Common Buckthorn, Rhamnus cathartica and Glossy Buckthorn, Rhamnus frangula, often have been planted to provide privacy for homeowners. On your property Buckthorns have revealed their ugly side by creating impenetrable thickets that will be very difficult to remove. Not surprisingly, Buckthorns are considered invasive in many states. Your neighboring state of Wisconsin presently lists both Buckthorns as invasive. Click on the link to see Invasive Species information provided by the Wisconsin Department of Natural Resources. The Plant Conservation Alliance, Alien Plant Working Group provides a contact person from whom you can find out how to remove the Buckthorns on your particular property.
An article from the American Rivers website describes the combined efforts of citizens and conservation groups in St. Paul who are attempting to re-claim five miles of Mississippi River shoreline presently choked by Common Buckthorn and Japanese Honeysuckle. They hope to replace the offending plants with native plants so that citizens can enjoy the river views in a natural setting. A media campaign that publicizes this volunteer effort will serve to educate St. Paul citizens about the problem of invasive exotic plants. These kinds of programs are springing up all over the United States and that is very encouraging.
Clearly, if we stop the introduction of potential new exotics from coming into the United States, if we get a handle on controlling those we already have, and if we increase the re-introduction of native plants, there is hope that we can turn things around. Just as with a fire that is out of control, it makes sense first to put out the fire and then deal with fixing the damage. Lively debates in professional magazines and journals suggest that the nursery trade is beginning to address the problem of invasive exotics. For example, several cultivars of Miscanthus sinensis, or Maiden Grass, face considerable scrutiny as growers and nursery professionals discover the ability of Miscanthus to escape cultivation and become invasive. A few years ago the same thing happened with Purple Loosestrife, Lythrum salicaria, a popular perennial for American gardens that moved into wetlands with disastrous results. It was banned in most states and is now virtually off the market. It would be interesting to find out if Buckthorns are still sold at your own local garden centers.
I mention these examples to show the severity of the problem. We have to make better choices, and in your case Barbara, the Elderberry or Juneberry would have been better choices for the former owners. But they didn't know then what we know now. Since our government spends billions on the invasive exotics problem, let's do our part by selecting garden plants responsibly. Getting off the soapbox now...