### Simulating competition for space using the “BacGo” model

To investigate how spatial positioning of populations affects the outcome of microbial competition, we simulated two populations competing for space with a limiting size by building an individual-based model (named “BacGo”). The model was implemented in discrete grid boxes of a 20 × 20 array. As shown in Fig. 1a, our simulations were based on three basic assumptions. First, the two competing populations possess the same inherent growth rate and equal initial cell numbers, thus the only differences between them are their manners of colonizing free space. Second, the newly born daughter cell is located around its mother cell but with a random direction of spatial positioning [34], resulted in a microcolony with different spatial patterning. Lastly, if the selected box has been occupied, the newborn cell will compete for the box against the original occupants of the box and possesses a probability of 50% to survive [37].

We first explored the outcome of spatial competition, which started by randomly distributing two populations on the grids with the same initial cell numbers of 10 for each. Based on our basic assumptions and the predictions of competitive exclusion theory [38], we hypothesized that only one population could win the competition and finally occupy all grids. As shown in 20,000 independent simulations with random initial distributions, we discovered that at the end of each simulation, only one population survived (Video S1 and Video S2). The Chi-square test showed no significant difference (*P* = 0.211) between the simulated winning times (10,177 of 20,000 simulations) and the random winning times (10,051 of 20,000 simulations) of the focus population. This result conformed with our initial assumption that cells possess a probability of 50% to survive in competing with original occupants. When we replicated simulations initiated with the same cell distribution, we found that the winning probabilities for each population changed in line with the initial distributions (Fig. S1). However, the winning probabilities never reached 100% no matter how the initial distribution changes. Together, these results suggested that unknown random factors may affect the final outcome of the competition.

Next, we analyzed the dynamics of microbial colonization during our simulations. As summarized in Fig. 1b, we divided the competition process into two stages, the “occupation stage” and the “exclusion stage” (see Methods). To statistically characterize the competitive outcome at t_{3}, we defined the winning asymmetry index, WinR, and the abundance asymmetry index, AbunR (see Methods). As shown in Fig. S2a, we found a strong positive correlation (*R*^{2} = 0.740, *P* < 0.001) between AbunR and WinR, indicating that if any population is more abundant at the “full occupied” time (t_{2}), it is more likely to finally win the competition (i.e., occupy the entire space at t_{3}) (Fig. S2b). These results strongly suggested that one population may obtain an asymmetric benefit from the random manners of colonizing space in the “occupation stage”, a benefit that assists this population in colonizing more space at t_{2}, thus largely determining the ultimate outcome of the competition.

All of these initial explorations of the model indicated that, in addition to the growth rate [39] and initial cell numbers [40], the random manners of colonizing space in the “occupation stage” may provide a considerable competitive edge for a population to colonize space.

### ‘Space Accessibility’ affects outcomes of spatial competition

#### A larger initial distance of cells is conducive to success in competition

We next investigated that what manners of colonizing space will help to win the competition. Since the competition outcome changes with different initial cell distributions (Fig. S1), we first explored how the differences in features of initial cell distributions affect the outcome of subsequent spatial competition. Our model assumed that the direct competition between different cells occurred only when cells are located adjacent to each other (assumption 2 and assumption 3). Based on these assumptions, if cells from one population possess greater distance among each other (in other words, distributed more scattered), the undesirable intrapopulation competition can be avoided, and thus they may possess a higher probability to occupy more space. Therefore, we hypothesized that if one population exhibited a higher degree of scatter at time point t_{1}, it will potentially occupy more space at time point t_{2}, resulting in a higher probability to emerge as the winner.

To compare levels of scatter (Fig. 1c) of the initial cell distribution between two populations, we defined the scatter asymmetry index, ScatR (see Methods). To investigate whether the initial scatter level affects the competition outcome, we selected 215 initial cell distributions randomly, which covered a gradient of ScatR values of the focus population ranging from –1.009 to 1.053 (Blue lines in Fig. S3). We then performed 100 replicated simulations for each initial distribution, to reveal the relationship between the competition outcome and ScatR. Our results showed that AbunR was positively associated with ScatR at significant levels (Fig. 2a; *R*^{2} = 0.284, *P* < 0.001), indicating that the population initialized with more scattered cell distribution would occupy more space at t_{2}. Moreover, a positive relationship was also observed between WinR and ScatR (Fig. 2b; *R*^{2} = 0.291, *P* < 0.001), further suggesting that the benefit obtained from more scattered initial cell distribution contributed to the ultimate dominance of this population.

