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Figure 1

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How variation in thermal physiology constrains microbial community species richness.

(A) Trait values increase with temperature following the Boltzmann-Arrhenius equation (boltz_maintext), with the shape governed by two parameters: $B_{0}$ - trait value ( $r$ or $a$ ) at a reference temperature $T_{r e f}$ and $E$ - thermal sensitivity. (B) The joint distribution of $E$ and $\log (B_{0})$ (here with empirically realistic negative covariance) determines how trait distributions vary across temperatures (C). (D) The distribution of trait values in turn determines the probability of feasibility $P_{f e a s}$ (and thus richness; Feas_sp_maintext). Specifically, $P_{f e a s}$ is determined by the proportion of relative growth rates ( $r_{i}^{'}$ ; blue shaded area) that are greater than the bound (solid black line) set by mean interaction strength ( $⟨ a ⟩$ ). Populations with relative growth rates below this bound (red shaded area) are unfeasible (cannot persist in the community). All else being equal, the size of the unfeasible region (i.e. richness), decreases with increasing variance in the growth rate distribution ( $Var (r_{i}^{'})$ ) and increasing interaction strength (which shifts the $f (⟨ a ⟩ (T))$ bound upwards). (E–H) The effects of varying different aspects of the joint distribution of $B_{0}$ and $E$ of $r$ and $a$ on the emergent trait distribution across temperatures. Each panel shows the effect of altering the labeled parameter relative to the baseline case (far left), with inset plots showing the effect on the resulting temperature-richness relationship.

Figure 2

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The effect of variation in trait thermal performance curves (TPCs) on the temperature-richness relationship in competitive microbial communities.

The analytical predictions (solid lines) are plotted along with the maximum richness reached in the numerical simulations (dots). (A) Mean thermal sensitivity of interactions $⟨ a ⟩$ determines the direction and steepness of the temperature-richness relationship. (B) Increasing variance of thermal sensitivity increases unimodality. (C) Negative covariance between $B_{0}$ and $E$ shifts the peak of richness to higher temperatures. Parameter values used were: $μ_{r 0} = 0.0, σ_{r 0}^{2} = σ_{a 0}^{2} = 0.2, μ_{E_{r}} = μ_{E_{a}} = 0.6, σ_{E_{r}}^{2} = σ_{E_{a}}^{2} = 0.01, σ_{{B_{0}, E}_{r}} = σ_{{B_{0}, E}_{a}} = 0.0$ .

Figure 3

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Sensitivity of theoretical results.

Bar plots show the Pearson correlation coefficient $ρ = (x, y) / σ_{x} σ_{y}$ of each thermal physiology parameter with the root mean squared error between the theory and numerical simulations across replicate communities. Positive correlations indicate that increasing the parameter value tends to increase the error whilst negative values indicate error decreases the parameter value increases. Each panel shows the effect of a given parameter.

Figure 4

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The bacterial temperature-richness relationship predicted by empirically-observed variation in thermal physiology.

(A) The relationship between $\log (B_{0})$ and $E$ for growth rate in the experimental thermal performance curve (TPC) data from Smith et al., 2021. Dots show each pair of $B_{0}$ and $E$ values estimated for a given species/strain with histograms showing the marginal distributions. Ellipses show the 95% quantiles of the fitted bivariate normal distribution. (B) The actual growth-rate TPCs (solid lines) from the dataset as well as the fitted trait-distributions across temperature (box plots). The dashed line shows the point of minimum variance in growth rates which occurs towards the upper end of the temperature range. (C–D) Analogous plots for the dataset from the literature synthesis (Smith et al., 2019). (E) The analytically- (solid line) and simulation- (points) predicted temperature-richness curves based on the TPC variation seen in both these experimental (blue) and literature-synthesised (red) empirical data. Both are generated using the parameters from their respective fitted distributions and mean normalisation constants of $μ_{r_{0}} = 0.0$ and $μ_{a_{0}} = - 5.0$ . We set the normalisation constants such that the magnitude of richness values is not too large to perform the numerical simulations.

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Tom Clegg
Samraat Pawar

(2024)

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

eLife 13:e84662.

https://doi.org/10.7554/eLife.84662

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