Spatial structure favors microbial coexistence except when slower mediator diffusion weakens interactions
- Biology Department, Boston College, United States
- Department of Aquatic Ecology, Swiss Federal Institute of Aquatic Science and Technology, Switzerland
Figures
Figure 1 with 9 supplements
A spatial environment favors coexistence more when interspecies facilitation is prevalent in the initial species pool.
(A) Species are engaged in metabolite-mediated interactions with other species. Each species produces a subset of mediators and consumes a subset. Each mediator can positively or negatively modulate …
Figure 1—figure supplement 1
There is little change in community composition after 100 generations of growth.
Here, we examine a simple case with five species and three mediators. Markers and error bars show mean and standard deviation of the percentage change in the community composition over 10 …
Figure 1—figure supplement 2
Shannon index shows the same overall trend as richness when comparing spatial versus well-mixed communities.
Similar to Figure 1C, simulations were run at different fac:inh ratios for both spatial communities (blue squares) and well-mixed communities (red circles). Each ratio was run 500 times with the …
Figure 1—figure supplement 3
Comparing the spatial distribution of species at different dispersal rates illustrates the impact of dispersal on coexistence.
(A) Species are initially stacked over the spatial extent of the community. We examine a simple case with five species and three mediators (interaction network shown in the inset). Different …
Figure 1—figure supplement 4
Species interactions and dynamics are different in spatial versus well-mixed environments, leading to different coexistence outcomes.
For simplicity, we consider an initial pool of five species with three mediators. We kept the same interaction network (A) in both spatial and well-mixed conditions and simulated the species …
Figure 1—figure supplement 5
Species interactions and dynamics are different in spatial versus well-mixed environments, even when inhibition is prevalent.
For simplicity, we consider an initial pool of five species with three mediators, but rather than fac:inh = 90:10 in Figure 1—figure supplement 4, here we initially assign fac:inh = 10:90. We kept …
Figure 1—figure supplement 6
Spatial distance between species can modulate the strength of their interaction.
For simplicity, here we consider only two species engaged in commensalism (Species 1 providing a benefit to Species 2) through a single mediator (see insets). We examined a no-interaction control (A)…
Figure 1—figure supplement 7
Within the same order of magnitude, the community’s spatial extent does not have a large impact on spatial coexistence.
All parameters other than the community’s spatial extent are kept fixed. Here, (A) DCell = 5 × 10−8 cm2/hr and (B) DCell = 5 × 10−9 cm2/hr. Legend shows the values of fac:inh assigned in the initial …
Figure 1—figure supplement 8
Imposing a local carrying capacity favors species coexistence.
All parameters other than the local carrying capacity kY are kept fixed. Imposing a local carrying capacity on the total cell number (see the equations described in Methods) lowers the competitive …
Figure 1—figure supplement 9
Rearranging the order of species can modulate the strength of interspecies interactions and impact spatial coexistence outcomes.
For simplicity, here we use the same examples as Figure 1—figure supplement 4 with five species and three mediators in the initial pool. We keep the same interaction network (A), but rearrange the …
Figure 2 with 4 supplements
The number of metabolites produced and number of species influenced affect coexistence in spatial and well-mixed communities.
Different ranges of production and mediator influence values were analyzed for both well-mixed and spatial communities at three different fractions of fac:inh influences in the initial pool of …
Figure 2—figure supplement 1
The number of metabolites produced and number of species influenced affect coexistence in spatial and well-mixed communities.
Different ranges of production and mediator influence values were analyzed for both well-mixed and spatial communities at three different fractions of fac:inh influences in the initial pool of …
Figure 2—figure supplement 2
Coexistence is favored when many metabolites are produced and influence an intermediate number of species, even with weaker interactions.
Different ranges of production and mediator influence values were analyzed for both well-mixed and spatial communities at three different fractions of fac:inh influences in the initial pool of …
Figure 2—figure supplement 3
Coexistence is favored when many metabolites are produced and influence an intermediate number of species, even with stronger interactions.
Different ranges of production and mediator influence values were analyzed for both well-mixed and spatial communities at three different fractions of fac:inh influences in the initial pool of …
Figure 2—figure supplement 4
Self-facilitation is prominent among low-diversity outcomes.
We separated the outcomes based on whether one (No coexistence) or more species (With coexistence) emerged from enrichment and examined the occurrence of self-facilitation. Occurrence is defined …
Figure 3 with 3 supplements
Coexistence is higher where there is a balance between production and consumption of mediators.
