I have a similar situation - except my dominant tree was red maple. I know that in "real" nature (not suburbia), something would have happened that would bring more diversity. So I help it along by removing the young ones, leaving the big ones and planting other things that naturally grow in the area.

Yes, I do think that forces would eventually outcompete most of those young trees - even if it is just the shade of their bigger cousins.

Thanks for your input esh. I think I need to take some seedlings out. There are a few basswoods and redbuds in the area and the paw paws which are common in the untouched forested areas are slowly making a comeback but the paw paws, in particular, seem to be sensitive to what's around them. The previous owners upset the balance by cutting all the big trees in this area...if I leave it I don't think I'm going to get anything but wall to wall poplars! So I will try to take a good look at the forest and space the poplars out a bit. If you can think of anymore tree thinning tips please let me know...I'm pretty new at "restoration". Thank-you!