To answer your question? I don't deal much with our local mulberry, so my experience is limited there, but I do handle alot of Osage and in my area, I have found that there is not one determining factor that I can rely on that will give me any hints as to how good the ring structure is in a given tree.
I cut primarily out of hedge rows and usually look for past cut trees that where taken down by the farmers for corner post. They are the best indicators as to the ring growth in that area. Over the years I have recorded row directions, prevailing winds,soil nutrients,or lack of,High moisture areas, and still there seems to be no conclusion.
All trees in my giving areas seem to hold the same genetic make up as their brothers and sister. whether that is tight rings or large rings.
I don't worry about it much anymore, as any ring ration will still make a bow,some just need to be treated a bit different.
Most people want thicker rings, just easier to chase the back down, but If I had to choose one over the other for cast, then I always go with the tighter ringed wood. Just seems to have more snap.