The logic should be quite simple but making your trees look like they are growing realistically is the tricky part.
If you could procedurally generate your tree trunks, branches and foliage then that would produce the best approximation, using maybe a fractal type algorithm. Conversely you could substitute in a series of pre sized models over time or simply scale a small model over time (wouldn't look very realistic).
A different approach would be forget the models all together and use a billboard with a video of a tree growing and eventually dying (if you can find or make such a thing), these could be spawned easily and simply run through their life cycle.
Not really sure how detailed and realistic you want this to be.