Spatial self-organization favors heterotypic cooperation over cheating

1Cooperation, providing a benefit available to others at a cost to self, has been postulated to drive major transitions in evolution. Cooperation may take place between similar individuals contributing and sharing identical benefits (homotypic cooperation) or between two populations exchanging distinct benefits such as in some forms of mutualism (heterotypic cooperation). Both homotypic and heterotypic cooperation are vulnerable to cheaters. Cheaters exploit cooperative benefits without contributing their fair share and are therefore competitively superior to their cooperating counterparts. How might cooperation avoid being taken over by cheaters? The answer lies in ‘positive assortment’, in which benefit-supplying individuals interact more with other benefit-supplying individuals than with cheaters.

2In homotypic cooperation that involves genetic relatives, positive assortment can be realized through ‘kin discrimination’, which is based on the active recognition and preferential treatment of more closely related individuals over distantly related ones. Positive assortment can also be realized through ‘kin fidelity’. For example, restricted migration in a spatial environment causes homotypic cooperators and cheaters to cluster with their respective progeny. This clustering allows cooperators to preferentially interact with each other (Figure 1A, top). Both mechanisms of positive assortment can favor cooperation. A spatial environment may also impede homotypic cooperation by intensifying competition among cooperators and in certain cases, by potentially encouraging cheating strategies.

3Heterotypic cooperation can occur between populations that are genetically related but phenotypically differentiated, such as between different cell types in a multicellular organism. Alternatively, heterotypic cooperation can involve two genetically unrelated populations (e.g., species) exchanging distinct benefits that are costly to produce. For example, legume plants supply organic carbon and other essential nutrients to rhizobia, and rhizobia reciprocate with fixed nitrogen. Positive assortment in heterotypic cooperation can be achieved through ‘partner choice’ and ‘partner fidelity feedback’. In partner choice, active mechanisms (disruptable through for example mutational or pharmacological means) enable an individual to differentially reward cooperative instead of non-cooperative partners based on a signal. Thus, discrimination mediated by partner choice can occur in advance of exploitation. For instance, in the mutualism between client fish and cleaner fish in which cleaner fish obtain food from removing client parasites, client fish recognize and avoid cheating cleaners that also bite healthy tissues. In partner fidelity feedback, fitness-feedback from repeated interactions ensures that aiding the partner helps self. Examples of partner fidelity feedback can be found in mutualism between hosts and their vertically transmitted symbionts, for example, between eukaryotes and their endosymbioic mitochondria and chloroplasts.

4Natural heterotypic cooperative systems often benefit from a combination of partner choice and partner fidelity feedback. Often, for a particular system, it is challenging to determine which mechanism is mainly responsible for fending off cheaters. For instance, the mutualism between fig and fig wasp and between legume and rhizobia have been thought to employ partner choice by some investigators and partner fidelity feedback by others.

5In this study, using engineered yeast strains and mathematical models devoid of possibilities for partner choice, we examined how through partner fidelity feedback heterotypic cooperation between microbes may be protected against cheaters. Spatial environment, which facilitates repeated interactions between neighboring individuals, has been shown to promote heterotypic cooperation. However, the mechanism for how partner fidelity feedback unfolds in a spatial environment is not well understood. Specifically, how might spatial correlation in the tendency to contribute arise between genetically unrelated heterotypic cooperators when such correlation was initially absent? If population viscosity was the sole driving force, then clusters of cooperators and clusters of competitively superior cheaters would be expected to have equivalent access to clusters of heterotypic cooperative partners. This would seem to favor cheaters (Figure 1A, bottom). Instead, we show that in a spatial environment, asymmetric fitness effects of cooperators and cheaters on partners during cell growth into open space drives assortment. This emergence of non-random patterns from initially random spatial distributions, known as self-organization, automatically grants cooperators instead of cheaters more access to heterotypic cooperative partners, disfavoring cheaters. Thus, partner fidelity feedback through self-organization excludes cheaters without evolving recognition mechanisms.

