Oh they reseed. Too difficult to find the seed pods but I know they reseed. Funny that you guys in colder zones have problems with it being a thug. Like Deb, I haven't really had a problem with it like that & the same was true when I lived in zone 10. In fact, I dug mine up from the side of the road & planted them in one of my "wild" areas & actually WISH they would increase more rapidly.