That's really interesting, i thought that age and size were directly related, i hadn't thought about the competition thing, there's a beautiful old beech pollard in a woodland where i volunteer it's huge, easily 8 feet across the trunk, it must be ancient
Age and girth are of course related, a tree has to cover its entire surface with at least one layer of new cells each year, if it can't it starts dying back. The amount of new wood varies enormously though depending on many factors the growth rings can be anything from 2 to the inch to 30 to the inch, more if it has a full crown and little root competition on fertile soil, less if it has a small crown, harsh climate or thin soil. I once cut down 2 ash trees both 10" diameter growing 100 feet from each other, one was less than 30 years old the other over 120.
There is a limit to how big the crown of a tree can grow and your beech and this oak are probably there so each year they are trying to cover a larger and larger area with new growth but from the same surface area of leaves producing nutrient, eventually it can't be done, the oak will simply die back, some of the ends of the branches will die and new growth will start from the trunk or branches. Some trees like beech do not put out new epicormic growth like this so when they reach that crisis stage they die, that is why you don't get many really old beech. (big but not really old)
The thing that slows growth down and prolongs a trees life most is what is called pollarding, this was common practice in the UK up to the 17th century, cut the top off the tree and you get a nice crop of firewood and leaves for your livestock but if it is done at head height the tree will regrow above the grazing animals below. This was done every 20 years or so and meant the trees always had very tiny crowns and grow very slowly thus achieving great age.
