Geometric ordering in bacterial communities

The organization of bacteria has a central role in shaping interactions, dynamics, and composition within communities and microbiomes. Bacteria form distinct spatial patterns that have often been attributed to microbial processes such as chemotaxis, nutrient transport, and signaling. However, common patterns are observed across distinct bacteria and conditions, suggesting that a general organizing principle could direct bacterial organization. Here, we find that the organization of bacteria is explained by geometric ordering that promotes space-filling efficiency, giving rise to geometric patterns known as Voronoi tessellations. We find that the Voronoi Growth Model accurately predicts bacterial pattern formation in diverse conditions including in biofilms at the liquid-air interface, swimming populations, the zebrafish gut, and conditions that promote swarming. The patterns are observed in two and three dimensions, at the cm and mm length scales, across diverse species (Vibrio cholerae, Pseudomonas aeruginosa, Escherichia coli), arise solely from the principles of Voronoi tessellation, and require no detailed knowledge of microbial processes. Entropic considerations show that bacteria provide little or no information about the pattern formation, which is determined solely by their initial positions and environmental conditions. These findings demonstrate that bacterial communities achieve robust, reproducible organization through a universal geometric principle, linking microbial patterning to the broader biological context of multicellular organization.