6To examine how partner fidelity feedback unfolds in a spatial environment, we started with an engineered experimental system incapable of partner recognition. This system consisted of three reproductively isolated Saccharomyces cerevisiae strains: a green-fluorescent strain requiring adenine and releasing lysine, a red-fluorescent strain requiring lysine and releasing adenine, and a cyan-fluorescent strain requiring lysine and not releasing adenine. Release of lysine or adenine was caused by metabolite overproduction due to a mutation that made the first enzyme of the biosynthetic pathway (Lys21 and Ade4, respectively) insensitive to end-product inhibition. still produced adenine for itself at the wild-type level, but without the overproduction mutation, the adenine produced by was not sufficient to support the growth of (Figure supplement 6 in ).

7These strains engaged in different types of interactions depending on the environment. In minimal medium supplemented with abundant adenine and lysine, they competed for nutrients required by all three strains (e.g., glucose and nitrogen) and limited space (Figure 1B, ‘Comp’). In minimal medium without supplements, in addition to competition, and exchanged essential metabolites lysine and adenine, while consumed lysine without releasing adenine. Not overproducing adenine, showed a ∼2% growth rate advantage over when lysine was abundant (competition assay in Figure 1 of ). In the absence of lysine, there was no significant difference in the death rates of and (Figure S1 in ). Finally, in media lacking lysine and adenine, binary cocultures of and could grow from low to high cell densities (Figure 1 in ), whereas cocultures of and failed to grow (Figure supplement 6 in ). These results collectively suggest that acts as a cheater variant of. In other words, in the absence of supplements, cooperator and the competitively superior cheater competed for the lysine supplied by the heterotypic cooperative partner (partner) (Figure 1B, ‘Co&Ch’). Cooperator ‘reciprocated’ by releasing adenine, which is essential for partner, but cheater did not release adenine.

8We first verified that a spatial environment could stabilize heterotypic cooperation against a competitively superior cheater in our system. We initiated experimental communities from randomly distributed equal proportions of the three cell populations on agarose pads (Figure 1—figure supplement 1A). During pure competition in the presence of supplemented adenine and lysine, the: ratio dropped below the original value of 1 after approximately six to eight generations (Figure 1C), consistent with the known 2% growth advantage of over. In contrast, during cooperation and cheating in the absence of adenine and lysine supplements, cooperating was favored over cheating (Figure 1C, time course in Figure 1—figure supplement 2).

9If the spatial aspect of the environment is disrupted, either by periodically mixing a community or by growing it as a well-mixed liquid coculture, partner fidelity feedback should not operate and cheaters are expected to be favored over cooperators. However, the ratio of cooperators to cheaters in periodically mixed replicate communities varied dramatically (Figure 2—figure supplement 1). This was because the lysine-limited environment strongly selected for adaptive mutants in and. Thus, and engaged in an ‘adaptive race’ akin to clonal interference: if had the best mutation to grow under lysine limitation, then the coculture was quickly destroyed by cheaters; if had the best adaptive mutation, then the coculture quickly purged cheaters. As a result, outcompeted or outcompeted depending on which population had a better mutation, not because of social interactions. This kind of phenomenon has also been observed for non-engineered cooperating and cheating microbes. We chose two evolving cocultures in which the populations were increasing in frequency, When we grew these two cocultures in well-mixed and in periodically perturbed spatial environments, was favored (Figure 2—figure supplement 2; ‘Materials and methods’). However, in a spatial environment, was favored (Figure 2—figure supplement 2), consistent with previous experiments on a different microbial system. Our experiments involved non-clonal and non-isogenic populations. In nature, cheaters can be of different species (such as the non-pollinating wasps of fig) and therefore not isogenic with their cooperating counterpart. Additionally, upon environmental stresses, originally isogenic cooperators and cheaters can quickly acquire different mutations and become nonisogenic. Regardless, we resorted to mathematical models to eliminate the confounding influence of adaptive mutations.

