{'fraction_non_alphanumeric': 0.025330578512396694, 'fraction_numerical': 0.028512396694214875, 'mean_word_length': 4.907005125701733, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Emergence of alternative stable states in microbial communities in a fluctuating environment

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, we have only a limited understanding of the circumstances in which other types of outcomes can occur 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.


Introduction 18
In nature, environmental conditions vary over time, and this variation can have significant 19 impacts on the structure and function of ecological communities. Examples of the impacts of 20 environmental variability on community composition include daily cycles of of light and 21 temperature that allow nocturnal and diurnal organisms to coexist, and seasonal variation that 22 causes reproducible succession patterns in communities of plants 1 , freshwater 2 and marine 23 microbes 3 . Community function can also be strongly influenced by varying environmental 24 conditions. For example, a single rain event can cause up to 10% of annual carbon dioxide 25 production of a forest 4 , due in part to enhanced microbial activity in rewetted dry soil 5 . Varying 26 environmental conditions may even cause ecosystems to abruptly and irreversibly change states, 27 such as lakes that shift from clear to turbid due to human-induced eutrophication 6 and reefs that 28 transform from kelp forests to seaweed turfs due to heat waves 7 . Given the inevitability of 29 temporal variability in nature, an improved understanding of how this variability affects ecological 30 communities is essential for understanding natural ecosystems. 31 Both theoretical 8-12 and empirical 13-17 studies have shown that disturbances can stabilize 32 communities and enhance diversity. For example, temporal fluctuations of light 18 and 33 temperature 19 have been shown to lead to stable coexistence of microbes. One possible mechanism 34 for this effect is that different species are favored at different times, such that no species can ever 35 dominate the system, and the result might be coexistence 20 . For example, species A may exclude 36 species B in one environment, whereas B excludes A in another environment. Fluctuating between 37 the two environments might lead to coexistence of the two species. If true, such an effect could 38 propagate to complex communities with more than two species, leading to more coexistence in the 39 fluctuating environment than in the constant ones. Another possible explanation for coexistence in 40 a fluctuating environment is time-averaging: species A and B might coexist when fluctuating 41 between two environments because they coexist in the constant average environment 21,22 . The 42 former theory predicts that fluctuations are necessary for coexistence, while the latter suggests that 43 coexistence depends upon the average environment, with or without fluctuations. 44 Compared to a wealth of studies of fluctuation-induced coexistence, less is known about 45 whether perturbations may lead to outcomes other than increased diversity. For example, 46 alternative stable states have been observed in fluctuating environments, such as in gut microbiota 47 communities subject to laxative treatments 23 , intertidal biofilms perturbed by climatic events 24 , and 48 regions of forest and barrens disturbed by frequent fires 25 . In these cases, however, it is often 49 difficult to distinguish between alternative states that are simultaneously stable and different states 50 that are stable in different environments. There is some theoretical support for fluctuation-induced 51 alternative stable states in particular systems 26,27 , but these predictions are challenging to test in the 52 field due to the difficulty of controlling all ecological factors. The proposition that environmental 53 fluctuations may have more complicated effects on ecosystems than simply affecting diversity is 54 therefore in need of systematic study and demonstration. 55 In this paper, we make use of highly controllable microbial microcosms to explore the 56 effects of temporal fluctuations on communities. We grow bacterial species in liquid culture with 57 daily dilution, and implement environmental fluctuations by alternating the amount of the dilution. 58 The growth-dilution process imposes a tunable death rate on the system, where the dilution factor 59 determines the fraction of cells discarded each day. In a two-species coculture, we observe that 60 fluctuating dilution factors leads to bistability, or two alternative stable states that depend on the 61 initial abundances of each species. To explain this result, we use a simple phenomenological 62 model: the Lotka-Volterra competition model adapted to incorporate a fluctuating global mortality 63 rate. This model with a fluctuating mortality rate predicts that the bistability is independent of the 64 timing of the fluctuations, and that the time-averaged mortality would also lead to alternative stable 65 states, a prediction that we confirm experimentally. The model predicts that fluctuating mortality 66 can result not only in bistability, but also in stable coexistence, depending on the strength of 67 interspecies inhibition, which we confirm experimentally. More broadly, the model predicts that 68 an environment with a fluctuating death rate equilibrates to the same outcome as the time-averaged 69 added mortality rate. We test this prediction both in two-species cocultures and in a more complex 70 community with three species, where a fluctuating death rate and a constant death rate lead to the 71 same qualitative outcome. These results suggest that fluctuations can in some cases have 72 predictable consequences on community structure. 73

