One of the fundamental questions in ecology is why species occur in some areas and not in others. Range limits, the boundaries between a species’ presence and absence, reflect the interplay of dispersal and population dynamics driven by biotic and abiotic conditions. As a result, range limits may shift as dispersal barriers are removed, climates change, and local species composition is altered, but the relative importance of these mechanisms is still not well understood. This is particularly true for introduced species, where current range limits may or may not reflect range limits at equilibrium, and is becoming more pressing under the effects of global climate change. To understand the drivers and stability of range limits in introduced Rumex conglomeratus, we used common garden experiments growing plants within, at the edge of and beyond their current range edge. Seeds were sourced from both lowland and upland populations and planted at all three sites. By measuring survival, growth, and the occurrence of reproduction, we tested whether upland populations are locally adapted to high elevation sites and whether plants were capable of surviving and reproducing above the current range edge. However, we found that upland populations were not better adapted to higher elevations, and often were small and performed more poorly than lowland populations across sites. Upland populations appear to be maintained by human-aided seed dispersal from lowland populations, which may constrain the opportunity for local adaptation. Although some plants survived above the current range edge, frost and growing season length restricted plant size and reproduction was infrequent. Therefore, the current range limit seems unlikely to expand as long as regular frost continues at the range edge and dispersal from the lowland continues to prevent local adaptation to upland environments.