Sunlight and the Geometry of Trees

The shape of a tree is largely determined by its need to gather light. Here we see how the light-gathering capacity of a tree's leaves depends upon the shape of the tree crown and upon the latitude at which the tree grows.{Horn} It also depends on the distribution of leaves throughout the crown. From these considerations of three-dimensional geometry and some simple assumptions we shed light, so to say, on the wide variety of forms adopted by trees. Thus, trees with flat, broad crowns (open umbrellas) are more common in equatorial and temperate regions while tall, slender trees (closed umbrellas) are more common in boreal forests/taiga. (We restrict attention to the Northern hemisphere, though our analysis is easily adapted to southern regions.) The same analysis---geometrical and statistical, rather than biological---tell us why leaves are sometimes distributed throughout the crown of a tree and sometimes are confined to the outer edges, defining a light-gathering surface.