When plants are planted outside of their normal hardiness zone, there may be no animals or other plants to keep them from taking over. The plants end up growing rapidly and reproducing exponentially until they overwhelm native plant species. At this point, the new plant is labeled "invasive."
Invasive plants don't have to be weeds. Blackberries, which when grown in areas that get plenty of snow and long, cold winters, die off each year. Grown in places like Colorado and Idaho, the plants are manageable. Vancouver Island, off the British Columbia mainland, is known for its relatively mild winters, however. Imported blackberry plants multiplied and now cover thousands of acres of private and public lands, replacing local vegetation. In this area, blackberries are considered invasive.
Scotch broom is another plant that has taken over Vancouver Island. Native to the Mediterranean, it normally grows in hot, dry conditions. On the island, the abundance of water causes the plant to rapidly spread along highways and in meadows, growing almost everywhere. Despite annual clean ups of Scotch broom, the plant continues to flourish, thanks to seeds that can lie dormant for decades. The flowers are a pretty shade of yellow, but on Vancouver Island, Scotch broom is considered an invasive weed.