Exploitation by cheaters facilitates the preservation of essential public goods in microbial communities

How are public goods1-4 maintained in bacterial cooperative populations? The presence of these compounds is usually threatened by the rise of cheaters that do not contribute but just exploit the common resource5,6. Minimizing cheater invasions appears then as a necessary maintenance mechanism7,8. However, that invasions can instead add to the persistence of cooperation is a prospect that has yet remained largely unexplored6. Here, we show that the detrimental consequences of cheaters can actually preserve public goods, at the cost of recurrent collapses and revivals of the population. The result is made possible by the interplay between spatial constraints and the essentiality of the shared resource. We validate this counter-intuitive effect by carefully combining theory and experiment, with the engineering of an explicit synthetic community in which the public compound allows survival to a bactericidal stress. Notably, the characterization of the experimental system identifies additional factors that can matter, like the impact of the lag phase on the tolerance to stress, or the appearance of spontaneous mutants. Our work emphasizes the unanticipated consequences of the eco-evolutionary feedbacks that emerge in microbial communities relying on essential public goods to function, feedbacks that reveal fundamental for the adaptive change of ecosystems at all scales.


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How are public goods 1-4 maintained in bacterial cooperative populations? The presence of 30 these compounds is usually threatened by the rise of cheaters that do not contribute but 31 just exploit the common resource 5,6 . Minimizing cheater invasions appears then as a 32 necessary maintenance mechanism 7,8 . However, that invasions can instead add to the 33 persistence of cooperation is a prospect that has yet remained largely unexplored 6 . Here, 34 we show that the detrimental consequences of cheaters can actually preserve public goods, 35 at the cost of recurrent collapses and revivals of the population. The result is made 36 possible by the interplay between spatial constraints and the essentiality of the shared 37 resource. We validate this counter-intuitive effect by carefully combining theory and 38 experiment, with the engineering of an explicit synthetic community in which the public 39 compound allows survival to a bactericidal stress. Notably, the characterization of the 40 experimental system identifies additional factors that can matter, like the impact of the lag 41 phase on the tolerance to stress, or the appearance of spontaneous mutants. Our work 42 emphasizes the unanticipated consequences of the eco-evolutionary feedbacks that emerge 43 in microbial communities relying on essential public goods to function, feedbacks that 44 reveal fundamental for the adaptive change of ecosystems at all scales. The threat of cheaters represents at a microbial scale a well-known public good 58 (PG) dilemma, known as the "tragedy of the commons" 9 , and can fundamentally interfere 59 with the sustainability of microbial communities. The necessity of recognizing the 60 consequences of social dilemmas in microorganisms thus becomes essential, given their 61 impact in many aspects of life on Earth, and also its particular relevance to humans in 62 matters of health (microbiome) 10 , and industry (bioremediation, biofuels, etc) 11 . We 63 considered specifically a scenario in which a community is organized as a dynamical 64 metapopulation (i.e., the community is transiently separated into groups) 12 , and the action 65 of a PG is essential for its survival. Spatial structure is a well-known universal mechanism 66 to promote cooperation 13 , which frequently emerges in bacterial populations, for instance, 67 due to the restricted range of microbial interactions 14,15 . However, it is much less 68 understood how the presence of structure affects the maintenance of cooperation when 69 combined with explicit population dynamics (earlier work usually assumed constant 70 population and only examined evolutionary dynamics) 16 . The change in population size 71 associated to the essentiality of the PG can indeed bring about complex eco-evolutionary 72 feedbacks 17-20 , in which both population density and frequency of "cooperators" influence 73 each other. The connection between these feedbacks and spatial structure remains thus an 74 open problem that has started to be addressed only recently [21][22] . We show in this work 75 how such connection can direct to the unforeseen consequence that cheater invasions 76 eventually support cooperation. 77

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To analyze this scenario, we first introduced a stylized in silico model considering 79 an initial finite population of agents -representing bacteria-with a given frequency of 80 cooperators (producers of a PG, with a fitness cost) and cheaters (nonproducers, that 81 could have emerged originally from the cooperators by mutation)(Methods). The 82 population is temporarily organized in groups, where interactions take place ( fig. S1).

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These interactions are modelled by means of a PG game with individual reproduction 84 being set by the game payoff 17,18 . Figure 1A displays a representative trajectory of the 85 model: an increase of the cheating strain, due to its fitness advantage, causes a decrease in 86 population density (less PG available). The demographic fall originates in the end 87 variation in the composition of the groups, facilitating population assortment and the 88 appearance of pure cooperator/cheater groups. Since the groups uniquely constituted by 89 cooperators grow larger, they can ultimately reactivate the global population promoting 90 again new cheater invasions. The whole process manifests in this way as a continuous 91 cycle of decay and recovery of the community (Figs. 1A-B) (Methods). Demographic 92 collapses consequently turn into an endogenous ecological mechanism that causes the 93 required intergroup diversity, supporting the overall increase of cooperators by means of a 94 statistical phenomenon known as Simpson's paradox 12,22 . To underline that an endogenous 95 ecological process naturally induces the variance that finally rescues cooperation, we 96 introduced the notion of "ecological Simpson's paradox". 97

