/sciadv.adq5038]. A better terminology for 'the number of foreign siderophores that a partial-producer can utilize' could be 'Siderophore Breadth', and instead of stating a 'Paradox of Cheating', it can be a 'Paradox of Multiple-receptor Producers'. The discussion of the authors aligns better with the presented results if the proposed terms 'single-receptor producer/multiple-receptor producer and cheater' are used, considering multiple-receptor producers as cooperative members rather than 'moderate cheating'. On the other hand, the Paradox of Multiple-receptor Producers (or Paradox of Cheating by the authors) could be a modeling artifact. Although some species possess multiple siderophore receptors in their genome (some studies suggest that Pseudomonas species and other environmental strains' genomes can have up to 20-30 siderophore receptors), that does not mean that they are all expressed simultaneously.

Regardless of the weaknesses and the major points to be improved, the findings presented in this work substantially advance our understanding of complex ecological interactions between cooperators and cheaters mediated by siderophore and siderophore-receptor syntheses, especially when multiple-receptor producers are present. Moreover, the modeling and graph-theory frameworks presented by the authors can be applied in other microbial systems, such as collaboration/competition/cheating for substrates or nutrients. Fundamental modeling exercises are indispensable to unveil ground ecological rules of complex microbial communities, accelerating the advances in ecology by developing theory-based hypotheses for future experimental and environmental studies.

Reviewer #2 (Public review):

Summary:

This study investigates how cheating affects microbial diversity, using a chemostat model of a microbial community in which species compete for a shared iron pool through siderophore-mediated uptake. After analyzing minimal communities, the study simulates large randomly generated communities in which species either produce no siderophore or produce a single siderophore type. Producers can differ in siderophore type and production level, while all species can differ in the siderophore-specific receptor types they express. Siderophore production trades off with resource allocation to growth. Total receptor expression is normalized, so increasing expression of one receptor type reduces expression of other receptor types. A key parameter in these simulations is the average number of "cheating receptor types," i.e., receptor types that allow a species to use siderophores it does not produce itself. The authors use this parameter as one axis for characterizing cheating behavior and term it "cheating breadth." The results reveal a statistical pattern the authors report as a "paradox": increasing cheating breadth increases the frequency of whole-community extinction, but also increases the mean number of surviving species per non-extinct community. To explain this pattern, the study reduces a community's producer-receiver network into components by retaining only the link from each producer to its maximal beneficiary, i.e., the species receiving the largest growth benefit from that producer. The study finds that the core topology of such a component predicts the community's ecological fate, namely, extinction, single-species survival, or multi-species coexistence, when biomass is concentrated in that component. The study argues that increasing cheating breadth reduces the probability that a community contains components predicting single-species survival, while increasing the probabilities that it contains components predicting extinction or multi-species coexistence. This argument is used to explain why greater cheating breadth increases both community extinction risk and diversity. Based on these results, the study concludes that microbial diversity not only tolerates but requires moderate cheating.

Strengths:

The major strengths of this study are that it presents an interesting mathematical model of microbial interactions mediated by diverse siderophores and that it reduces simulation results to simple predictive patterns by focusing on one primary beneficiary per producer, as summarized above.

Weaknesses:

The study also has two major weaknesses. First, the observed diversity is not shown to be evolutionarily stable, which limits the biological relevance of the findings. The cycle structure that supports this diversity may be vulnerable to invasion by mutants that disrupt this structure and can thereby drive many species, or even the whole community, extinct. This concern is suggested by previous studies on the hypercycle, which is analogous to the cycle structure found in this study (Eigen and Schuster, The Hypercycle, Springer-Verlag, pages 32-57, 1979 https://doi.org/10.1007/978-3-642-67247-7). For example, a community with a cyclic network may be invaded by mutants that increase growth allocation at the cost of siderophore production (Maynard Smith, Nature 280:445-446, 1979 https://doi.org/10.1038/280445a0). It may also be destabilized by mutants that increase the expression of the "self-receptor," the receptor for the siderophore they produce themselves. Another possibility is a "short-circuit mutant" that expresses receptors in a way that bypasses intermediate species in a cycle (Bresch et al., Journal of Theoretical Biology 85:399-405, 1980 https://doi.org/10.1016/0022-5193(80)90314-8). Cyclic networks may remain evolutionarily unstable even when spatial self-organization is considered (Hogeweg and Takeuchi, Origins of Life and Evolution of the Biosphere 33:375-403, 2003 https://doi.org/10.1023/A:1025754907141). Without demonstrating robustness to these plausible evolutionary hazards, the study's coexistence results may have limited biological relevance.