10We extended a three-dimensional individual-based model of community growth (previously described as the ‘diffusion model’ in ) to include cooperators, cheaters, and heterotypic partners. The main assumptions of this model were: (1) that the growth of individual cells depended on consumption of the limiting metabolite, and the consumption rate in turn depended on the local concentration of the limiting metabolite according to Michaelis–Menten kinetics; (2) that spatial distribution of metabolites was governed by release, diffusion, and consumption; and (3) that cells rearranged when necessary to accommodate new cells as per experimental observations (‘Materials and methods’). Parameters of this model (such as the rates of growth, death, and metabolite consumption and release) were experimentally determined, mostly through characterizing properties of monocultures (Figure 2—source data 1). was assumed to have a constant intrinsic fitness advantage over at all lysine concentrations, as modeled by a higher maximum uptake rate ( in ‘The diffusion model’ in ‘Materials and methods’). In the absence of adaptations, simulation results confirmed that a spatial environment favored cooperators over cheaters and that disrupting the spatial aspect of the environment gave cheaters an advantage over cooperators (Figure 2).

11During spatial growth of the yeast community, ancestral and should also engage in an adaptive race to adapt to the lysine-limited environment. However, unlike in the liquid environment, mutants in and were spatially restricted to the neighborhood of their origins, and thus these mutants could not sweep through the entire community. Consequently, population dynamics from different replicates were highly reproducible (Figure 1—figure supplement 2). Thus, we used ancestral and for all other experiments.

12How might a spatial environment promote heterotypic cooperation? The relative positioning of cells in a community, the ‘spatial pattern’ of a community, can develop differently based on the fitness effects of cell–cell interactions. Due to the inability of confocal or two-photon microscopy to yield three-dimensional patterns of cells in yeast communities, we only had access to the top-views (xy) and vertical cross-sections (z), with the latter being obtained through cryosectioning. In vertical cross-sections, we have previously shown that in the absence of adenine and lysine supplements, and as a strongly cooperative pair (i.e., there is a large fitness gain from interacting with the other population) are expected to spatially mix. In contrast, and, a competing pair, should form segregated columns, with each column consisting primarily of a single cell type. Finally, for the commensal pair and in which each cell can support the local growth of multiple cells, is expected to grow over. However, it is unclear what patterns would form when the three strains grow together in a community and how the patterns might impact cooperators and cheaters differently.

13To examine how cooperation and cheating might affect community patterns, we compared communities grown in a spatial environment under conditions of competition (‘Comp’) or cooperation and cheating (‘Co&Ch’) (Figure 1B). Specifically, equal proportions of,, and cells were randomly distributed on top of an agarose surface and allowed to grow. Top-views of experimental (‘Exp’) communities grown in the presence of adenine and lysine supplements revealed that,, and, when engaged in pure competition, were evenly distributed in the horizontal xy plane (Figure 3A, top panel). This pattern was caused by the initial cells growing into microcolonies which, after running into each other, were forced to grow upward (Figure 3—figure supplement 1A). Indeed, vertical cross-sections exhibited patterns consistent with our expectations that competitive populations should form segregated columns (Figure 3A, bottom panel).

14In the absence of adenine and lysine supplements, the three populations engaged in heterotypic cooperation and cheating in addition to competition for shared resources. Top-views of these experimental communities showed patterns distinct from those of purely competitive communities. Regions dominated by a mixture of the cooperating pair and appeared isolated from regions dominated by the cheater (Figure 3B, top panel and Figure 3—figure supplement 1B). Vertical cross-sections of these communities revealed that cooperating and intermixed and formed tall ‘pods’. In contrast, cheating was relegated to the periphery of these pods and grew relatively poorly (Figure 3B, bottom panel).

15To quantify differential partner association, the result of partner fidelity feedback, we define ‘partner association index’: for those and cells bordering at least one other cell type (‘Materials and methods’), is the ratio of the average number of in the immediate neighborhood of to the average number of in the immediate neighborhood of. A partner association index > 1 indicates more neighbors surrounding than surrounding. Using a two-dimensional neighborhood to quantify in top-views and vertical cross-sections, we found that significantly exceeded 1 during cooperation and cheating but not during competition (Figure 3C). This self-organization—the formation of non-random patterns from initially randomly distributed individuals purely driven by internal local interactions—automatically makes partner more accessible to cooperating than to cheating.

