Successful microbial colonization of space in a more dispersed manner

Competition for limited resources, especially nutrients and space, is a central driver of biodiversity and evolution across micro- and macro-organisms. In microbial systems, rapid growth and small size enable dense colonization of surfaces (biofilms), where competition is intense. While many evolved biotic strategies (e.g., resource privatization, metabolic diversification, motility, adhesion) affect competitive outcomes, abiotic factors can also modulate competition, often by altering growth rates (e.g., temperature, pH). Recent work suggests some abiotic processes (e.g., emigration) can change outcomes without changing fitness. A key open question is whether spatially related abiotic factors that do not alter growth rates nonetheless affect competitive outcomes, helping explain how slow-growing microbes persist alongside faster competitors. Prior work indicated that, even with equal initial abundance and fitness, spatial competition outcomes are influenced by relative positions and order of appearance, paralleling macroscopic plant ecology phenomena (chance dispersal, site history). Inspired by the board game Go, where spatial layout and expansion strategies determine territorial success, the authors hypothesize that spatial colonization manners—initial spatial positions and subsequent expansion directions—significantly influence competitive success. To test this, they construct an individual-based model (BacGo) to simulate two populations competing for limited space and quantify how spatial colonization manners affect outcomes.

Model framework (BacGo): An individual-based, lattice model on a 2D 20×20 grid represents a microhabitat. Each grid cell can be occupied by one microbial individual. Two populations compete to occupy the grid. Assumptions and growth: Nutrients are unrestricted and each cell grows at a constant rate μi per dBi/dt = μi×Bi. Default μi is 0.1 fg/fg-min for all cells of both populations. Initial biomass per individual is 150 fg. Upon reaching a biomass threshold (upper threshold noted as 28), a cell divides: the mother remains; the daughter randomly selects one of the 8 neighboring grids (edge: 5; corner: 3). If the chosen grid is occupied, the newborn competes with the occupant with a 50% survival probability. Random death events occur with probability 1e-6. Two stages define dynamics: occupation stage (from initial time t1 until full occupancy t2) and exclusion stage (from t2 until one population exclusively occupies all space at t3). Simulation environment and data: Simulations run for ≥50,000 steps until a winner emerges. Code is in C++ (GitHub: https://github.com/Neina-0830/BacGo-model), executed on Windows Server 2019 (AliCloud). Positions, biomass of every cell, and population abundances are recorded at each time point. Visualization and analysis use Wolfram Mathematica scripts (GitHub), videos assembled via ImageJ and encoded H.264. Outcome metrics: Abundance asymmetry at t2 (AbunR) = log(Abun1/Abun2), where Abun1 and Abun2 are relative abundances at t2. Win asymmetry (WinR) = log(winpro1/winpro2) from 100 replicate runs per initial distribution. Spatial colonization parameters: Initial scatter asymmetry (ScatR) = log(σ1/σ2), where σk is the mean Euclidean distance of cells from the population centroid (scatter level). Expansion freedom asymmetry (FreeR) = log(Σt freedom1,t / Σt freedom2,t) where freedomk,t is the average number of empty neighboring grids around daughters born at time t. Space Accessibility (SAk,t) is defined by a mathematical induction algorithm to assess the ease for a population to reach empty grids from time t to t2; its integrated asymmetry SAR = log(SA1/SA2) quantifies overall accessibility advantage during occupation. Definitions and computation details reside in Supplementary Information S1. Smart vs normal strategies: SmartBac is a “smart” population designed to always place daughters to maximize current SA (i.e., more dispersed colonization), determined by evaluating all feasible daughter placements each division and selecting the configuration with maximal SAkt. NormalBac follows random daughter placement per basic model. SmartGo simulations pit SmartBac vs NormalBac; a null model pits NormalBac vs NormalBac. Growth advantage experiments: GrowAdvNormalBac = (GroNormalBac − GroSmartBac)/GroSmartBac quantifies NormalBac’s growth-rate advantage; simulations vary this to assess how spatial strategy compensates growth disadvantages. Additional experiments vary the proportion of SmartBac placements within a population. Heterogeneity and robustness: Additional simulations test robustness to different growth rates, initial cell numbers, and space sizes (see Supplementary S2; Table S4, Fig. S7). Multi-factor simulations: Define GroR (growth-rate difference between populations) and InifR (difference in initial abundances). Run 89,100 simulations spanning gradients of SAR, GroR, and InifR. Address multicollinearity between SAR and InifR by defining perSAR (a generalized SAR that equals SAR when InifR=0 and decouples from initial abundance when InifR≠0). Perform multiple regression to quantify relative contributions of perSAR, GroR, and InifR to AbunR (Table S5). Statistics: Chi-square tests (chisq.test), two-sample two-tailed t-tests (t.test) with subsampling 1000 values per group to control for data size, linear regressions (lm), Cohen’s D (Isr::cohensD), and multiple regression/multicollinearity (IBM SPSS 27).