#### The higher degree of expansion freedom helps populations to win space competition

In addition to initial distance, we found that for a given initial distribution, AbunR considerably varied across different expansion processes, indicating that in addition to the randomness in the initial cell distribution, the random events occurring during population expansion in the “occupation stage” also affected the competition outcome. Our model assumed that after a successful division of one cell, all adjacent grids around the mother cell are randomly selected to accommodate the newly born cell (Fig. 1a; assumption 2). If the selected box has been occupied, the newborn cell will compete for the box with the aborigine of the box and has a 50% probability to survive (assumption 3). We defined the number of empty grids surrounding the newborn cell as the degree of expansion freedom. Thus, if the daughter cell possesses a higher degree of expansion freedom, the probability for its offspring to survive will be higher (Fig. 1d; the purple cell). In contrast, if the degree of expansion freedom of the daughter cell is low, it has to compete for space with other cells for further reproduction and expansion, which should be less favored for the space competition afterward (Fig. 1d; the orange cell). This assumption leads to a prediction that the population whose daughter cells possess a higher degree of expansion freedom will be more likely to win the competition.

To test this prediction, we defined the expansion freedom asymmetry index, FreeR (see Methods). We selected 363 initial cell distributions with a zero ScatR (Fig. S3) from 1,000,000 random distributions and performed 100 replicated simulations with each initial distribution. During these simulations, we recorded the degrees of expansion freedom of every newborn cell during the ‘occupation stage’ (Fig. 1d; Fig. S4) and then compared the FreeR of the focus population with its AbunR in each simulation. We observed a strong positive relationship between FreeR and AbunR (Fig. 2c; *R*^{2} = 0.679, *P* < 0.001), suggesting that the population with greater ‘expansion freedom’ would occupy more space at t_{2}. Furthermore, the FreeR of the focus population was significantly higher when it won than it lost (Fig. 2d; *t*-value = 5.343, df = 999, *P* < 0.001), which is consistent with our prediction.

Together, these results demonstrated that the randomness during the “occupation stage” of spatial competition, including the initial scatter level and the degree of expansion freedom, can affect the outcome of competition for space.

#### Populations with higher ‘Space Accessibility’ have a higher winning probability in spatial competition

Because both the initial scatter level and the degree of expansion freedom affect the number of empty grids that surrounded individuals of the focus population at each time point, we then searched for a more general parameter that considered both of the two factors. We applied a mathematical induction algorithm to define a new parameter, Space Accessibility (SA_{k,t}, k = 1 means the focus population and k = 2 means its competitor; Fig. S5). Individuals of a population are further away from the aggregation area, where more grids have been occupied, the ‘Space Accessibility’ of this population is higher. The ‘Space Accessibility’ at each time point (SA_{k,t}) assesses the maximum probability of cells of one population colonizing all the empty grids in the subsequent steps from this time point to the “full occupied” time (t_{2}), which reflects the ease with which offspring cells occupy these empty positions. Next, we integrated SA_{k,t} value over time (obtaining SA) for each population. To estimate which population generally was more likely to occupy the empty positions during the “occupation stage”, we next defined an index called SAR (see Methods). A SAR index greater than zero indicates that the focus population has a higher probability of reaching empty positions than its competitor across the “occupation stage”.

To investigate whether the difference in ‘Space Accessibility’ affects the competition outcome, we performed 20,000 simulations covering SAR values of the focus population ranging from −1.808 to 1.754. In these simulations, we found that ScatR (Fig. S6a; *R*^{2} = 0.271, *P* < 0.001), as well as FreeR (Fig. S6b; *R*^{2} = 0.986, *P* < 0.001), was positively correlated with the SAR, suggesting that SAR reflected the change of both ScatR and FreeR. To test the influence of ‘Space Accessibility’ for competition, we next analyzed the relationship between SAR of the focus population and its AbunR at t_{2} time point. The results showed an extremely significant positive correlation between SAR and AbunR (Fig. 3a; *R*^{2} = 0.833, *P* < 0.001), suggesting that the population with higher ‘Space Accessibility’ would occupy more space at t_{2}. The correlation coefficient between AbunR and SAR was higher than the coefficients of both AbunR-ScatR and AbunR-FreeR, indicating that SAR represented a more suitable parameter to evaluate competition outcomes. Furthermore, the SAR of the focus population was significantly higher when it won than it lost (Fig. 3b; *t*-value = 8.392, df = 999, *P* < 0.001), further indicating that the ‘Space Accessibility’ predicted the outcome of spatial competition between two populations with a high degree of reliability.

We also performed numerous well-designed simulations (see Supplementary Information S2 for details) to test whether the effect of ‘Space Accessibility’ on the outcome of spatial competition was statistically significant under various initial conditions (robustness test), including varied initial growth rates, total numbers of initial cells, as well as sizes of the space (Table S4). Our analysis showed that the effect of ‘Space Accessibility’ on the outcome of spatial competition was significant (Table S4; Fig. S7), and largely unperturbed by changes in initial growth rates, space sizes, and initial total numbers of cells (not exceed 10% of the maximum population size). In summary, colonizing space in a more dispersed manner contributes to microbial competitive success.

#### A ‘smart population’ occupies more space

Next, we tested whether ‘Space Accessibility’ determined the competition outcome from another perspective. We designed simulations of competition between SmartBac and NormalBac (called ‘SmartGo’; see Methods). We hypothesized that SmartBac would obtain a higher competitive edge from its superior strategy of space colonization, and win the competition for space against NormalBac.

