Significance Many microbial populations proliferate in small channels. In such environments, reproducing cells organize in parallel lanes. Reproducing cells shift these lanes, potentially expelling other cells from the channel. In this paper, we combine theory and experiments to understand how these dynamics affects the diversity of a microbial population. We theoretically predict that genetic diversity is quickly lost along lanes of cells. Our experiments confirm that a population of proliferating Escherichia coli in a microchannel organizes into lanes of genetically identical cells within a few generations. Our findings elucidate the effect of lane formation on populations evolution, with potential applications ranging from microbial ecology in soil to dynamics of epithelial tissues in higher organisms.