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Abstract Bacterial biofilms, surface-attached microbial communities, grow horizontally across surfaces and vertically above them. Although a simple heuristic model for vertical growth was experimentally shown to accurately describe the behavior of diverse microbial species, the biophysical implications and theoretical basis for this empirical model were unclear. Here, we demonstrate that this heuristic model emerges naturally from fundamental principles of active fluid dynamics. By analytically deriving solutions for an active fluid model of vertical biofilm growth, we show that the governing equations reduce to the same form as the empirical model in both early- and late-stage growth regimes. Our analysis reveals that cell death and decay rates likely play key roles in determining the characteristic parameters of vertical growth. The active fluid model produces a single, simple equation governing growth at all heights that is surprisingly simpler than the heuristic model. With this theoretical basis, we explain why the vertical growth rate reaches a maximum at a height greater than the previously identified characteristic length scale. These results provide a theoretical foundation for a simple mathematical model of vertical growth, enabling deeper understanding of how biological and biophysical factors interact during biofilm development. 

Surface attached communities of microbes grow in a wide variety of environments. Often, the size of these microbial community is constrained by their physical surroundings. However, little is known about how size constraints of a colony impact the outcome of microbial competitions. Here, we use individual-based models to simulate contact killing between two bacterial strains with different killing rates in a wide range of community sizes. We found that community size has a substantial impact on outcomes; in fact, in some competitions the identity of the most fit strain differs in large and small environments. Specifically, when at a numerical disadvantage, the strain with the slow killing rate is more successful in smaller environments than in large environments. The improved performance in small spaces comes from finite size effects; stochastic fluctuations in the initial relative abundance of each strain in small environments lead to dramatically different outcomes. However, when the slow killing strain has a numerical advantage, it performs better in large spaces than in small spaces, where stochastic fluctuations now aid the fast killing strain in small communities. Finally, we experimentally validate these results by confining contact killing strains ofVibrio choleraein transmission electron microscopy grids. The outcomes of these experiments are consistent with our simulations. When rare, the slow killing strain does better in small environments; when common, the slow killing strain does better in large environments. Together, this work demonstrates that finite size effects can substantially modify antagonistic competitions, suggesting that colony size may, at least in part, subvert the microbial arms race.