Interspecific interactions are fundamental drivers of animal space use. Yet while non-consumptive effects of predation risk on prey space use are well-known, the risk of aggressive interactions on space use of competitors is largely unknown. We apply the landscape of risk framework to competition-driven space use for the first time, with the hypothesis that less aggressive competitors may alter their behaviour to avoid areas of high competitor density. Specifically, we test how aggressive risk from territorial algal-farming damselfishes can shape the spatial distribution of herbivore fish competitors. We found that only the most aggressive damselfish had fewer competitors in their surrounding area, demonstrating that individual-level behavioural variation can shape spatial distributions. In contradiction to the landscape of risk framework, abundances of farming damselfish and other fishes were positively associated. Our results suggest that reef fishes do not simply avoid areas of high damselfish abundance, but that spatial variation in aggressive behaviour, rather than of individuals, created a competitive landscape of risk. We emphasize the importance of individual-level behaviour in identifying patterns of space use and propose expanding the landscape of risk framework to non-predatory interactions to explore cascading behavioural responses to aggressive risk.