As it stands currently, the lifespan of a tree is indefinite, so long as that tree is tended to. I would recommend that trees are given a natural lifespan within the game since there are quests for new players to tend patches, plant beans, etc., and there are also several street projects calling for clumps of earth and loam which are becoming a rarity. If trees had a lifespan, the amount of time they lived for could vary based upon the number of trees (and maybe the number of a given kind of tree) in the area with more prevalent trees having shorter lifespans and rarer trees having longer ones.
Right now, trees can be poisoned, but it has become obvious that this might need some regulation. My suggestion is that either poisoning trees should have a cooldown placed upon it or, like capturing piggies, a player could only poison so many trees per street. Placing such limits would prevent griefing/trolling. However, it may have been the developers' intention to have players act as the lifespan of the tree, they becoming the natural forces of creation and destruction. If that was the intent, then carry on! This has been a Vexia suggestion; thanks for reading! :P