Probably the most-common use of the term "invasive species" is to refer to non-native species that are causing a problem. Kudzu in the US South, rabbits in Oz, hogs in Texas, etc. Most people don't refer to, for example, cattle, as an invasive species though they are not native to much of the world.

85lc commented that hogs have become more of a problem in the past 25-30 years. There are a couple of reasons for this. Hogs aren't stupid: they are going to live where the livin' is easy: a biologist friend calls this "Hog World". Population gradually grows, until it reaches the point where in a few years the population goes from "some kind of acceptable number" to "too many". This causes problems in Hog World, one of which is the need for more room.

So the hog population expands into the periphery, and Hog World grows. As with other animals some have always lived out beyond the core population, but when the core population expands past the edges of "Hog World" it bumps the outliers even further out, and to people living in the expansion area it looks like suddenly there are hogs everywhere. With lots of room in the new area, population can easily more than double in a year.

Most of the farmers and ranchers I've talked with do want help controlling (eliminating!) the feral hogs. Unfortunately, sport hunting doesn't really accomplish this: taking a few hogs is only a statistical blip in the population. Control shooting does help, to an extent, at least temporarily, if the numbers killed are large enough.