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  1. Evaluation Summary:

    This paper will be of interest to scientists within community ecology. The authors present a mathematically solid analysis of how nonlinear constraints influence resource-competition models with trade-offs, with the conclusions being similar to those of previous studies in which trade-offs are not exact.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 agreed to share their name with the authors.)

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  2. Reviewer #3 (Public Review):

    There has been considerable recent interest in understanding the high degree of diversity observed in microbial communities. From a theoretical perspective, this has led to a resurgence of interest in resource-competition models. Several recent papers have studied the effects of trade-offs on total enzyme budgets within these models. An interesting observation is that with exact trade-offs, communities can self-organize to a state with an arbitrarily large number of species coexisting. One assumption of these models is that the total "cost" of enzymes is a linear function. The current work relaxes this assumption, and shows that this state of arbitrarily high coexistence relies on the linearity of the cost function.

    Strengths: This study is rigorous, clearly presented, and the conclusions are mathematically sound. The authors analyze both chemostat and serial dilution systems.

    Weaknesses: The results are qualitatively as expected from previous studies of the role of inexact trade-offs, and are more limited. The nonlinear trade-offs explored here are essentially equivalent to the unequal enzyme budgets explored in prior work. Indeed, these nonlinearities can be directly mapped to unequal budgets: for example, a nonlinearity that favors expression of a single enzyme is directly equivalent to a larger enzyme budget for species that produce only a single enzyme. Previous studies showed that unequal enzyme budgets lead to a loss of diversity, as is found in this work. Moreover, these prior studies found that even if trade-offs are not exact, the slow loss of diversity due to inexact trade-offs can be offset by invasion of new strategies and can therefore still lead to a large number of coexisting species.

    The likely impact of this work on the field is modest, given that those who are already experts in the field will recognize that nonlinear trade-offs are equivalent to unequal enzyme budgets. Moreover, the current study does not actually provide any specific support for nonlinear trade-offs other than a few remarks in the Introduction.

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  3. Reviewer #2 (Public Review):

    This paper deals with the diversification of metabolic strategies in an evolving population. The authors consider a consumer-resource model under different metabolic trade-offs (sublinear, linear, and superlinear). They show that the linear case is a marginal scenario that corresponds to high diversity as a consequence of neutral evolution. Both the sub- and superlinear cases lead to the coexistence of fewer species than resources, as expected by the competitive exclusion principle.

    The manuscript is well written and easy to follow. The derivation using adaptive dynamics is interesting and the results are robust. I am mainly concerned by the premises of the work.

    l 70 "This is a very interesting finding because it violates the competitive exclusion principle". This is not strictly correct (and I think this is a central point). To violate the competitive exclusion principle, more species than resources should *stably* coexist. The stability requirement is essential. Otherwise, the principle can be easily falsified by a neutral model: in presence of even 1 single resource, an arbitrary number of ecologically equivalent species coexist (neutrally). Neutral coexistence is, as well known, structurally unstable: arbitrary small differences (which break the ecological equivalence) drive many species to extinction (restoring the bound on diversity given by the number of resources).

    In the model by Posfai et al. (2017) coexistence is in fact only neutral. There is a manifold of fixed points and stability is marginal (several eigenvalues of the community matrix are equal to zero, e.g. see https://arxiv.org/pdf/2002.04358 ). The fixed point of their dynamics (abundance of different species) depends on the initial conditions. The high levels of diversity are, as a consequence, structurally unstable. This can be shown in multiple ways: introducing an (arbitrarily small) species variability in the trade-off (E depends on species identity), introducing variability in the dilution rate d (appearing in eq 3), or, as done in the paper, by altering the functional form of the trade-off.

    This is a central point. It explains why many species are observed in the model by Posfai et al. And it explains why the result is extremely (infinitely) sensitive to the parameterization. These ecological considerations are mirrored in the fact that for gamma = 1 the evolutionary dynamics are neutral.

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  4. Reviewer #1 (Public Review):

    Previous theoretical work argued that among species that compete for resources, physiological tradeoff (e.g. consuming more of food 1 leads to consuming less of food 2) can give rise to species diversity that greatly exceeds the number of resources, even in a well-mixed environment not conducive for species diversity. If previous work were to be general, it would be exciting because this offers a clue to the puzzle scientists have been trying to solve for a long time: what supports high species diversity? Caetano et al show that the finding from previous work only holds under a very restrictive condition (tradeoff function being linear). When that condition is violated (which can frequently occur in biology), we end up with either a single generalist species, or specialists each specializing on a single resource. Thus, in general, the total number of species cannot be larger than the total number of limiting resources in a well-mixed environment, as posited by the competitive exclusion principle. In short, we are back at where we were.

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