Tom, here is the system we use. We have a piece of webbing tied to the trunk of the tree (at least 3 wraps around), tied with a water knot. Then as the climbers go up, we periodically put a safety loop in their downrope and clip that loop to the tree with a non-locking biner.
NOTE: When we do programs, the climbers are climbing on a DdRT system using a Blake's hitch.
Clipping to the tree makes it much safer for the climbers because they can't come down all the way to the ground; their downrope is clipped to the tree.
Patrick
You can see a couple of ropes clipped to the tree in this picture.