As expected, SmartBac won (Video S3) 7302 times during 10,000 mathematical simulations of the SmartGo model, accounting for 73.02%. While, in the corresponding null model (competition between NormalBac and NormalBac), the focus NormalBac won 5088 times during 10,000 mathematical simulations, accounting for 50.88%. In these 20,000 simulations, SAR values of the SmartBac in the SmartGo model were significantly higher than those of the focus NormalBac in the null model (Fig. 4a; *t*-value = 30.104, df = 999, *P* < 0.001). Furthermore, the AbunR values of SmartBac in SmartGo model were also significantly higher than those of focus NormalBac in null model (Fig. 4b; *t*-value = 40.763, df = 999, *P* < 0.001).

We also designed simulations of competition between SmartBac and NormalBac, and the latter has a growth advantage. A parameter ({{{{{{{mathrm{GrowAdv}}}}}}}}_{NormalBac}) was defined to reflect the growth rate advantage of NormalBac relative to SmartBac (see Methods). The results showed that as the ({{{{{{{mathrm{GrowAdv}}}}}}}}_{NormalBac}) increased, the winning probability of SmartBac decreased (Fig. S8). The winning probability curve of SmartBac intersects the line of 50% winning probability at (0.0083, 0.5), which means that SmartBac can compete with NormalBac, which has a 0.83% growth advantage, by compensating for the growth disadvantage with a more dispersed strategy.

In order to explore the impact of ‘Space Accessibility’ on competition from a wider perspective, we further defined an attribute for SmartBac, namely the proportion of SmartBac (see Methods). We ran *60,000* simulations of competition in total between NormalBac and different proportions of SmartBac (see Supplementary Information S1). The results showed that populations with higher proportions of SmartBac had average higher SAR values across all competitive simulations (Fig. S9a). Moreover, the population with a higher proportion of SmartBac had a higher probability of winning in the competition with Normalbac (Fig. S9b).

Together, the results further indicated that microbial colonization of space in a more dispersed manner helped to win the competition.

### Space colonization manners, growth rates, and initial abundances synergistically affect spatial competition

It is well established that microbial competition for space is influenced by the growth rate and initial abundance of competing populations. The population possessing a faster growth rate, or higher initial abundance will outcompete other strains present within the newly occupied space. To assess the relative contribution of space colonization manners, growth rates, and initial abundances in spatial competition, to microbial competitive success, we performed simulations in which the growth rates and initial abundances of the two populations were set to be different (see Supplementary Information S1 for details). In these simulations, we defined the parameter GroR as the difference in growth rate between a population and its competitor, as well as defined InifR to characterize the difference in initial abundances (see Supplementary Information S1; Fig. 5a). In addition, we calculated SAR of the focus population in each simulation to quantify the asymmetry of ‘Space Accessibility’.

As shown in Fig. 5, even when one population exhibited a lower growth rate, or was characterized by the lower initial abundance, colonization of space in a more dispersed manner, such as choosing positions for new cells to have a higher ‘Space Accessibility’, may neutralize these disadvantages and allow this population to occupy more space at t_{2} (Fig. 5b), thus winning the spatial competition (Fig. 5c). To more clearly display comparison results between the spatial advantage obtained by the dispersed strategy and the growth rate or initial abundance advantage, we added two-dimensional plots of GroR and SAR, InifR and SAR in Fig. S10.

The collinearity analysis showed that when strains differed in their initial abundances, SAR and InifR exhibited significant collinearity (VIF = 13.062, VIF is short for variance inflation factor). To eliminate this collinearity effect, we generalized our definition of SAR by defining a new parameter perSAR (see Supplementary Information S1), which is equal to SAR when the initial cell number of both populations are same (InifR = 0), but allows for better quantification of the asymmetry of ‘Space Accessibility’ when InifR is unequal to zero. A subsequent collinearity test showed that the collinearity among the variables perSAR, GroR, and InifR disappeared (Table S5). Moreover, the population possessing a higher perSAR value was characterized by a higher probability for ultimate survival at the end of the simulation and won the competition even when its growth rate or initial abundance was lower (Fig. S11).

We next performed multiple regression analysis to quantify the relative contributions of these three factors during the spatial competition (Table S5). Our analysis showed that the ratio of relative contributions of perSAR, GroR, and InifR to AbunR was ~1.027, 55.393, and 1.027 (1:53.94:1), suggesting that the competitive disadvantage derived from lower GroR of a population could be eliminated by possessing 53.94 times higher perSAR, and the competitive disadvantage derived from lower InifR could be neutralized by 1-time higher perSAR. Together, these results indicated that microbial colonization of space in a more dispersed manner could benefit the competitive success of slow-growing species or species possessing lower seeding abundance.

In summary, compared with the evident competitive edge derived from a faster growth rate and higher initial abundance of one competitor, colonization of space in a more dispersed manner (e.g., possessing higher ‘Space Accessibility’) also played a critical role in determining the success rate during the competition for space between microbial strains.

Source: Ecology - nature.com