Different average production and consumption rates were analyzed for both well-mixed and spatial communities at three different fractions of fac:inh influences in the initial pool of species (10:90, …
Figure 3—figure supplement 1
In spatial communities with many facilitation interactions among species, coexistence is favored at lower consumption rates of mediators.
Different average production and consumption rates were analyzed for both well-mixed and spatial communities at three different fractions of fac:inh influences in the initial pool of species (10:90, …
Figure 3—figure supplement 2
Coexistence is higher where there is a balance between production and consumption of mediators independent of the interaction strength (here, with weaker interactions).
Different average production and consumption rates were analyzed for both well-mixed and spatial communities at three different fractions of fac:inh influences in the initial pool of species (10:90, …
Figure 3—figure supplement 3
Coexistence is higher where there is a balance between production and consumption of mediators, independent of the interaction strength (here, with stronger interactions).
Different average production and consumption rates were analyzed for both well-mixed and spatial communities at three different fractions of fac:inh influences in the initial pool of species (10:90, …
Figure 4 with 4 supplements
Lower dispersal rates allow more microbial coexistence.
Communities in spatially structured environments were simulated with different dispersal coefficients at three different fractions of fac:inh influences (10:90, 50:50, and 90:10). Mean richness …
Figure 4—figure supplement 1
Lower dispersal rates allow more microbial coexistence.
Communities in spatially structured environments were simulated with different dispersal coefficients at three different fractions of fac:inh influences (10:90, 50:50, and 90:10). Mean richness …
Figure 4—figure supplement 2
Self-facilitation contributes to lower richness at intermediate levels of dispersal.
For these cases, we use fac:inh = 90:10, because it showed the strongest change at intermediate dispersal values. Mean richness (i.e. average number of species stably present at the end of a …
Figure 4—figure supplement 3
Rearranging the order of species affects spatial coexistence.
For each of the cases of (A) fac:inh = 10:90, (B) fac:inh = 50:50, and (C) fac:inh = 90:10, we simulated 100 instances and in each instance, we examined coexistence outcome (final richness) in 100 …
Figure 4—figure supplement 4
Rearranging the order of species affects spatial coexistence more in communities in which facilitation is prevalent.
Similar to Figure 4—figure supplement 3, we simulated 100 instances each of fac:inh = 10:90, 50:50, and 90:10, and in each instance, we examined coexistence outcome (final richness) in 100 …
Figure 5
At higher diffusion coefficients of mediators more coexistence is possible.
A range of metabolite diffusion coefficients were simulated in spatial communities (squares) at three different fractions of fac:inh influences (10:90, 50:50, and 90:10). We simulated corresponding …
Author response image 1
Tables
Table 1
Parameters used in our simulations are listed.
| Parameter | Value (unit) |
|---|---|
| Number of instances examined () | 500 |
| Number of cell types in the initial pool () | 10 |
| Number of interaction mediators () | 5 |
| Total initial cell density (TID) | 104 (cells/ml) |
| Interaction strength saturation level () | 104 (cells/ml) |
| Population extinction threshold (ExtTh) | 0.1 (cells/ml) |
| Population dilution threshold (DilTh) | 107 (cells/ml) |
| Consumption rate () | 0.075–2.25 (fmol per cell per hour; avg. 0.15) Stochastic with a uniform distribution |
| Production rate () | 0.1–0.2 (fmol per cell per hour; avg. 0.1) Stochastic with a uniform distribution |
| Probability of production link per population () | 0.5 |
| Probability of influence link per mediator () | 0.5 |
| Maximum interaction strength magnitude () | 0.2 (1/hr) |
| Basal growth rate of species () | 0.1–0.2 (1/hr); stochastic with a uniform distribution |
| Number of generations for enrichment (nGen) | 100 |
| Dispersal coefficient for cells (DCell) | 5 × 10−9 (cm2/hr) |
| Diffusion coefficient for mediators (DMed) | 1.8 × 10−2 (cm2/hr) |
| Local carrying capacity per dz (kY) | 109 cells/ml |
| Total community spatial extent (Z) | 0.5 cm |
| Spatial resolution for species distributions (dz) | 0.005 cm |
| Cell growth update and uptake timescale (dtau) | 0.01 hr |
| Mediator diffusion time-step (dt) | 0.1dz2/DMed |
| Cell dispersal simulation time-step (dc) | 0.1dz2/DCell |
