The term "invasive" only applies to introduced species that outcompete native species. The American Beech is native. At worst it is an aggressive spreader.

That being said, I understand your concern. Beech can sucker, but your job as a gardener is to bring order even when the intent is "natural". Beech seeds are a valuable food source for birds and mammals, which I think outweighs any other concern. Lawn grass is said not to grow well under Beech trees, so planting them near the ravine makes sense. HERE is an article.

One final thought, even forest plants do better with more light. If your ravine is dark, consider removing lower limbs next winter to allow in more light.

Tho they can sucker, I've never noticed beech suckering much if at all in its wild setting. They do have a dense and shallow root system tho, like say sugar maple.

Thank you both for the information. I meant to describe American Beech as non native to Minnesota. Although at one time they may have been. Yes the ravine lot is darker below with maples at the bottom and the rest of the list on the hillsides. I do try to limb trees down there as it's is fun watching the small maples rise quickly towards the canopy. I can definitely try to keep up on gardening and pruning the beech but not sure if future owners would. I assume beech sucker more in disturbed logging areas so hopefully left undisturbed they wouldn't take over the diversity of trees in the ravine now.

"I assume beech sucker more in disturbed logging areas so hopefully left undisturbed they wouldn't take over the diversity of trees in the ravine now."

That's generally true. Undisturbed Kentucky coffee tree behaves, but cut it down, and suckers appear all around.

Interestingly, Minnesota has delcared black locust invasive and prohibited despite it being a north American native. American beech is not native to MN.

Yes our first home in MN had 4 large black locusts on the lot and when we moved I thought about planting one to remember our first place. Found out it was not allowed. They prefer we plant the native Kentucky coffee tree instead.