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We then tested these ideas experimentally, by engineering a synthetic PG 99 interaction that is essential for the survival of a microbial population to a bactericidal 100 antibiotic (Fig. 1C). Specifically, we constructed an experimental system in which a 101 synthetic Escherichia coli strain (the cooperator/producer) constitutively secretes an 102 autoinducer molecule acting as PG. This molecule is part of a quorum-sensing (QS) 103 system foreign to E. coli, which includes a cognate transcriptional regulator. We 104 connected this machinery to the expression of a gene that enables the synthetic strain to 105 tolerate the bactericidal antibiotic gentamicin (gm) (fig. S2, the system is a variation of an 106 earlier one 22 )(Methods). A second strain (the cheater/nonproducer) that only utilizes the 107 PG can also be part of the community (we labelled the cooperative and cheater strains 108 with a green and red fluorescent protein, respectively, to make possible population 109 measures) (Methods). Two crucial aspects distinguish in this way the designed setup. 110 First, the presence of PG becomes an essential requirement to tolerate stress ( Fig. 1D) 111 ( fig. S3). Second, the system exhibits an intrinsic vulnerability, as cheaters could 112 overtake the entire community since they evade the cost of producing the PG (Fig. 1E) 113 ( fig. S4). While in this case the presence of cheaters is part of the synthetic design, their 114 emergence as result of mutations is well documented in natural settings 5,6 . 115

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The validation of the presented ecological Simpson's paradox is done using a 117 minimal experimental protocol integrating the most important features of the model: the 118 demographic collapse induced by cheaters, and the subsequent recovery of cooperation 119 supported by the spatial constraints, i.e., the metapopulation. Specifically, the protocol 120 includes two growing periods of PG accumulation and later exposure to stress (gm). 121 Densities of cooperators and cheaters are quantified by plating (Methods). Both the in 122 silico model and the main attributes of the experimental system predict that a community 123 with different frequency of cooperative and noncooperative strains would accumulate a 124 distinct amount of PG, and thus present different tolerance to stress. To confirm this, we 125 engineered an initial population with density ~10 4 cells/ml and different composition ( fig.  126 S5)(Methods). Figure   Next, by distributing the initial full population into a metapopulation structure -133 before the rounds of QS accumulation and stress-we showed experimentally the basic 134 features of the ecological Simpson's paradox. In particular, we selected as initial 135 conditions the ones obtained after a large mixed population experienced a first round of 136 comparatively strong stress ( Fig. 2B, outcomes of an earlier round with a initial density of 137 ~ 10 4 cells/ml constituted by 20% producers). As in the model, the reduced accumulation 138 of PG in the mixed population causes a demographic collapse, which depends on how 139 essential the PG becomes (the strength of stress). We considered explicitly the resulting 140 populations after experiencing a medium (9.5µg/ml) and strong (13µg/ml) gm stress. 141 These corresponded on average to ~24cfu/ml, and ~8cfu/ml, respectively (in what 142 follows, we labelled them as "pop 1" and "pop 2"; the frequency of cooperators remains 143 ~20%). When we subsequently implemented a second round of the protocol with these 144 initial population conditions, and the corresponding (medium and strong) gm dosages, we 145 obtained two drastically different initial metapopulation distributions ( Notably, a low-density population ("pop 2") generates groups with very few cells and 147 assortment of cooperators, which is the group class that best tolerate stress (the 148 characteristic behavior of this class is shown in Fig. 2D). Moreover, mixed groups and 149 those composed by only cheaters do not grow, on average, with strong gm dosage ( shorter lag, i.e., revival is under these conditions mostly linked to the action of the PG. 173 The second constraint relates to the spontaneous emergence of mutants, which can resist 174 the antibiotic and thus enable recovery of cheater populations in the absence of PG. This 175 type of rescue is more difficult as the antibiotic dosage is increased, e.g., 25 (fig. S10), and 176 also underlines a constraint on the accumulation time of PG (the longer this period, the 177 bigger the population and the chance for a mutant to arise) ( Fig. 3B-C). Of note, both of 178 these restrictions are less significant when the collapse of the population is very strong 179 ("pop 2" situation), that is when the best conditions exist for the ecological Simpson's 180   color codes as Fig. 2). We repeated the experiment for each strain and dosage, so that one 278 can quantify the typical resulting population, and also the mutant subpopulation (by 279 plating with -gmand without -no gm-antibiotic; the specific plating dosage corresponds 280 to that of the matching growing conditions). Emergence of spontaneous mutants is 281 reduced at higher dosage (C). Tolerance is most significantly associated in this regime to 282 the presence of the PG.