74
To explore the effect of a fluctuating environment on an experimentally tractable microbial 75 community, we performed coculture experiments with fluctuating as well as constant dilution 76 factors. The cultures were allowed to grow for 24 hours and then diluted by transferring a small 77 amount of culture into fresh growth media. Because the total experimental volume remains 78 constant, the amount of culture added from the previous day determines the dilution factor. We 79 began by coculturing Pseudomonas veronii (Pv) and Pseudomonas putida (Pp). At a low dilution 80 factor (10), Pv competitively excludes Pp, as the fraction of Pp goes to zero from all initial 81 fractions ( Fig. 1A). At a high dilution factor (10 4 ), the outcome is reversed, with Pp excluding Pv 82 as its fraction goes to one from all initial fractions (Fig. 1B). We refer to both of these outcomes as 83 competitive exclusion because the final state does not depend on starting conditions; all starting 84 fractions move toward one stable state, which is either zero or one. 85 86 87 Given that there was a single stable state at low dilution and a single stable state at high dilution, 88 we expected that alternating between the two dilution factors would also lead to a single stable 89 state (which could be survival of just one species or possibly stable coexistence of the two). To 90 our surprise, when we performed the coculture experiment alternating between the two dilution 91 factors, we instead observed the emergence of alternative stable states-only a single species 92 survived, but the surviving species depended on the species' initial fractions (Fig. 1C). We 93 therefore observe bistability in the fluctuating environment despite the fact that neither 94 environment alone showed bistability. 95 To explain a possible origin of this emergent bistability, we employed the Lotka-Volterra 96 (LV) competition model with added mortality, which previously provided powerful insight into 97 how microbial competitive outcomes shift with dilution rate 28 . The two-species LV model with 98 added mortality is: 99 where is the abundance of species normalized by its carrying capacity, is the maximum 101 growth rate for species , is the competition coefficient that determines how strongly species 102 inhibits species , and is the imposed mortality rate, which is experimentally controlled by the 103 dilution factor, which specifies the fraction of cells discarded per day. In the absence of added 104 mortality , the outcome is independent of growth rates and solely determined by whether the 105 competition coefficients are greater or less than one: coexistence and bistability result when 106 both are less than or greater than one, respectively, and dominance results when only one 107 coefficient is greater than one (Fig. 2B). The presence of mortality makes the competition 108 coefficients, and thus the outcome, functions of growth and mortality, as can be seen in the 109 reparameterized model (Supplementary Note 1): 110 111 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, 10 4 , fast grower Pp dominated. C: Surprisingly, 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).
where 112 If a slow grower dominates at low mortality/dilution, the model predicts that increasing dilution 114 will reverse the outcome and cause the fast grower to win, and at some range of intermediate 115 dilution the pair passes through either a region of bistability or coexistence (Fig. 2B). Moreover, a 116 fluctuating dilution rate will lead to the same outcome as the time-averaged rate in the absence of The constant dilution factor experiments revealed a range of fixed points varying with dilution 132 factor: in addition to domination of slow-growing Pv at low dilution and that of fast-growing Pp at 133 high dilution, we observed bistability at two intermediate dilution factors (Fig. 2E). The separatrix, 134 or starting fraction dividing the two stable states, shifts in favor of the fast grower at the higher of 135 these two dilution factors, consistent with the model. These experimental results confirm the 136 model's prediction that the dilution factor can be time-averaged to result in the same qualitative 137 outcome; namely, bistability (see Supp. Fig. 3). 138 As previously mentioned, the LV model also predicts that pairs of species can coexist at 139 intermediate mortality rates. Given this additional prediction, we sought to experimentally verify 140 that coexistence can also result from time-averaging the dilution factors. Based on results of 141 previous cocultured experiments in a similar growth medium 28 , we chose another fast grower, 142 Enterobacter aerogenes (Ea), which is also excluded by the slow-growing Pv at low dilution 143 factor. At intermediate dilution factor Ea and Pv coexist, and Ea dominates at high dilution factor 144 (Fig. 3D). We then fluctuated between the dilution factors in which either species dominated, as in 145 our initial experiments. This time, we observed stable coexistence in the fluctuating environment 146 (Fig. 3). Furthermore, the stable fraction of Ea fluctuated in the neighborhood of the stable 147 fraction of Ea in the constant dilution experiment. In both the bistable pair ( Fig. 2C-D) and the 148 coexisting pair (Fig. 3B-C), simulations match the experimental trajectories over time, in both 149  Fig. 1, we employed a modified Lotka-Volterra model. A: We model daily dilutions by adding a community-wide death rate term to the two-species Lotka-Volterra (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 outcomes of a fluctuating environment should be the same as that of the time-averaged environment (Supplementary Note 1). B: The solutions to the LV model can be represented by a phase space of the reparameterized competition coefficients ⍺, which are functions of death and growth . 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 timeaverage of the fluctuating dilution factors in Fig. 1, and  While pairwise interactions in a fluctuating environment appear to be well-described by the LV 155 model, the same might not be true of more complex communities. To address this question, we 156 cocultured all three of the previously mentioned species, Ea, Pp, and Pv. Across a range of 157 constant dilution factors, we saw changes in community outcome as a function of the dilution 158 factor (Supp. Fig. 6), shifting from a Pv-dominated final state at low dilution to coexistence of Pp 159 and Ea at high dilution. At an intermediate dilution factor, bistability occurs in the trio between a 160 Pp-Ea coexistence state and a Pv-Ea coexistence state (Fig. 4A). This bistability of coexisting 161 states can be predicted from the corresponding pairwise results, using our previously developed 162 community assembly rules 29 . When we fluctuated the dilution factor between the low and high 163 values that average to this intermediate dilution factor, we again observed bistability, with each 164 initial condition ending in the same final state as it did in the constant environment (Fig. 4B). 165 These results show that even in a more complex community of three species, a fluctuating 166 mortality rate still leads to the same results as the constant average environment, which is in line 167 with the predictions of the modified LV model. 168  Fig. 2, the LV model phase space shows qualitative outcomes divided by the zero-points of the logarithm of the re-parameterized 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 Supp. Fig. 2). Error bars are the SD of the beta distribution with Bayes' prior probability (see Methods). The IDH, which predicts a diversity peak at some undefined range of intermediate disturbance 194 frequencies, has left some unconvinced 21 , and a meta-study of the phenomenon found little 195 evidence of the trend 35 . This paper provides a case study for how the effect of fluctuations can be 196 Figure 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) 10 3 . 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 10 3 ; left column) and fluctuating (between DF 10 3 and DF 10 5 ; 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 Supp. Fig. 6).
understood without adhering to any particular hypothesis of disturbance-diversity relationships, 197 with guidance from a simple phenomenological model. 198 The absence of resources from the LV model is not its only simplification-it also assumes 199 perfect logistic growth and interactions that are not density-dependent. While these assumptions 200 are clearly simplifications of the dynamics present within any actual community, the model 201 nonetheless worked well in predicting the outcome of fluctuations in the dilution rate in our 202 microbial community. We used regularly alternating and moderate disturbances, but as the 203 duration and intensity of disturbances increases one expects that eventually the model's predictions 204 will fail due to stochastic extinction caused by finite population sizes. Still, its success here 205 highlights the relevance of simple, phenomenological models to biological systems. 206 Environmental disturbances have long been thought to weaken competition, thus leading to 207 increased biodiversity 36 . This logic is oversimplified 22 , however, and has inhibited exploration of 208 other potential outcomes of fluctuations, such as alternative stable states. can be time-averaged. 220 The effect of environmental disturbances on community structure has become more urgent 221 as many habitats face the effects of climate change. The question of which types of disturbances 222 can be time-averaged is one that may provide insight into the effects of environmental fluctuations 223 on natural communities. Our system was composed of three species of soil bacteria, raising the 224 question of whether communities with more than three species would be similarly affected. A 225 linear time-dependence of interactions and growth rates on added mortality may be more dominant 226 in simple communities, while higher-order effects may become more important in complex 227 communities. Additionally, our simple community results do not mean that there were no 228 nonlinearities or covariances in our system, but only that they were not sufficiently large so as to 229 alter the experimental outcome. Many studies of natural systems have found evidence of 230 nonlinearities and covariances, such as the storage effect 37-39 . In such systems, it may be difficult 231 to disentangle which effects are independent of fluctuations, but our results argue that in some 232 cases, simple models retain their predictive power even in fluctuating environments. 233 234

