I don't agree that common carp are an invasive species. Back in the 1800's when they were originally introduced to the United States, I might have considered them "invasive", but it's now 150 years later. At this point they are well-established throughout 48 states. I checked the Michigan DNR website to make sure "common" carp are not identified on the "invasive" list - they are not on the DNR list of "invasive" plants or animals. Here's a link to the page on the DNR site. That site does list various species of Asian carp that are considered invasive here in Michigan as follows:
•bighead carp (Hypophthalmichthys nobilis)
•black carp (Mylopharyngodon piceus)
•grass carp (Ctenopharyngodon idella)
•silver carp (Hypophthalmichthys molitrix)
•large-scale silver carp (Hypophthalmichthys harmandi)
Here is the link to that information.
The Michigan DNR actually tags and releases common carp back into Michigan waters while looking for Asian carp: Read about that activity here . While fishing on July 4th I had the opportunity to speak to a Michigan DNR officer about carp fishing, so I asked him whether they would expect common carp to be "destroyed" rather than returned to the water. He answered that returning common carp to the water is perfectly normal/acceptable. He spent 15 minutes asking questions about how we fish for carp and seemed to enjoy learning about carp fishing the way we do it. He agreed that more people should give common carp a chance as a sport fish.
Fishing for common carp is one of the fastest growing segments of sport fishing. If you want to catch big fish from the shoreline without a boat, give carp fishing a try.
When Asian carp are caught in Michigan, they should not be released back into the water. Read more at AsianCarp.us
What happens if I find an Asian carp?
Do not release the fish back into the water. If you catch or find an Asian carp in the Great Lakes or any of its tributaries, freeze the fish in a sealed plastic bag, note the date and location, and call your state or provincial natural resource agency. Note: if you are in Illinois on the Chicago Sanitary and Ship Canal, the above instructions pertain to any Asian carp found above the electric barrier.
I hope this helps add some clarity to what the DNR currently classifies as "invasive" in the State of Michigan.