Variation in thermal physiology can drive the temperature-dependence of microbial community richness

  1. Tom Clegg
  2. Samraat Pawar

  • Curated by eLife

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    eLife assessment

    This important study proposes a phenomenologically motivated theoretical framework to explain observed patterns of the temperature dependence of microbial diversity. The methodology is overall convincing, but the explanations of approximations and assumptions, and of their regime of validity, are incomplete. The manuscript should be of interest to microbial ecologists.

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Abstract

Predicting how species diversity changes along environmental gradients is an enduring problem in ecology. Current theories cannot explain the observation that microbial taxonomic richness can show positive, unimodal, as well as negative diversity-temperature gradients. Here we derive a general empirically-grounded theory that can explain this phenomenon by linking microbial species richness in local communities to variation in their temperature-driven competitive interaction and growth rates. It predicts that richness depends on variation in shape of the thermal performance curves of these metabolic traits across species in the community. Specifically, the shape of the microbial community temperature-richness relationship depends on how the strength of competition across the community and the degree of variation in growth rates changes across temperature. These in turn can be predicted from the variation in thermal performance across the community. We show that empirical variation in the thermal performance curves of metabolic traits across extant bacterial taxa is indeed sufficient to generate the variety of community-level temperature-richness responses observed in the real world. Our results provide a new mechanism that can help explain temperature-diversity gradients in microbial communities, and provide a quantitative framework for interlinking variation in the thermal physiology of microbial species to their community-level diversity.

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  1. eLife

    eLife assessment

    This important study proposes a phenomenologically motivated theoretical framework to explain observed patterns of the temperature dependence of microbial diversity. The methodology is overall convincing, but the explanations of approximations and assumptions, and of their regime of validity, are incomplete. The manuscript should be of interest to microbial ecologists.

  2. eLife

    Reviewer #1 (Public Review):

    In this work, the authors propose a phenomenological grounded theoretical framework to explain why microbial taxonomic richness can show positive, unimodal, as well as negative diversity-temperature gradients. They thus propose to introduce a temperature dependence in the form of the Boltzmann-Arrhenius equation in both species' competitive interaction and growth rates. By means of a mean-field-like approximation, they estimate the probability of having N feasible coexisting species as a function of the normalized growth rate, and average competition strength, which in turn depends on temperature. They find that the shape of the microbial community temperature-richness relationship depends on how rapidly the strength of competition between species pairs increases with temperature relative to an increase in the variance of their growth rates. Furthermore, the mean-field result predicts that the position of richness peak depends on the sign of the covariance between the two main parameters of the Boltzmann-Arrhenius law. Finally, they show that the real-world community-level temperature-richness responses observed are qualitatively reproduced by their model.

    I found the work interesting and stimulating, surely tackling a relevant research question such as the effect of thermal physiology on biodiversity patterns through a simple, but quantitative model. Overall, I like the proposed approach.

    At the same time, the central mathematical results are not clear in my view, some strong approximations are not discussed, but they hold only in very specific conditions. A lot of important details are missing or scattered here and there, the notation is a little sloppy, and in general, it has been difficult for me to reproduce their finding.

    The overall structure and flow of the manuscript can be remarkably improved.

  3. eLife

    Reviewer #2 (Public Review):

    In their paper Variation in thermal physiology can drive the temperature dependence of microbial community richness, Clegg and Parwar present a relatively simple phenomenological model for explaining the wide variety of empirically observed relationships between temperature and diversity in the microbial world. Previous theories such as the Metabolic theory of biodiversity (MTB) and the metabolic niche hypothesis have emphasized the role of energy through either more efficient cellular kinetics or temperature-dependent niches. This paper builds on these works by showing that if one accounts for the variation of temperature sensitivity across species, one can get a much richer set of behaviors consistent with empirical observations.

    Overall, I find the manuscript quite compelling and the model presented as a very nice summary of how variability in temperature dependence, simple Arrhenius scaling, and arguments based on modern coexistence theory can be combined to explain empirical observations of species abundance distributions and temperature.

