Abstract The island rule is a putative pattern in island evolution, where small species become larger on islands and large species become smaller. Despite decades of study, a mechanistic explanation for why some taxonomic groups obey the island rule, while others do not, has yet to be identified. Here, we explore whether the island rule might result from evolutionary drift. We derived a simulation model that predicts evolutionary size changes on islands based on random evolutionary trajectories along bounded trait domains. The model consistently predicted the island rule and could account for its occurrence in plants inhabiting islands in the Southwest Pacific. When support for the island rule was not detected, insular gigantism was often observed, suggesting that natural selection was at work. Overall results indicate that evolutionary drift can provide a parsimonious explanation for the island rule, suggesting future work should focus on circumstances where it does not occur.