Ecological public good model 295
We used a model first described in 21 to simulate the dynamics of a population whose 296 growth is based on an essential public good (PG). It is based on a one-shot PG game 27 297 in which agents can contribute ("cooperators") or not ("cheaters") to the PG in 298 groups of size N. Contributing implies a cost c to the agents. Group contributions are 299 then summed, multiplied by a reward factor r (that determines the efficiency of the 300 investments and the attractiveness of the PG) and redistributed to all group 301 members, irrespectively of their contribution. The PG game is characterized by the 302 parameters N, r and c (group size, efficiency and cost of the PG, respectively, where 303 we fixed c = 1 without loss of generality). 304 Every simulation starts with an initial population constituted by a common pool of k 305 identical agents in the cooperator state, where k is the maximal population size 306 (carrying capacity), to be updated in a sequential way as follows (see also Figure S1): 307 (i) The common pool is divided in randomly formed groups of size N (i.e. N is the 308 total number of individuals and empty spaces in each group). The number of formed 309 groups is then ⌊k/N⌋. 310 (ii) In each one of the (non-empty) groups, a one-shot PG game is played. This means 311 that cheaters receive the payoff Pcheater = icr/(i + j), while cooperators receive the 312 same payoff minus a cost, i.e. Pcooperator = Pcheater − c; with i,j being the number of 313 cooperators and cheaters in the group, respectively, and i + j ≤ N. After the 314 interaction the grouping of individuals is dissolved. 315 (iii) Each individual can replicate (duplicate) with a probability that is calculated by 316 dividing its payoff by the maximal possible one (i.e. the payoff obtained by a cheater 317 in a group of N−1 producers). Each cooperator that replicates generates an offspring 318 that is either a cheater (with probability ν) or an identical cooperator (with 319 probability 1−ν). 320 (iv) Individuals are removed with probability δ (individual death rate). 321 In simpler words, the life cycle of the computational model is characterized by two 322 distinct stages. In stage I (steps i-ii), the population is structured in evenly sized 323 randomly formed groups in which the PG game is played. In stage II (steps iii-iv, 324 after groups disappear), each individual replicates according to the group 325 composition (and payoff) experienced in stage I. Replication can happen only when 326 the current total population is less than the maximal population size, k, i.e. there 327 exits empty space (empty spaces are calculated by considering k minus the current 328 amount of individuals in the population). If more individuals could replicate than the 329 available empty space, only a random subset of them ultimately replicates (of size 330 the number of empty spaces available). 331

GFP expression assay to estimate QS signal concentration 383
To estimate the concentration of the quorum sensing signal produced (C4-HSL), in 384 different experimental conditions we used the reporter "biosensor" bacteria. We 385 grew the "biosensor" strain overnight, adjusted the OD600 to 0.

Engineering of initial conditions 399
Initial populations for the "accumulation of PG and stress" protocol and others were 400 prepared by mixing cooperators and cheaters at a defined population density (10⁴ 401 cells/well for high initial density experiments and 1-10 cell/well for low initial 402 density experiments) and cooperator frequency. Overnight cultures of producers 403 and nonproducers were washed twice with PBS by centrifugation for 15min at 404 3800rpm and room temperature. Then, OD600 was adjusted to 0.15. We assembled 405 populations at the desired P frequency in a fixed final volume (2.5ml), which was 406 then serially diluted to the required cell density. This dilution was done in large 407 volumes of medium (20ml) and applying low dilution factor (¼) each step to 408 minimize the introduction of error in strain frequencies. Initial dilution steps were 409 performed in PBS and the final 3 steps were performed in LB with Km, Sp. The 410 robustness of this procedure is shown in Fig. S5. 411

Invasion of nonproducers 412
We prepared washed cultures of producers and nonproducers as described above. 413 After adjusting OD600, to 0.15 we mixed both strains at the indicated frequency. Then, 414 we inoculated three replica 50ml Erlenmeyer flasks with 5ml of LB, Km, Sp. After 415 24h, we reseeded a new flask with a 1/100 dilution and fresh medium. In order to 416 estimate producer frequency in grown cultures, cells were 1/10 serially diluted in 417 PBS using a total of 10ml of medium, plated onto LB agar plates, and colonies 418 counted after 24h at 30 o C. We followed this process for 4 consecutive days. 419

"Accumulation of PG and stress" 420
Populations with a given initial cell density and cooperator frequency were 421 prepared, distributed into a 96-multiwell plate and incubated for 15.5h (T1). used directly in the initial inoculation. We used additional wells without antibiotic in 433 parallel to obtain a reference population size. We express the sensitivity to the 434 antibiotic as "fraction surviving" (population size after exposure to antibiotic / 435 reference population size without antibiotic). 436

Effect of synthetic quorum-sensing on gentamicin tolerance 437
Overnight cultures of nonproducers were resuspended into LB with Km, Sp and the 438 indicated concentrations of synthetic quorum-sensing molecule (C4-HSL). Then, we 439 proceeded with the antibiotic sensitivity assay as described above. 440

Mutation rate 441
We generated replica populations of the nP strain and initial density of ~1 cell/well. 442 We distributed these cultures in 96-multiwell plates and allowed them to grow for 443 15.5h (T1). We plated the whole well content on LB agar plates with the specified gm 444 dosage and counted viable cells. From the distribution of gm R CFU observed in a set 445 of replica populations the mutation rate was estimated with a maximum likelihood 446 method as described in 30 , using the online application "FALCOR: Fluctuation Analysis 447 Calculator