There's a problem with invasive species. The carp was deliberately introduced into North American waters in the nineteenth century and has now become a competitor of the native fishes for food and space. The European milfoil and the zebra mussel are exotic species that have accidentally found a home in an American environment where they don't appear to have any natural enemies, at least at this time. There are serious government programs to prevent the spread of these organisms, much like there is with Mexicans and other Latin Americans.
We have to keep in mind, however, that there are three dimensions to "problem species". There are those that are truly exotic, like the zebra mussel, but then there are those that are perhaps recovering from reduced numbers and those that were here all along in a domestic mode but have now become "feral". The two outstanding examples of the second category in the Upper Midwest are the wolf, no longer an endangered species in its native habitat of northern Minnesota and Wisconsin, and the Canada goose, a creature that has successfully adapted to modern times to the extent that many people now regard them as a nuisance.
One example of the third group is the feral hog, recently classified as a pest in most of Wisconsin.
There are several implications to this state of affairs. First of all, just as with climate change, regarding new species as undesirable interlopers implies a "steady state" environment, where any change is a negative. This would imply that the celebrated walleyed pike has always had a pre-eminent position in Minnesota lakes and either never had any competition for its place in the ecosphere or managed to overcome what competition it did have. It's entirely possible but unlikely that the carp could displace the walleye or any other species entirely in its natural environment. But isn't it also just as likely that the walleye itself spread from some other area and displaced a competitor?
At the present time, moose are spreading west in Alaska, from their modern range on the middle Yukon to the Seward Peninsula where they've never been seen before. In fact, old timers in the Yukon-Koyukuk district, an area with large concentrations of moose, remember when a moose passing through was a remarkable event. No one seems to be very upset about moose expanding their range, however. Their only real competition would be the caribou, a migratory herd animal whose numbers ebb and flow over time. It's likely that the spread of moose to caribou country wouldn't necessarily be good for the caribou.
In fact, many other species of wildlife go through population cycles. Snowshoe hares and ruffed grouse are prime examples. Unwitting observers would think that ruffed grouse were becoming extinct when they reach the bottom of their cycle but in a few years their numbers recover. There may well be other cycles in nature that are longer than our lifetimes.
Feral hogs in Wisconsin and other places have created a stir. The point is that change, for whatever reason, is inevitable, and not just in the composition of surrounding wildlife. It can be resisted. The spread of the lamprey eel in the Great Lakes system seems to have been fairly successful. On the other hand, building a fence across the southern border of the country may not prevent the movement of human populations intent on bettering their lives.