Summary The impact of invasive species across their native and nonnative ranges is poorly quantified and this impedes a complete understanding of biological invasions. We compared the impact of the native North American plant, Conyza canadensis, which is invasive to Eurasia, on species richness at home and in a number of introduced regions through well replicated transcontinental field studies, glasshouse experiments and individual‐based models. Our results demonstrated mostly negative relationships between C. canadensis abundance and native species richness in nonnative ranges, but either positive or no relationships in its native North American range. In glasshouse experiments, the total biomass of Conyza was suppressed more by species from its native range than by species from regions where it is nonnative, but the effects of Conyza on other species did not show a consistent biogeographical pattern. Finally, individual‐based models led to the exclusion of Conyza from North American scenarios but to high abundances in scenarios with species from the nonnative ranges of Conyza. We illustrate biogeographical differences in the impact of an invader across regional scales and suggest that inherent differences in one specific aspect of competitive ability, tolerance to the effects of other species, may play some role in these differences.