Mono-dominance by invasive species provides opportunities to explore determinants of plant distributions and abundance; however, linking mechanistic results from small scale experiments to patterns in nature is difficult. We used experimentally derived competitive effects of an invader in North America, Acroptilon repens, on species with which it co-occurs in its native range of Uzbekistan and on species with which it occurs in its non-native ranges in North America, in individual-based models. We found that competitive effects yielded relative abundances of Acroptilon and other species in models that were qualitatively similar to those observed in the field in the two ranges. In its non-native range, Acroptilon can occur in nearly pure monocultures at local scales, whereas such nearly pure stands of Acroptilon appear to be much less common in its native range. Experimentally derived competitive effects of Acroptilon on other species predicted Acroptilon to be 4-9 times more proportionally abundant than natives in the North American models, but proportionally equal to or less than the abundance of natives in the Eurasian models. Our results suggest a novel way to integrate complex combinations of interactions simultaneously, and that biogeographical differences in the competitive effects of an invader correspond well with biogeographical differences in abundance and impact.