Microbial communities display alternative stable states in a fluctuating environment

Abstract

The effect of environmental fluctuations is a major question in ecology. While it is widely accepted that fluctuations and other types of disturbances can increase biodiversity, there are fewer examples of other types of outcomes in a fluctuating environment. Here we explore this question with laboratory microcosms, using cocultures of two bacterial species, P. putida and P. veronii. At low dilution rates we observe competitive exclusion of P. veronii, whereas at high dilution rates we observe competitive exclusion of P. putida. When the dilution rate alternates between high and low, we do not observe coexistence between the species, but rather alternative stable states, in which only one species survives and initial species' fractions determine the identity of the surviving species. The Lotka-Volterra model with a fluctuating mortality rate predicts that this outcome is independent of the timing of the fluctuations, and that the time-averaged mortality would also lead to alternative stable states, a prediction that we confirm experimentally. Other pairs of species can coexist in a fluctuating environment, and again consistent with the model we observe coexistence in the time-averaged dilution rate. We find a similar time-averaging result holds in a three-species community, highlighting that simple linear models can in some cases provide powerful insight into how communities will respond to environmental fluctuations.

Fig 1. Experimental observation of alternative stable states in a fluctuating environment.

A: When a coculture of Pp (purple) and Pv (green) was diluted by a factor of 10 each day (1/10 of the previous day’s culture transferred to fresh media, keeping the volume constant), the slow-growing Pv dominated, sending the fraction of fast grower Pp to zero from several starting fractions. B: When the same culture was subject to a much higher dilution factor, 10⁴, fast grower Pp dominated. C: Fluctuating between the low and high dilution factors shown in A and B resulted in alternative stable states. Either Pp or Pv can dominate, depending on their relative initial abundances. In all plots, we qualitatively indicate the dilution factor for that day by the shading of the plot; low dilution factors have a lighter shading, while high dilution factors have a darker shading. Error bars are the SD of the beta distribution with Bayes’ prior probability (see Methods).

Fig 2. Bistability occurs in both fluctuating and average environments, confirming model prediction.

To understand the results from Fig 1, we employed a modified Lotka-Volterra (LV) model. A: We model daily dilutions by adding a community-wide death rate term 𝛿 to the two-species LV competition model. The per-capita growth rate is a function of a species’ maximum growth rate, self-inhibition, and competition with the other species. Because the per-capita growth rate is linear and additive, the model predicts that the outcome of a fluctuating environment should be the same as that of the time-averaged environment (S2 Text). The LV model can be reparametrized to eliminate the death rate 𝛿 by defining new competition coefficients ${\tilde{\alpha }}_{ij}$, which are functions of death 𝛿 and growth r, as shown (S1 Text). B: The solutions to the LV model can be represented by a phase space of the re-parameterized competition coefficients ${\tilde{\alpha }}_{ij}$. If a slow grower dominates at low or no added death, increasing mortality will favor the fast grower, causing the pair to pass through a region of bistability or coexistence on the way to fast grower dominance. Here we have illustrated the trajectory of a bistable pair. C-D: To test the prediction that the fluctuating and time-averaged environments are qualitatively equivalent, we cocultured Pp and Pv at a dilution factor equal to the time-average of the fluctuating dilution factors in Fig 1, and we observed bistability, confirming this prediction (lower right). The experimental data shown in C here is a technical replicate of the same experiment shown in Fig 1C. Additionally, we simulated daily dilutions of the model with both constant (upper left) and fluctuating (lower left) dilution factors and observed good agreement between the model and experimental results. E: A bifurcation diagram of the Pp-Pv outcomes at all constant dilution factors shows that the fast-growing Pp is favored as dilution increases. At each dilution factor, gray arrows represent time trajectories from initial to final fractions; solid lines represent stable equilibria, and dotted lines represent unstable fractions. This diagram was used to estimate the competition coefficients used in simulations (see Methods and S1 Fig). Error bars are the SD of the beta distribution with Bayes’ prior probability (see Methods).

Fig 3. Coexistence occurs in both fluctuating and average environments, confirming model prediction.

A: As in Fig 2, the LV model phase space shows qualitative outcomes divided by the zero-points of the logarithm of the reparametrized competition coefficients. Here we have illustrated the trajectory of a pair that passes through the coexistence region as the death rate increases. B-C: When we cocultured slow-growing Pv with another fast grower, Ea, we observed coexistence in an environment that fluctuated between dilution factors in which either species dominated (upper right). At a dilution factor equal to the mean of fluctuations, we also observed coexistence (lower right), confirming the model’s prediction about a time-averaged environment for both types of trajectories across the phase space. Once again, simulations of daily dilutions showed good agreement between the model and experimental results (left). D: A diagram of outcomes at all constant dilution factors shows that fast-growing Ea is favored as dilution increases. Arrows represent time trajectories from initial to final fractions; solid lines represent stable equilibria, and dotted lines represent unstable fractions. We used this diagram to estimate the competition coefficients used in simulations (see Methods and S2 Fig). Error bars are the SD of the beta distribution with Bayes’ prior probability (see Methods).

Fig 4. Fluctuating environment predictably leads to alternative stable states in a three-species community.

To ensure that the time-averaging prediction is not only applicable to simple two-species communities, we tested our results in a three-species environment. A: A ternary plot shows the outcomes of a coculture with all three species, Pv, Pp, and Ea, in a constant environment with dilution factor (DF) 10³. The time trajectories, indicated by the grey lines, end at one of two alternative stable states (shown in blue; for state B, we plot the average of the three trajectories). In state A, Pv and Ea coexist, while Pp and Ea coexist in state B. B: Time series plots show the results of three-species coculture experiments in both constant (DF 10³; left column) and fluctuating (between DF 10¹ and DF 10⁵; right column) environments. As indicated in A, three initial fractions end in state B and one ends in state A. We find that the outcomes of a given initial fraction go to the same final state in both the constant and fluctuating environments. This suggests that the ability to time-average the outcomes extends to communities with more than two species (see S6 Fig).