Diverse communities promote the coexistence of closely-related strains through emergent equalization and stabilization

Abstract

Microbial communities harbor extensive fine-scale diversity: closely-related strains of the same species coexist alongside many distantly-related taxa. Yet strain coexistence remains poorly understood, largely because most studies neglect the diverse communities in which strains are embedded. Here we combine community ecology and statistical physics to study the dynamics of closely-related strains in a community context. We demonstrate that in a diverse community, indirect interactions between strains -- mediated through the surrounding community members -- can be as strong as direct ones. These community-mediated feedbacks cause conspecific strains to behave as if they have correlated growth rates and reduced competition. Using modern coexistence theory, we show that these effects correspond to equalizing and stabilizing mechanisms which together promote strain coexistence. The same equalizing and stabilizing mechanisms also qualitatively transform strain abundance correlations: strains that compete strongly and show negative correlations in isolation instead show positive correlations in a community, appearing mutualistic despite being competitors. Our results demonstrate that strain dynamics are emergent consequences of the surrounding community, and that capturing community feedbacks does not require the full interaction network; only a small number of emergent parameters.

Figures (13)

• Figure 1: Dynamics of closely-related strains in highly-diverse ecological communities. (a) Schematic of model setup with $S\gg1$ species (we show two: $i$ and $j$) in a community having two distinct strains $\alpha$ and $\beta$. All strains interact through a Generalized Lotka-Volterra (GLV) model with interaction matrix $A_{i\alpha j\beta}$ (Eqs. \ref{['eq:Asetup1']}--\ref{['eq:Asetup2']}). (b) Schematic showing that interaction strengths are random variables with a characteristic species dissimilarity $\sigma$ and interstrain interaction dissimilarity $\lambda$. For conceptual illustration we show these strains in a high-dimensional niche space. (c) Using the cavity method, we coarse-grain the GLV model describing the full highly-diverse community (left) into an effective two-strain GLV model (right) for a typical strain pair of the same species. This model shows that strains behave as if they have different apparent growth rates $K^{\mathrm{eff}}$ and interaction strengths $A^{\mathrm{eff}}$.
• Figure 2: Community feedbacks enhance strain coexistence. (a) Two closely-related strains competing strongly in isolation: the strain with higher growth rate excludes the other. (b) The same two strains (red) embedded in a diverse community (gray) now stably coexist. (c) Explanation using modern coexistence theory due to niche differences $\mathcal{N}$ and fitness ratio $\mathcal{F}$. In isolation, strains in (a) sit in the exclusion region (circle). Community feedbacks serve as both an equalizing mechanism (vertical arrow) and stabilizing mechanism (horizontal arrow), together pushing the strains into the coexistence region (triangle). (d) Phase diagram of the ratio of coexistence probability in community versus isolation, with strain interaction dissimilarity $\lambda$ and direct interstrain interaction strength $\tilde{\mu}$. Communities enhance coexistence (blue) when strains are similar and compete strongly.
• Figure 3: Competing strains appear mutualistic due to community feedbacks. (a) Two closely-related strains $\alpha$ and $\beta$ competing in isolation show a strong negative abundance correlation. Red ellipse shows 90% confidence ellipse from theory. (b) The same strain pair embedded in a diverse community now shows a positive abundance correlation; ellipse shows cavity theory prediction. (c) Explanation using the effective two-strain model (Eqs. \ref{['eq:effModel1']}--\ref{['eq:effModel2']}). Heatmap shows strain abundance correlation as a function of effective inter-strain interaction strength $\tilde{\mu}^{\text{eff}}$ and effective growth rate correlation $\rho_K$. Community feedbacks both stabilize (reduce $\tilde{\mu}^{\text{eff}}$) and equalize strains (increase $\rho_K$), together moving the strain pair from negative (circle) to positive (triangle) correlations. Positive correlations make strains appear mutualistic in a community despite having the strongest competition in isolation. (d) $\rho_{\alpha\beta}$ as a function of species dissimilarity $\sigma$, comparing simulations (dots) and cavity theory (curve). Inset: the strength of both equalization ($\rho_K$, green) and stabilization ($\langle 1/\mathrm{det}(A^{\mathrm{eff}})^2 \rangle$, magenta) increases with $\sigma$.
• Figure 4: Strain dissimilarity governs strength of community feedbacks and strain abundance correlations. (a) Strain abundance correlation versus strain interaction dissimilarity $\lambda$ for a community with fixed species dissimilarity $\sigma$. Correlations transition from positive to negative at a critical dissimilarity $\lambda_c$ (dotted line). (b) The reason: both equalization ($\rho_K$, green) and stabilization ($\langle 1/\mathrm{det}(A^{\mathrm{eff}})^2 \rangle$, magenta) weaken with increasing $\lambda$. Shown are values normalized to the maximum. When both these community feedbacks weaken, abundance correlations return to being negative, as they would in isolation. (c) Phase diagram of strain abundance correlations in $(\lambda, \sigma)$ space. The black line marks the theoretically predicted boundary from the cavity method separating positive and negative correlations. Gray region is disallowed since strains cannot be more dissimilar than species. (d) Regimes of strain abundance correlations in $(\sigma, \tilde{\mu})$ space: always negative (top), transitioning from positive to negative with increasing $\lambda$ (middle), and always positive (bottom). Black line shows the analytical boundary from the cavity method.
• Figure S1: Joint distribution of strain abundances is a truncated bivariate Gaussian for closely-related strains (low $\lambda$). Panels in the top row show scatter plots for the abundances of strains $\alpha$ and $\beta$ of the same species at steady-state within a diverse community with $S=100$ species. On the left, we show results from simulations of the full community with $2S$ strains; on the right, theoretical predictions from the cavity method for the same parameter set. The points in the right panel were generated using Monte Carlo sampling based on a truncated bivariate Gaussian distribution with moments as calculated from the cavity method. Bottom left panel shows a QQ plot to confirm that the distributions (both analytic and simulations) were bivariate normal. To check for the normality of the distributions we plotted the square of the Mahalanobis distance of the sample distributions against a theoretical $\chi^2$ distribution following which we performed a KS test to check for deviations from the theoretical distributions. Inset box shows $p$-values; $p > 0.1$ suggests that both joint distributions --- from simulations and cavity theory --- are consistent with a truncated bivariate Gaussian. In the bottom right panel we show contours for the joint distributions obtained from simulations and cavity theory at $1\sigma$, $2\sigma$, and $3\sigma$. Wiggles indicate low sampling. Parameters: $\mu = 0.3, \tilde{\mu} = 0.5, \sigma = 0.2, \sigma_K = 0.02, S=100, \rho = 0.99, \mathrm{Realizations} = 500$