• Basic competition outcome: With equal growth rates and initial numbers (10 cells/population), 20,000 simulations with random initial distributions yield a single winner in each run, consistent with competitive exclusion. The focus population won 10,177/20,000 vs expected 10,051/20,000; Chi-square P=0.211, consistent with the 50% survival assumption in grid contests. Replicates from the same initial distributions show winning probabilities depend on initial positions but never reach 100%, implicating stochastic colonization events.
• Abundance at full occupancy predicts ultimate victory: AbunR at t2 strongly predicts WinR at t3 (R^2=0.740, P<0.001), indicating early space capture largely determines final outcome.
• Initial scatter matters: More dispersed initial distributions increase competitive advantage. Across 215 initial distributions (100 replicates each), ScatR correlates positively with AbunR (R^2=0.284, P<0.001) and with WinR (R^2=0.291, P<0.001).
• Expansion freedom during occupation matters: With ScatR=0 (363 initial distributions; 100 replicates each), FreeR correlates strongly with AbunR (R^2=0.679, P<0.001). FreeR is significantly higher in wins vs losses (t=5.343, df=999, P<0.001).
• Space Accessibility unifies predictors: SAR (integrated accessibility) correlates extremely strongly with AbunR (R^2=0.833, P<0.001) and is higher in wins than losses (t=8.392, df=999, P<0.001). SAR reflects both ScatR (R^2=0.271, P<0.001) and FreeR (R^2=0.986, P<0.001). Effects are robust across varied growth rates, space sizes, and initial total cell numbers (within tested ranges; Table S4, Fig. S7).
• Smart colonization strategy outcompetes random: SmartBac (maximizing SA at each division) vs NormalBac: SmartBac wins 7302/10,000 (73.02%) vs 5088/10,000 (50.88%) for the focus population in NormalBac vs NormalBac null model. SAR is significantly higher in SmartGo SmartBac vs null-model focus NormalBac (t=30.104, df=999, P<0.001); AbunR is also higher (t=40.763, df=999, P<0.001).
• Compensation for growth disadvantage: As NormalBac’s growth advantage increases (GrowAdvNormalBac), SmartBac’s win probability declines, intersecting 50% at GrowAdvNormalBac≈0.0083 (0.83%), showing that dispersed colonization can offset a modest growth-rate disadvantage.
• Partial “smart” strategies: Increasing the proportion of SmartBac behaviors raises average SAR and winning probability against NormalBac across 60,000 simulations (Fig. S9), reinforcing the benefit of dispersed colonization.
• Joint effects of space strategy, growth, and initial abundance: In 89,100 simulations spanning SAR (or perSAR), GroR, and InifR, more dispersed colonization (higher SAR/perSAR) can neutralize disadvantages in growth rate or initial abundance, increasing AbunR at t2 and win probability at t3 (Figs. 5, S10, S11). Multiple regression indicates relative contributions to AbunR of perSAR:GroR:InifR ≈ 1.027:55.393:1.027 (~1:53.94:1). Thus, a substantial increase in perSAR can offset a growth-rate disadvantage, and perSAR comparable in magnitude to InifR can offset initial seeding disadvantage.

The study demonstrates that spatially related abiotic factors—specifically, how populations disperse to and expand within free space—substantially influence outcomes of microbial competition independently of intrinsic growth rates or initial abundances. Early space capture (higher AbunR at t2) largely determines the final winner, and two key spatial processes drive this: (1) initial scatter reduces intrapopulation interference, enabling broader frontier access; (2) higher expansion freedom for daughter cells minimizes immediate conflicts and supports continued outward growth. Space Accessibility (SAR) integrates these aspects and reliably predicts competitive success. A strategy that intentionally maximizes accessibility (SmartBac) secures more territory and often wins, even against slightly faster-growing competitors, suggesting a plausible route by which slow growers persist via superior spatial tactics. These findings parallel strategic principles from the Go board game and align with empirical observations of surface colonization dynamics, while offering a quantitative framework to parse stochastic events during occupation. The results imply that in spatially structured habitats (biofilms, soils), variability in colonization histories across microhabitats can foster coexistence and maintain biodiversity. They also suggest that traits enabling sensing and directed movement toward emptier regions (e.g., via quorum sensing gradients or surface trail-following modulation) could be under positive selection during spatial competition.

• Main contributions: Introduces BacGo, an individual-based spatial competition model quantifying how colonization manners affect microbial competitive success. Identifies initial scatter and expansion freedom as key stochastic spatial factors, unified by Space Accessibility (SAR), which strongly predicts outcomes. Demonstrates that a dispersed colonization strategy (maximizing SAR) increases space capture at full occupancy and final win probability, and can compensate for modest disadvantages in growth rate or initial abundance.
• Broader implications: Provides a quantitative, generalizable perspective for understanding how spatial competition shapes community assembly and biodiversity. Insights may extend to macroorganisms and inform ecological restoration strategies where initial spatial seeding patterns matter.
• Future directions: Extend the model to multi-species and higher-order interactions; incorporate environmental stressors and trade-offs between aggregation (stress resistance) and dispersion (competitive space capture); perform experimental evolution and real-time imaging assays to test whether microbes evolve strategies to maximize space accessibility; refine mechanistic links to sensory/motility systems that could implement dispersed colonization in vivo.

• Model scope: Pairwise competition only; higher-order interactions and multispecies dynamics are not modeled.
• Environmental simplifications: Unlimited nutrients, constant growth rates, 2D fixed-size lattice, and no environmental stressors (e.g., antibiotics, desiccation, predation) considered.
• Placement and conflict rules: Daughter placement is local (Moore neighborhood) with random choice in the basic model; occupied-cell contests resolved by a fixed 50% survival chance; random death rate fixed at 1e-6.
• Parameter idealizations: Some thresholds (e.g., biomass at division) and rates are simplified and may not map directly to specific organisms.
• Empirical validation: Findings are based on simulations; direct experimental validation across taxa and environments is needed to confirm generality.