The second weakness is that the study treats cheating breadth as if it were a pure measure of increased cheating, framing the observed pattern as a paradox that increasing cheating breadth increases diversity within surviving communities while also increasing community extinction risk. However, increasing cheating breadth decreases the mean expression level of all expressed receptors, a confounding effect that arises from the normalization of total receptor expression. Consequently, increasing cheating breadth also reduces the mean benefit a producer gains from its own siderophore production. In other words, increasing cheating breadth spreads each producer's dependence across diverse siderophores at the cost of a reduced return on the self-produced siderophore. Once these coupled effects are recognized, the reported pattern is less paradoxical: increasing cheating breadth might be expected to increase diversity within surviving communities by distributing dependence, while also increasing extinction risk by reducing self-reliance. Therefore, the apparent paradox may arise from the way cheating behavior is parameterized rather than from a direct effect of increased cheating alone.

Additional context:

The present study can be considered alongside previous studies proposing that cheating can, in some contexts, promote microbial diversity by generating ecological dependencies. The Black Queen hypothesis proposes that such dependencies can be created by adaptive gene loss and reliance on functions performed by other community members (Morris et al., mBio 3:e00036-12, 2012, https://doi.org/10.1128/mbio.00036-12). A related study by Fullmer et al. discusses how mutual cheating can contribute to microbial diversity (Frontiers in Microbiology 6:728, 2015, https://doi.org/10.3389/fmicb.2015.00728).

Author response:

We would like to express our sincere gratitude for your time and constructive feedback. We are highly encouraged by the positive assessment highlighting the solid evidence and convincing methods of our study. We also deeply value the insightful and constructive comments regarding our conceptual framing, the integration with established ecological theories, and the underlying dynamic mechanisms. We believe that incorporating these excellent suggestions will substantially enhance the conceptual clarity and theoretical depth of our manuscript. To achieve this, we are fully committed to conducting a comprehensive revision to address all the points raised. Below, we outline our main strategies for the forthcoming revision:

(1) Structural Reorganization

We fully agree with the reviewers and the Editor that the manuscript's structure requires improvement. We are especially grateful to Reviewer 1 for providing such a detailed and constructive roadmap for the revision. We will adopt all of the suggested changes. Specifically, in the revised manuscript, we will:

(1.1) Rewrite the Abstract: provide a clearer introduction to the "Tragedy of the Commons" and a more accessible description of our modeling framework.

(1.2) Establish a dedicated Methods section: move the core model equations, key assumptions, parameter choices, and the detailed explanation of our graph-theoretic framework (the Benefit Transfer Graph) from the Supplementary Information (SI) into the main text.

(1.3) Restructure results and figures: We will reorganize the Results section to improve the logical flow. As suggested, we will split the current Figure 2, move critical diagrams from the SI into the main text, and expand our figure captions to ensure all data representations are immediately clear.

(2) Reframing the Conceptual Framework and Terminology

We thank Reviewer 1 for the insightful critique regarding the use of the term “cheating.” We have reflected on our previous phrasing and fully agree that "cheating" introduces an unnecessarily humanized judgment and conflates pure exploitation with metabolic generalism. To ensure mechanistic accuracy and alignment with recent ecological literature, we will systematically update our terminology throughout the text, from title to supplement:

(2.1) Species strategies: "Pure-producers," "partial-producers," and "pure-cheaters" will be redefined as "single-receptor producers," "multi-receptor producers," and "non-producers," respectively.

(2.2) Receptor types: "Cheating-receptors" will be renamed to "exogenous-receptors" (or foreign-receptors, exploitative-receptors) to objectively describe the uptake of siderophore types that are not produced by the focal microbe.

(2.3) Updating the key parameter: To avoid ambiguity regarding synthesis versus uptake, we will rename "Cheating Breadth (CB)" to "Siderophore Exploitative Breadth (SEB)," defined strictly as the number of distinct exogenous-receptors expressed by a species.

(2.3) Updating the core paradigm: We will reframe "The Paradox of Cheating" to "The Paradox of Siderophore Exploitation." We will clarify that the transition to high-diversity coexistence is not driven by "cheating", but by the topological connectivity of the mBTG.

(3) Contextualizing within BQH and Hypercycles

We sincerely thank the Editor and Reviewer 2 for highlighting the connections between our work, the Black Queen Hypothesis (BQH), and Hypercycle theory. We will dedicate a new section in the Discussion to thoroughly compare our siderophore-mediated network with these established frameworks.

We will explicitly discuss the key similarities and differences. While the exploitation of siderophores in our model resembles the producer-beneficiary dependency described in BQH, the evolutionary drivers are distinct, in that BQH is primarily driven by the adaptive loss of costly genes (reductive evolution), whereas siderophore exploitation is driven by the acquisition of exogenous-receptors (e.g., via horizontal gene transfer). More importantly, the high diversity and lock-and-key specificity of siderophore-receptor interactions, renders each siderophore a "mixed good." This dynamic can actually drive the community into a Red Queen-like arms race, as suggested by the high probability of oscillatory dynamics observed in our simulations. Although we did not explicitly consider genetic mutations in the current ecological framework, unidirectional exploitation typically drives the involved species to extinction; consequently, the system naturally selects for communities where exploitation is reciprocated, organically giving rise to closed, distributed loops of benefit transfer.

