Microbial populations often assemble in dense populations in which proliferating individuals exert mechanical forces on the nearby cells. In https://doi.org/10.1073/pnas.1809587115, we showed that mechanical interactions among cells affect the competition between different genotypes in growing yeast colonies. Our experiments demonstrate that these physical interactions have two related effects: they cause the prolonged survival of slower-growing strains at the actively-growing frontier of the colony and cause faster-growing strains to increase their frequency more slowly than expected in the absence of physical interactions. These effects also promote the survival of slower-growing strains and the maintenance of genetic diversity in colonies grown in time-varying environments. A continuum model inspired by overdamped hydrodynamics reproduces the experiments and predicts that the strength of natural selection depends on the width of the actively-growing layer at the colony frontier. We verify these predictions experimentally. The reduced power of natural selection observed here may favor the maintenance of drug-resistant cells in microbial populations and could explain the apparent neutrality of inter-clone competition within tumors.