16Similar to the experiments, top-views and vertical cross-sections in the communities simulated through the diffusion model (‘Sim’) also showed that cooperating and preferentially associated with each other and formed tall pods, while cheating was isolated (Figure 3E). Such self-organization was absent in pure competition (Figure 3D). We quantified the partner association index of simulated communities using a three-dimensional neighborhood averaged across the entire community, which turned out to be much less variable than analyzing two-dimensional slices (Figure 3—figure supplement 2). During cooperation and cheating, increased from an initial value of 1 to a steady level greater than 1 (Figure 3F, top). This greater-than-1 favored cooperating over cheating, as the ratio: continued to increase even after had leveled off (Figure 3F, bottom). In contrast, during pure competition, was close to 1 and was favored over (Figure 3F).

17In addition to generating information difficult to obtain from experimental communities (such as the detailed time course of described above), simulations enabled us to explore a broader class of cooperator–cheater communities. Simulations showed that self-organization also allowed discrimination among cooperators of varying quality (Figure 4). Specifically, we initiated diffusion-model simulations using three populations:,, and. The adenine release rate of was a fraction d (< 1) of that of, and like, had a constant growth rate advantage over at all lysine concentrations. When grown in the absence of supplements, were isolated and outcompeted by. This effect was quantitative, as a lower d value resulted in a larger (i.e., the less released, the more it was excluded; Figure 4A,B), and a greater advantage of over (Figure 4C,D). In contrast, was not highly sensitive to the intrinsic growth rate advantage of over (Figure 4—figure supplement 1). was still strongly disfavored even when it had relatively large (50%) intrinsic growth rate advantage over (Figure 4—figure supplement 1). Taken together, self-organization favors cooperators that supply the most benefits.

18One might hypothesize that among the initially randomly distributed cell populations, the occasional fortuitous proximity of a cooperator cell to a partner cell is necessary for self-organization. To examine this hypothesis, we simulated communities starting from a periodic and symmetric initial distribution of cells (Figure 5A). In the absence of initial spatial asymmetry, other stochastic effects such as the initial metabolite-storage state of the cell, cell rearrangement, and death events broke the symmetry and self-organization still emerged (Figure 5B). Even though the final partner association index from random initial distribution was greater than that from periodic distribution, the latter was still significantly greater than 1 (Figure 5C). Consequently, cooperators still outperformed cheaters in periodic initial distribution, even though the degree of outperformance was greater in random initial distribution (Figure 5D). These simulation results suggest that the heterogeneity in the initial spatial distribution of cells promoted but was not required for self-organization.

19What drives differential partner association during self-organization? Since self-organization was only observed during cooperation and cheating but not during competition, the very acts of cooperation and cheating are required. When the fitness effects of interactions are the major driving force of patterning, interacting populations are expected to intermix if both supply spatially localized large fitness benefit to the other. In contrast, lack of benefit to either population causes population segregation. Thus, we reason that the asymmetry between cooperators and cheaters in their capacity to reciprocate partner’s benefits drives self-organization.

20To examine how this asymmetry leads to self-organization, we simulated a community in which a center stripe of partners was initially bordered by a stripe of cooperators on one side and cheaters on the other (Figure 6). This simulation configuration allowed us to examine the process of self-organization from the simplest form of initial symmetry. Near the cooperator side, partners intermixed with cooperators due to the spatially localized large benefits to both (; red and green in Figure 6). In contrast, near the cheater side, the lack of benefits to partners caused minimal intermixing between cheaters and partners (; blue and green in Figure 6). This isolation of cheaters allowed cooperators to increase in frequency despite the intrinsic fitness advantage of cheaters over cooperators.

