Random motility regulation as a generic mechanism of community formation.

The self-organization of microbial ecosystems involves a large variety of mechanisms, ranging from biochemical signaling to population dynamics. Among these, the role of motility regulation has been little studied, despite the importance of active migration processes. Here we show how weak, random motility regulation suffices to induce complex forms of organization in bacterial mixtures comprising a large number of coexisting strains. First, we simulate microscopic models of run-and-tumble bacteria whose self-propulsion speeds are weakly regulated by the local density of each strain, mimicking the impact of weak, random metabolic interactions. Our simulations reveal that, as the heterogeneity of the interaction network increases, the system undergoes a phase transition leading to the emergence of distinct, spatially segregated communities. To account for these results and assess their robustness, we use random-matrix theory to analyze the hydrodynamic description of the bacterial mixture, obtaining a quantitative agreement with our microscopic simulations. Our results hold for a variety of motility-regulation mechanisms and highlight the need to characterize the role of motility regulation in experimentally relevant situations.