Background: The wetland grass, Phalaris arundinacea, is invasive in North America but native to Europe. Aim: Compare experimentally how a native species and an invasive species may respond to changing environmental conditions. Methods: Sample both native and invasive populations from near the centre and the margin of their ranges. Native, centre: Czech Republic; native, range margin: Mediterranean France; invasive, centre: Vermont; invasive, range margin: North Carolina. Use 18 invasive and 18 native genotypes of P. arundinacea. Plant them into four common gardens along a latitudinal gradient in the eastern USA (Vermont, North Carolina, Georgia, Florida). Measure mean phenotypic traits, phenotypic plasticity, and genetic variances in each garden. Results: The plants grew best in the North Carolina garden, where the invasive genotypes are larger, taller, and produce more tillers than their native counterparts. But these differences did not appear in the other gardens. In addition, although we predicted higher phenotypic plasticity for the invasive genotypes, we found only modest differences in phenotypic plasticity between native and invasive genotypes. Populations growing close to their presumed ideal growing conditions (as measured by plant biomass) have similar and relatively high genetic variances. Thus, populations growing under favourable conditions have the greatest potential to evolve in response to changing environmental conditions. However, where conditions became stressful (as defined by high mortality), only the southern marginal invasive individuals (North Carolina) showed higher genetic variances than the native marginal populations (Mediterranean France). Conclusions: When confronted with a new environment, invasive populations at the range margin had a higher evolutionary potential than native populations.