21If the cell densities in the initial inoculum were so high that all cell types were forced to be each other’s immediate neighbor, then the degree of self-organization might be limited. To test whether access to open space is required for self-organization, we initiated communities at high initial cell densities such that two cell layers covered the inoculation spot. We then allowed communities to grow unperturbed in a spatial environment (Figure 1—figure supplement 1B). Compared to the center, the expanding front where open space offered opportunities for self-organization showed a significantly higher partner association index (Figure 7, Figure 7—figure supplement 1). In the community center, cooperators were not favored over cheaters. In contrast,: increased progressively above the initial value of 1 as the community grew into open space away from the inoculum (Figure 7). Thus, similar to what has been observed for homotypic cooperation, growth into open space during range expansion also favors heterotypic cooperation over cheating.

22Using an engineered yeast community and a mathematical model devoid of partner recognition, we examined how partner-fidelity feedback unfolds in a spatial environment at the individual cell level. In our system, partner cells released essential metabolites for cooperators and cheaters, and cooperators reciprocated with a different essential metabolite while cheaters did not. We found that despite an initially random or periodic spatial distribution, cells ‘self-organized’ into a non-random and non-symmetric pattern: cooperators had more partner neighbors than cheaters did. The level of differential partner association, as quantified by the partner association index, is correlated with how much cooperators outperform cheaters despite the intrinsic fitness advantage of cheaters over cooperators.

23What is required for self-organization? Self-organization is driven by the asymmetry between cooperators and cheaters in the amount of spatially localized benefits they supply to the heterotypic partner during cell growth into open space. Our previous work has shown that if two distinct populations receive spatially localized large fitness benefits from each other, then the two populations are expected to intermix. In contrast, when the fitness benefit to at least one population is small, then cell types are not expected to intermix. Consequently, partners intermix with cooperators but not cheaters (Figures 3–7). This difference in the tendency to intermix causes differential partner association, which facilitates the growth of cooperators and isolates and disfavors cheaters. Indeed in simulations, if intermixing was prevented through delocalizing benefits, or if intermixing was imposed on all cells through high initial cell densities, self-organization and cooperator advantage over cheaters diminished (Figure 6—figure supplement 1, Figure 7). Similar trends are observed in recent works which mathematically examined diffusion of public good in homotypic cooperation.

24Simulations showed that spatial self-organization could discriminate among cooperators that supply different levels of benefits (Figure 4). When cooperative benefits were limiting, the most ‘helpful’ cooperator ended up with the highest number of partners and was most favored. In our mathematical model, we could be sure that this was not due to partner recognition. Thus, in theory, self-organization through partner fidelity feedback is capable of achieving finer levels of discrimination without requiring sophisticated cognition and memory. Without knowing the molecular mechanisms of interactions, one could easily confuse partner fidelity feedback with partner recognition, because both are capable of discriminating partners of varying cooperative qualities. Our work suggests that any argument on partner recognition in a system that is intrinsically spatial (such as legume and rhizobia and fig and colonizing fig wasp) will require identifying variants that fail to distinguish cooperators from cheaters. Otherwise, interpreting cheater discrimination as ‘partner choice’ can be misleading.

25Spatial self-organization can fend off cheaters with large fitness advantages over cooperators (Figure 4D). However, if (non-isogenic) cheaters are much better than cooperators at taking up low concentrations of benefits, then cheaters will destroy heterotypic cooperation even in a spatial environment (experimental results in Figure 4—figure supplement 2). In byproduct mutualism (benefit production incurs no cost and thus non-producers have no fitness advantage over producers), non-producers are excluded and disfavored in a spatial environment (Figure 4—figure supplement 3). Furthermore, high levels of non-producers can still destroy byproduct mutualism in a spatial environment (simulation results in Figure 4—figure supplement 3). This is because non-producers compete with producers for benefits from the partner. If the initial level of non-producers is too high, producers receive few benefits and suffer, which in turn negatively impacts the partner.

26Conceptually, spatial self-organization favoring heterotypic cooperation can be considered as an example of niche construction or environmental feedback. Cooperators construct favorable niches and cheaters construct unfavorable niches for partners. Through differential partner association, partners construct better niches for cooperators than for cheaters. Niche construction not only affects the growth of current cells, but also that of the future progeny. This reciprocal niche construction favors heterotypic cooperation over cheating.

