They don't. That is a good question.
Keep in mind that in their native range they have evolved with the entire fish community over a very long time, over hundreds of thousands of years, depending on where they are found. I've collected them within their native range in eastern Russia, where they were just one component of the environment. There they are in an equilibrium. They've evolved with other species, including predators that have learned to feed on the young of these Asian carp. If they get into the Great Lakes, the Great Lakes ecosystem is entirely naïve. They have not evolved with them, and there will be an immediate impact because of the naiveté of the fish, which have been in the Great Lakes for the last 10,000 year in the absence of Asian carp.