Species and media 236
The soil bacterial species used in this study were Enterobacter aerogenes (Ea, ATCC#13048), 237 Pseudomonas putida (Pp, ATCC#12633) and Pseudomonas veronii (Pv, ATCC#700474 Growth curves were captured by measuring the optical density of monocultures (OD 600 nm) in 250 15-minute intervals over a period of ~40 hours (Fig. S3). Before these measurements, species were 251 grown in 1X LB broth overnight, and then transferred to the experimental medium for 24 hours. 252 The OD of all species was then equalized. The resulting cultures were diluted into fresh medium at 253 factors of 10 -8 to 10 -3 of the equalized OD. Growth rates were measured by assuming exponential 254 growth to a threshold of OD 0. the desired species composition, and then diluting mixtures by the factor to which they would be 267 diluted daily (except for dilution factor 10 -6 , which began at 10 -5 on Day 0, to avoid causing 268 stochastic extinction of any species). Relative abundances were measured by plating on nutrient 269 agar plates. Each culture was diluted in phosphate-buffered saline prior to plating. Multiple 270 replicates were used to ensure that enough colonies could be counted. Colonies were counted after 271 48 h incubation at room temperature. The mean number of colonies counted, per plating, per 272 experimental condition, was 49. During competition experiments, we also plated monocultures to 273 determine whether each species could survive each dilution factor in the absences of other species. 274 Pv went extinct in the highest two dilution factors (10 -5 and 10 -6 ); other species survived all 275 dilution factors. 276