27In summary, spatial self-organization is the mechanism for partner fidelity feedback. Not requiring the evolution of partner recognition, spatial self-organization offers a simple and fundamental mechanism solely driven by acts of strong cooperation and cheating during cell growth into open space. Even in natural heterotypic cooperative systems with long evolutionary histories, self-organization may act either alone or in synergy with potential recognition mechanisms to exclude cheaters.

28,, and were respectively WS950 (MATa ste3::kanMX4 lys2Δ0 ade4::ADE4(PUR6) ADHp-DsRed.T4), WS954 (MATa ste3::kanMX4 ade8Δ0 lys21::LYS21(fbr) ADHp-venus-YFP), and WS962 (MATa ste3::kanMX4 lys2Δ0 ADHp-CFP).

29To grow yeast communities, agarose columns were prepared by pouring 2× concentrated SD minimal medium with 2% low melting temperature agarose either into flat-bottom 96-well plates (Figure 1—figure supplement 1A) or into rectangular petri dishes (Figure 1—figure supplement 1B). Agarose in the rectangular petri dishes was subsequently cut into 24 mm × 24 mm × 4 mm pads. For competition experiments, 2× SD was supplemented with lysine and adenine (650 μM and 430 μM final concentrations, respectively). The communities on agarose were inoculated either from a uniform distribution of all cells (Figure 1—figure supplement 1A at 3000 or 10,000 total cells/mm2) or a high-density inoculum of ∼2 mm diameter (Figure 1—figure supplement 1B at ∼8 × 104 total cells/mm2), as specified. We grew well-mixed liquid cocultures in 3 ml of 1× SD without supplementing adenine or lysine, with initially 5 × 105 total cells/ml. In all cases, cultures were initiated from equal proportions of,, and populations. Flow cytometry was used to measure population sizes of different types in a community. Fluorescent imaging equipment and procedures are described in. Cryosectioning to obtain vertical cross-sections of yeast communities followed.

30We quantified the relative association of cooperators and cheaters with the heterotypic partner by dividing the average number of immediate neighbors per focal cell by the average number of immediate neighbors per focal cell when a focal cell neighbored at least one different population (, partner association index). We chose to count the immediate neighbors because nearest neighbors presumably had the greatest impact on the growth of the focal cell due to spatially localized benefits. We chose to analyze focal cells neighboring at least one different population because cells surrounded by their own types do not contribute as much to population growth as cells surrounded by partners.

31In simulations, a three-dimensional neighborhood around each cell was used to quantify the association index, whereas in experiments, a two-dimensional neighborhood was used in two-dimensional top-views or cross-sections of the community. Based on fluorescence intensities in the DsRed, YFP, and CFP channels, cell types were assigned to each pixel in fluorescent images. Pixels having fluorescence intensities less than 30% above the background in all fluorescence channels were defined as ‘no signal’. Otherwise, fluorescence intensities in each channel were normalized to their respective image-wide 90th percentile values and pixel identity was assigned to be the same as the fluorescence channel with the highest normalized intensity. For cross-sections taken from the center of communities in Figure 7, the top crown of cross-sections appeared very bright, whereas the middle and lower regions appeared dim (Figure 7—figure supplement 1). This large dynamic range caused artifacts in cell identification. The intensity thresholds in these sections were therefore manually adjusted to increase the accuracy of cell identification. Eliminating manual adjustments did not alter the conclusions.

32To simulate the growth of three-dimensional yeast communities, we used the agent-based diffusion model. In this model, metabolites are released by cooperators and partners, diffuse throughout the community and agarose, and are consumed by cells that need the metabolite. Most parameters were measured experimentally (Figure 2—source data 1). We provide a summary of the most relevant features of the model below, without repeating the implementation details that can be found in.

