ABSTRACT Conjugation is the primary mechanism of horizontal gene transfer that spreads antibiotic resistance among bacteria. Although conjugation normally occurs in surface-associated growth (e.g., biofilms), it has been traditionally studied in well-mixed liquid cultures lacking spatial structure, which is known to affect many evolutionary and ecological processes. Here we visualize spatial patterns of gene transfer mediated by F plasmid conjugation in a colony of Escherichia coli growing on solid agar, and we develop a quantitative understanding by spatial extension of traditional mass-action models. We found that spatial structure suppresses conjugation in surface-associated growth because strong genetic drift leads to spatial isolation of donor and recipient cells, restricting conjugation to rare boundaries between donor and recipient strains. These results suggest that ecological strategies, such as enforcement of spatial structure and enhancement of genetic drift, could complement molecular strategies in slowing the spread of antibiotic resistance genes.