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Biofilms inhabit a range of environments, such as dental plaques or soil micropores, often characterized by noneven surfaces. However, the impact of surface irregularities on the population dynamics of biofilms remains elusive, as most experiments are conducted on flat surfaces. Here, we show that the shape of the surface on which a biofilm grows influences genetic drift and selection within the biofilm. We culture Escherichia coli biofilms in microwells with a corrugated bottom surface and observe the emergence of clonal sectors whose size corresponds to that of the corrugations, despite no physical barrier separating different areas of the biofilm. The sectors are remarkably stable and do not invade each other; we attribute this stability to the characteristics of the velocity field within the biofilm, which hinders mixing and clonal expansion. A microscopically detailed computer model fully reproduces these findings and highlights the role of mechanical interactions such as adhesion and friction in microbial evolution. The model also predicts clonal expansion to be limited even for clones with a significant growth advantage--a finding which we confirm experimentally using a mixture of antibiotic-sensitive and antibiotic-resistant mutants in the presence of sublethal concentrations of the antibiotic rifampicin. The strong suppression of selection contrasts sharply with the behavior seen in range expansion experiments in bacterial colonies grown on agar. Our results show that biofilm population dynamics can be affected by patterning the surface and demonstrate how a better understanding of the physics of bacterial growth can be used to control microbial evolution. [ABSTRACT FROM AUTHOR]