  4. eLife

    Reviewer #3 (Public Review):

    In empirical data, the dependence of microbial diversity on environmental temperature can take multiple different functional forms, while the previous theory has not established a clear understanding of when the temperature-dependence of diversity should take a particular form, and why. The authors seek to understand what forms are possible, and when they will occur, via analysis of the feasibility (i.e. positivity) of Lotka-Volterra equation solutions. This is combined with an assumption for the way that species' growth rates depend on temperature, along with an assumption for the way species interaction rates depend on temperature. Together, this completely specifies the form of the Lotka-Volterra equations, and whether all species in the model can coexist indefinitely at a given temperature, or whether only a lower-diversity subset can persist.

    The overall goal is valuable, and the overall approach of using this classic model of species interactions is justifiable. My main question marks relate to the way the conditions on feasibility (i.e. when all species will have positive equilibria), whether and when we need to consider the stability of these feasible solutions, and finally how general the way in which model parameters are specified to depend on temperature. I will expand on these three issues below. A more minor issue is that the authors set up this problem with extensive reference to the interaction of consumers and resources, referencing previous approaches that explicitly model these. Since resources are not explicitly present in the Lotka-Volterra formalism, it would be helpful to have a clearer justification for the authors' rationale in choosing this kind of model.

    (1) Conditions on growth and interaction rates for feasibility and stability. The authors approach this using a mean field approximation, and it is important to note that there is no particular temperature dependence assumed here: as far as it goes, this analysis is completely general for arbitrary Lotka-Volterra interactions.

    However, the starting point for the authors' mean field analysis is the statement that "it is not possible to meaningfully link the structure of species interactions to the exact closed-form analytical solution for [equilibria] 𝑥^*_𝑖 in the Lotka-Volterra model.

    I may be misunderstanding, but I don't agree with this statement. The time-independent equilibrium solution with all species present (i.e. at non-zero abundances) takes the form

    x^* = A^{-1}r

    where A is the inverse of the community matrix, and r is the vector of growth rates. The exceptions to this would be when one or more species has abundance = 0, or A is not invertible. I don't think the authors intended to tackle either of these cases, but maybe I am misunderstanding that.

    So to me, the difficulty here is not in writing a closed-form solution for the equilibrium x^*, it is in writing the inverse matrix as a nice function of the entries of the matrix A itself, which is where the authors want to get to. In this light, it looks to me like the condition for feasibility (i.e. that all x^* are positive, which is necessary for an ecologically-interpretable solution) is maybe an approximation for the inverse of A---perhaps valid when off-diagonal entries are small. A weakness then for me was in understanding the range of validity of this approximation, and whether it still holds when off-diagonal entries of A (i.e. inter-specific interactions) are arbitrarily large. I could not tell from the simulation runs whether this full range of off-diagonal values was tested.

    As a secondary issue here, it would have been helpful to understand whether the authors' feasible solutions are always stable to small perturbations. In general, I would expect this to be an additional criterion needed to understand diversity, though as the authors point out there are certain broad classes of solutions where feasibility implies stability.

    (2) I did not follow the precise rationale for selecting the temperature dependence of growth rate and interaction rates, or how the latter could be tested with empirical data, though I do think that in principle this could be a valuable way to understand the role of temperature dependence in the Lotka-Volterra equations.

    First, as the authors note, "the temperature dependence of resource supply will undoubtedly be an important factor in microbial communities"

    Even though resources aren't explicitly modeled here, this suggests to me that at some temperatures, resource supply will be sufficiently low for some species that their growth rates will become negative. For example, if temperature dependence is such that the limiting resource for a given species becomes too low to balance its maintenance costs (and hence mortality rate), it seems that the net growth rate will be negative. The alternative would be that temperature affects resource availability, but never such that a limiting resource leads to a negative growth rate when a taxon is rare.

    On the other hand, the functional form for the distribution of growth rates (eq 3) seems to imply that growth rates are always positive. I could imagine that this is a good description of microbial populations in a setting where the resource supply rate is controlled independently of temperature, but it wasn't clear how generally this would hold.

    Secondly, while I understand that the growth rate in the exponential phase for a single population can be measured to high precision in the lab as a function of temperature, the assumption for the form of the interaction rates' dependence on temperature seems very hard to test using empirical data. In the section starting L193, the authors seem to fit the model parameters using growth rate dependence on temperature, but then assume that it is reasonable to "use the same thermal response for growth rates and interactions". I did not follow this, and I think a weakness here is in not providing clear evidence that the functional form assumed in Equation (4) actually holds.

  5. Version published to 10.1101/2022.10.28.514215v1 on bioRxiv