Trees grow from the top, not from the bottom as is commonly believed. A branch's location on a tree will only move up the trunk a few inches in 1000 years. No tree dies of old age. They are generally killed by insects, disease or by people.
Revelation 22:2 In the midst of the street of it, and on either side of the river, was there the tree of life, which bare twelve manner of fruits, and yielded her fruit every month: and the leaves of the tree were for the healing of the nations.