33Cells take up their required metabolites depending on the local concentration of the metabolite according to the Michaelis–Menten equation:where, i =,, or corresponding to each cell type, Si is the concentration of the required metabolite for each cell type (Si = SL, lysine concentration for and, and Si = SA, adenine concentration for ), vm,i is the maximum uptake rate when metabolites are abundant, and Ki is assumed to be equal to the Monod constant (the concentration of limiting nutrient at which half maximal growth rate is achieved) for each cell type. and cells require fmole of lysine and cells require fmole of adenine to produce a new daughter cell.

34The distribution of metabolites is modeled using the diffusion equation, with uptake and release as sinks and sources. Using simplified notations of and at time t, the metabolite distributions after a time step tu are calculated as and

35Here, nR, nC, and nG are, respectively, the densities of live,, and cells in a focal community grid. is the vector differential operator. is the density of cells that die (which is distributed as binomial (nG, p) where p = tu·dG, with dG being the death rate of ) and release lysine in the time step tu. D is a spatially varying function representing the diffusion coefficient in the environment (the value of D was 360 μm2/s inside agarose, 20 μm2/s inside yeast communities, and 0 μm2/s in the surrounding air, according to experimental measurements). Considering D as a spatially varying function simplifies the numerical calculations by automatically incorporating the boundary conditions at the community–air interface., the maximum uptake rate of the limiting nutrient per cell, relates to the maximum growth rate through, where is the amount of limiting nutrient required to produce a new cell ( and ). has a fixed intrinsic fitness advantage over at all lysine concentrations. This advantage was modeled as a higher uptake rate for the limiting nutrient. For example, a 2% fitness advantage of cheaters means or equivalently. βL is the amount of lysine released upon the death of a cell, and γA is the release rate of adenine per cell. cheaters do not release any adenine. For other types of cheaters that release adenine with a lower rate compared to cooperators (e.g., in Figure 4), a corresponding release term is included in the equation.

36To solve this diffusion equation, we follow the above finite difference time-domain equations over time. The diffusion equation is solved over two separate spatial domains, one containing the agarose (with a 60 μm grid size), and the other containing the community and the air above it (with a 15 μm grid size). These grid sizes accommodated different diffusion coefficients in agarose and in community and represented the average distance nutrient molecules diffuse in 3.5 s. When we used the same diffusion coefficient (360 μm2/s and one grid size of 50 μm) for agarose and community, similar results were obtained. No-flow boundary conditions are applied to the top and bottom surfaces of the simulation domain and periodic boundary conditions are applied to the four vertical sides of the domain.

37To incorporate the effects of competition for other shared resources, the growth of all cells also depended on, in addition to adenine or lysine, a shared resource (for instance, glucose) that was initially supplied in the medium (Figure 2—source data 1). In such simulations, diffusion and uptake of glucose were also simulated in a way similar to the above equations. Each cell divided only after acquiring enough glucose, in addition to adenine or lysine. Once a cell had accumulated one metabolite sufficient for one cell division, it stopped consuming that metabolite and continued to acquire the second metabolite until a sufficient amount had been acquired to trigger the birth of a daughter cell.

38In simulations,,, and cells are initially randomly distributed on the surface of solid medium. The cells start from random initial storage of their required metabolites. In each tu time step, each live cell takes up its required metabolites according to the Michaelis–Menten equation shown above. Each cell type is assumed to require its limiting metabolite and a shared metabolite ( lysine for and, adenine for, and for the shared glucose for all cell types, all listed in Figure 2—source data 1) to divide. The state of cells is examined at every τ time interval (τ = 6 min, which contains several diffusion tu time steps, but is still much shorter than the minimum cell doubling time of ∼2 hr). The cells that have acquired the required amount of limiting metabolites divide.

