|A coypu or nutria (Myocastor coypus)|
They are considered a serious problem species, with their major impacts involving erosion and destruction of dykes through burrowing and feeding on rhizomes, which are horizontal stems used to propagate species of grass. I large numbers, they can also reduce a marsh to nothing but an open stretch of water, putting a great number of marsh species at risk. They will also destroy crops.
The coypu is used as a source of meat and fur, and you can find the meat online, complete with recipes and meal suggestions. Management methods remain trapping and shooting, and a bounty system is set up in certain areas. Several states have managed to eradicate them from their area. Interestingly enough, the World Wildlife Fund opposed eradication attempts in Sicily. I wonder what their reasoning was?
The nutria is on the list of 100 World's Worst Invasives at #60.