In the revised text, we will cite recent theoretical progress on structured and multi-goods BQH networks. We will also discuss how our topological loops link to Eigen's Hypercycle theory by illustrating how specific structures of exploitative interactions foster community diversity.

(4) Addressing Siderophore Exploitative Breadth (SEB) Interpretations

(4.1) The biological realism of the SEB range

Both reviewers raised insightful questions regarding the settings and impacts of SEB (previously "CB"). While some of these questions will be addressed through new control simulations, we would like to immediately clarify the biological realism of the SEB parameter, particularly addressing Reviewer 1's concern about the simultaneous expression of multiple receptors.

We completely agree that possessing a vast genomic repertoire of siderophore receptors does not mean a microbe expresses all of them simultaneously. Receptor expression in nature is a highly regulated and substrate-specific process. In Gram-negative bacteria like Pseudomonas, the expression of exogenous-receptors is tightly regulated by cell-surface signaling pathways (e.g., ECF sigma/anti-sigma factor systems). Under iron-limited conditions, a specific receptor is upregulated only when it detects its corresponding siderophore in the environment. Based on our literature review, while a bacterium may not express 30 receptors at once, expressing a substantial subset (e.g., 5–15) is biologically realistic. Therefore, in our model, SEB does not represent a static genomic capacity, but rather the number of active receptors that actually have corresponding siderophore producers present within the local community. We extended the SEB axis up to 30 in our initial figures primarily to capture the complete theoretical phase transition. However, following the reviewer's excellent suggestion, we will adjust the x-axis in our primary revised figures to highlight the more realistic regime (e.g., SEB 0–15) and add a dedicated paragraph detailing these biological regulatory mechanisms, with appropriate citations.

(4.2) Disentangling the receptor allocation trade-off

We highly appreciate Reviewer 2’s perceptive insight regarding the confounding effect: under a normalized allocation scheme, increasing SEB inevitably decreases the expression level of the self-receptor, thereby reducing self-reliance. We completely agree that explicitly addressing this trade-off is crucial.

Biologically, this strong trade-off is realistic: receptor operations are energetically costly, and the initiation of their expression requires competing for a finite pool of RNA polymerase core enzymes. Therefore, investing in the capacity to exploit heterologous siderophores inherently incurs a cost to self-reliance. To rigorously test whether our central paradox is merely an artifact of this specific trade-off, we immediately initiated a series of control simulations. In these new models, we mathematically decoupled the variables by fixing the allocation fraction of the self-receptor as a constant.

We are encouraged to report that our preliminary results support the core of the original paradox. Even when self-reliance is mathematically maintained, community-level extinction risk and the biodiversity of surviving communities remain positively linked. Interestingly, these controlled simulations exhibit an even clearer non-monotonic pattern, where both diversity and extinction risk peak at a biologically realistic SEB of approximately 5. This suggests that the paradox is fundamentally driven by network topology changes rather than the allocation trade-off alone：Viewed through our maximal Benefit Transfer Graph (mBTG) framework, a higher probability of non-self-directed edges in the mBTG forces the community to "gamble" between collapsing into a Sink Core or surviving in a high-diversity Cyclic Core. We are currently performing exhaustive simulations to gather detailed statistics on this decoupled model, particularly the non-monotonic behavior, which will be prominently featured in the revised manuscript.

(5) Evolutionary Stability and Topological Resilience

We also deeply appreciate Reviewer 2’s insightful critique regarding the evolutionary stability of our proposed cyclic networks, particularly their potential vulnerability to self-serving or short-circuit mutants that bypass intermediate species in a loop.

To rigorously address this, we are currently conducting invasion simulations in which established communities are challenged by randomly generated mutant species. While the exhaustive computational analysis is ongoing, our preliminary results suggest the absence of a strict, static Evolutionarily Stable Strategy (ESS). Instead, the topological space fosters complex, intransitive competition. Intriguingly, these early data suggest that communities exhibiting oscillatory dynamics are actually more robust against invaders than those at a stable equilibrium. We intend to explore this phenomenon fully.

Furthermore, we will expand our Discussion to address the implications of longer evolutionary timescales. When true structural mutations occur (e.g., the appearance of novel siderophore-receptor pairs to evade existing exploitation), the system will likely transition into a continuous Red Queen regime of ongoing molecular arms races. We will thoroughly discuss these evolutionary horizons and present our complete invasion simulation data in the revised manuscript.