39Cell divisions in a three-dimensional community often required cell rearrangement. Assumptions concerning cell rearrangement were derived from experimental observations. Time-lapse images of the growth of a single fluorescent cell into a microcolony showed that the center of the microcolony became brighter due to multiple cell layers when the microcolony grew to larger than a five-cell radius. Thus, we assumed that each cell initially budded in the horizontal plane and pushed others in its immediate neighborhood to the side along the shortest path to empty space. Once a cell was completely surrounded on each side by roughly five cells, it either budded directly upward with a probability of 70% or randomly budded to one of the sides at the same level, pushing up the displaced cell and all the cells above. The probability of 0.7 (instead of 1) of dividing directly upward is estimated from experimental observations: when individual green-fluorescent cells were surrounded by many equally fit competing red-fluorescent cells, vertical cross-sections showed that as z increased, the progeny of the green-fluorescent cell ‘diffused’ laterally (instead of remaining a vertical line) (Figure 3—figure supplement 1F in ). Since we cannot experimentally track all possible outcomes of cell rearrangement, this assumption is a simplification of reality. This simplification could have contributed to the discrepancy between experimental and simulation patterns, although our conclusions from experiments and simulations are similar.

40The cells also die stochastically corresponding to their fixed death rates (dR, dG, or dC as listed in Figure 2—source data 1). After each cell state update (τ), the diffusion coefficient is updated: the diffusion coefficient in each community diffusion grid (15 μm × 15 μm × 15 μm, maximally containing 3 × 3 × 3 = 27 cells of size 5 μm × 5 μm × 5 μm) is assumed to be proportional to the occupancy of that grid, changing from 0 to 20 μm2/s. In this three-dimensional agent-based model of community growth, the initial conditions of cells, cell death, random direction of growth, and cell rearrangement are the only sources of stochasticity; metabolite uptake and diffusion of metabolites in the environment are modeled as deterministic phenomena.

41Most of the parameters used for the simulations (Figure 2—source data 1) are measured experimentally. More details of the implementation and assumptions can be found in. An example of the implementation of this model as a MATLAB code is included in additional files (Source code 1).

42When the ancestral,, and were periodically mixed on an agarose pad lacking adenine and lysine, the final: ratios were stochastic, either in favor of cheaters or cooperators (Figure 2—figure supplement 1). This is consistent with previous experiments in liquid cocultures that also yielded stochastic cheater outcomes due to an adaptive race between and. During the adaptive race, both and sampled from the same set of mutations that enhanced cell fitness in the lysine-limited cooperative environment. The population with the fittest mutant rapidly dominated the coculture (Figure 2—figure supplement 1; ).

43To mitigate the confounding effect of adaptive race, we used and populations preadapted to the cooperative environment. First, containing a mutation in RSP5 (CT8, see Table 1 in ), known to significantly improve the fitness of lysine-requiring cells under lysine-limitation, was crossed to the ancestral to produce a diploid (WS1421). Sporulation of the diploid yielded a cyan-fluorescent cooperator (WS1447) and a red-fluorescent cheater (WS1448), both harboring the rsp5 mutation. The temperature sensitivity of this rsp5 allele allowed its easy selection at 37°C. To avoid confusion, we indicate these cooperators and cheaters as rsp5 and rsp5, respectively. Several well-mixed cocultures consisting of rsp5, rsp5, and the ancestral partner (WS954) were initiated at a ratio of 1:1:1. The initial stochastic phase in population dynamics was indicative of additional rounds of adaptive races between rsp5 and rsp5 (Figure 2—figure supplement 2A). After 250 hr, the: ratios showed steady trends, suggesting the absence of further rapid adaptive races (Figure 2—figure supplement 2A). After ∼500 hr, two of the lines (brown) that displayed a steady change of the rsp5:rsp5 ratio in favor of cheaters and a final ratio close to 1:1 were frozen down. After reviving these preadapted cocultures (hereafter marked as “ ’ ”),: continued to decline steadily (Figure 2—figure supplement 2B). Propagating well-mixed liquid cocultures from these lines for an additional 400 hr, we observed that the: ratio exhibited a steady decline (Figure 2—figure supplement 2C, ‘In liquid, well-mixed’), suggesting a cheater fitness advantage of around 8% (7.5 ± 0.8% SD) over. It should be noted that since and are not isogenic, the fitness advantage of over is likely not solely due to the lack of adenine overproduction by. Nevertheless, this case models an advantage for the cheating type over the cooperating type, similar to what might be observed in nature if cheaters and cooperators are of different species.