Estimating competition coefficients for simulations 277
In order to simulate the effect of a fluctuating environment on the pairs (Fig. 2C-D, Fig. 3B-C), we 278 measured growth rates and carrying capacities (Supp. Fig. 5) and estimated the competition 279 coefficients . We used the diagrams of pairwise coculture outcomes at all constant dilution 280 factors (Fig. 2E, Fig. 3D) to estimate the competition coefficients as follows. The different 281 outcomes (dominance/exclusion, coexistence, and bistability) are divided by the zero points of 282 log(̃) and log(̃), meaning that the qualitative pairwise outcome changes at a dilution factor 283 where one of the reparamaterized coefficients ̃ is equal to one. We used Eqn. 3 of the main text 284 to solve for the competition coefficient at the boundary dilution factor where unstable (dotted) and 285 stable (solid) lines intersect on the diagrams (Fig. 2E, Fig. 3D). 286

Statistical analysis 287
The p-values given in Supplementary Figures 5 and 6 were obtained using two-tailed t-tests. The 288 error bars shown in the time-series plots in Fig. 1, Fig. 2, and Fig. 3 are the SD of the beta 289 distribution with Bayes' prior probability: 290 = √ ( + 1)( + 1) ( + + 2) 2 ( + + 3) 291 Here, and are the number of colonies of two different species. 292

Code availability 293
Code for data analysis is available upon request. 294

Data availability 295
The source data underlying all figures are provided as a Source Data File. Access to the data is 296 also publicly available at TBD. A reporting summary for this Article is available as a 297 Supplementary Information file. 298 299 300