Diane:

>> "... don't have time to adapt..."

Yes, the pace of evolution compared to the pace of propagation of the plants leaves us with an invasion by the introduced species. Spartina alterniflora and Spartina townsendii found friendly physical conditions when they were introduced to the West Coast. In time, organisms that consume other plant species may gradually evolve toward exploiting these grasses as a food source and reduce their abundance. While that is happening, other species of plants that live in tidal marshes may gradually become more adept at competing with these grasses for space. But there is no guarantee that this will happen, as evidenced by the natural tendency for Spartina alterniflora to dominate the portions of tidal marshes below the mean high tide line on the East Coast.

The Japanese Beetle is an example of an introduced species that overwhelmed roses, willows, and other species of plants when it was introduced to the United States, but has since become much less abundant due to natural enemies.

Another interesting case is the introduced Ginkgo. While not invasive, it is noteworthy for its few natural enemies, perhaps because it nearly became extinct, which could have wiped out the organisms that depended on it as food.