Stabilization of Microbial Communities by Responsive Phenotypic Switching

TL;DR

The paper investigates how responsive phenotypic switching, as opposed to purely stochastic switching, influences the ecological stability of microbial communities. It develops a two-phenotype, multi-species framework and contrasts it with averaged stochastic-switching models, revealing that equilibrium stability can differ generically between these formulations, especially as species number grows. Through a minimal two-species model that includes a rare persister-like phenotype, the authors show that responsive switching can stabilize coexistence under certain conditions, and that non-steady attractors may underpin permanence even when steady states are unstable. The work combines analytic reductions, exact results for simplified systems, and extensive numerical experiments to uncover mechanisms by which responsiveness shapes coexistence, with implications for understanding persistence strategies in real microbial ecosystems and guiding future theoretical and experimental studies. Overall, the findings underscore the subtle and substantial role of sensing-driven phenotypic changes in stabilizing or destabilizing ecological communities, suggesting that experimental validation and spatial extensions are important next steps.

Abstract

Clonal microbes can switch between different phenotypes and recent theoretical work has shown that stochastic switching between these subpopulations can stabilize microbial communities. This phenotypic switching need not be stochastic, however, but could also be in response to environmental factors, both biotic and abiotic. Here, motivated by the bacterial persistence phenotype, we explore the ecological effects of such responsive switching by analyzing phenotypic switching in response to competing species. We show that the stability of microbial communities with responsive switching differs generically from that of communities with stochastic switching only. To understand the mechanisms by which responsive switching stabilizes coexistence, we go on to analyze simple two-species models. Combining exact results and numerical simulations, we extend the classical stability results for the competition of two species without phenotypic variation to the case in which one species switches, stochastically and responsively, between two phenotypes. In particular, we show that responsive switching can stabilize coexistence even when stochastic switching on its own does not affect the stability of the community.

Figures (13)

• Figure 1: Models of stochastic and responsive phenotypic switching. (a) In the model of Sec. \ref{['sec:model']}, each species has two phenotypes, B and P, and switches stochastically between them. Moreover, the B phenotype of each species responds to other species by switching to the P phenotype. (b) In the minimal two-species model of Sec. \ref{['sec:2model']}, the second species has a single competitor phenotype A, which causes B to switch to P. Dashed lines: stochastic switching. Solid lines: responsive switching.
• Figure 2: Stability of random microbial communities with responsive phenotypic switching. (a) Probability of a random equilibrium that is stable in the model with responsive switching $\mathcal{R}$ [Eqs. \ref{['eq:fullmodel']}] or in the model with stochastic switching only $\mathcal{S}$ [Eqs. \ref{['eq:fullmodels']}] being unstable in the other model, as a function of the number $N$ of species in the system. (b) Same plot, but focused on low probabilities. (c) Ratio of the probabilities of random equilibria of $\mathcal{R}$ and $\mathcal{S}$ being stable. Inset: same plot, focused on small probability differences. Probabilities were estimated from up to $5\cdot10^8$ random systems each. Parameter values: $\varepsilon=1$ and $\varepsilon=0.01$[Relative persister abundances are typically very smallsay ${\varepsilon=10^{-5}}$ for E. coli \citation{balaban04}but can vary widelyas reported by ][. ]hofsteenge13*[The value $\varepsilon=0.01$ used in Figs. \ref{fig2}--\ref{fig4} is towards the upper end of the experimental range for E. coli in culture (vide ibid.)but typical for P. aeruginosa biofilms [][]. Anywaythe mechanism underlying the differences between $\varepsilon=0$ and $\varepsilon\ll1$ that we have identified in Ref. \citation{haas20} is genericwhich justifies choosing $\varepsilon=0.01$ for numerical convenience.]lewis08; for the latter value, both exact and asymptotic equilibria were computed. Error bars are $95\%$ confidence intervals *[The confidence intervals computed for Figs. \ref[[\ref{fig2}'(a)(b)']]{fig2}\ref{fig3}\ref{fig4} are Wilson intervals [seee.g.] []; those computed for Fig. \ref[[\ref{fig2}'(c)']]{fig2} are derived from the Fieller-type statistic introduced by ] brown01*nam02 larger than the plot markers.
• Figure 3: Distributions, in the models with responsive switching $\mathcal{R}$ [Eqs. \ref{['eq:fullmodel']}] or with stochastic switching only $\mathcal{S}$ [Eqs. \ref{['eq:fullmodels']}], of the long-time dynamics of unstable equilibria that are stable in the other model. Distributions are shown for exact equilibria with (a) $\varepsilon=1$, (b) ${\varepsilon=0.01}$hofsteenge13, and different numbers of species $N$. Each distribution was estimated by numerical integration of up to $5\cdot 10^3$ unstable systems. For a small proportion of the systems ($\#$), the numerical solution did not converge. Vertical bars represent $95\%$ confidence intervals brown01.
• Figure 4: Permanent coexistence in random microbial communities with responsive phenotypic switching. (a) Probability, in the models with responsive switching $\mathcal{R}$ [Eqs. \ref{['eq:fullmodel']}] and with stochastic switching only $\mathcal{S}$ [Eqs. \ref{['eq:fullmodels']}], of extinction of some species of a random system perturbed away from an equilibrium that is stable in the other model, as a function of the number of species in the system, $N$. (b) Same plot, but focused on low probabilities. Exact equilibria were obtained for $\varepsilon=1$ and $\varepsilon=0.01$hofsteenge13. Each probability was computed from up to $5\cdot 10^8$ random systems and up to $5\cdot 10^3$ random systems having an equilibrium with different stability in models $\mathcal{R}$ and $\mathcal{S}$. Thick error bars correct the estimated probabilities for the systems in which the numerical solution of the long-time behavior did not converge (Fig. \ref{['fig3']}); thin error bars add $95\%$ confidence intervals brown01. Only those error bars larger than the plot markers are shown.
• Figure 5: Numerical stability diagrams of Eqs. \ref{['eq:model']} in the $(\zeta,\beta)$ diagram in the cases (a) $\eta/\alpha>\vartheta$ and (b) ${\eta/\alpha<\vartheta}$. The color of each point in the stability diagrams represents the proportion of $N=1000$ random systems for which coexistence is stable or permanent at that point. The insets plot the proportion of systems for which coexistence is destabilized, $\ominus$, compared to the averaged model with stochastic switching only. The symbol $\oplus$ in parentheses [panel (b), inset] indicates that a nonzero proportion of systems (too small to be visualizable by the color scheme) is stabilized (or becomes permanent) compared to the averaged model. Parameter values: $\alpha=0.8$, $\eta=1.2$, $\vartheta=1.1$ [panel (a)] or $\vartheta=1.9$ [panel (b)], $\gamma,\iota,\kappa,\mu,\xi,\varpi,\varsigma\sim\mathcal{U}[\varepsilon,2\varepsilon]$, with $\varepsilon=0.1$, and $\delta\sim\mathcal{U}[0.8,1.6]$.