Many ecosystems worldwide are dominated by introduced plant species, leading to loss of biodiversity and ecosystem function. A common but rarely tested assumption is that these plants are more abundant in introduced vs. native communities, because ecological or evolutionary-based shifts in populations underlie invasion success. Here, data for 26 herbaceous species at 39 sites, within eight countries, revealed that species abundances were similar at native (home) and introduced (away) sites - grass species were generally abundant home and away, while forbs were low in abundance, but more abundant at home. Sites with six or more of these species had similar community abundance hierarchies, suggesting that suites of introduced species are assembling similarly on different continents. Overall, we found that substantial changes to populations are not necessarily a pre-condition for invasion success and that increases in species abundance are unusual. Instead, abundance at home predicts abundance away, a potentially useful additional criterion for biosecurity programmes.