I hate to say this but we have to add Bradford pear and butterfly bushes to the invasive list. I heard about this from master gardener Laurie Proctor and googled this for more information.
It stands to reason that a plant with pretty flowers and produces seeds would be able to spread. Last year while driving to Florida, I did notice Bradford pear trees growing wild along the highway here and there in Tennessee and Alabama.
I would like to quote from the Missouri Columbia Parks and Recreation website. "In the past, the potential for self-fruiting had generally been minimal because cultivars of Pyrus calleryanna were considered to be self-incompatible, unable to self-pollinate or produce fertile fruit from a genetically identical cultivar.
However, by the late 1990s, it had become apparent in communities with large numbers of ornamental pear trees that many cultivars had unexpectedly begun to interbreed fairly readily. The hybrid fruit is eaten by starlings and other birds. The seeds are then dispersed into nearby fields, right-of-ways, parks or other natural open areas. Highly variable, many of the seedlings show characteristics such as thorniness that had been purposely bred out of their parent cultivar."
I have to admit the pear trees planted along the street and at Headwaters Park are pretty in the spring. I even have one planted in my yard, so I find this a sad reality.
I also have a butterfly bush in my yard. A number of states now ban the planting of butterfly bushes on public lands. Some states even prohibit the sale or commercial cultivation of the plant.
I can keep it from spreading by deadheading the flowers before they go to seed, but I am just going to cut it down. Turns out it really isn't that beneficial for the butterflies. Yes, it attracts butterflies, but so will other flowers. In fact, not a single native North American caterpillar will feed on its leaves.
I am including a few weblinks that you might find interesting.