Physical Limits to Leaf Size in Tall Trees

Leaf sizes in angiosperm trees vary by more than 3 orders of magnitude, from a few mm to over 1 m. This large morphological freedom is, however, only expressed in small trees, and the observed leaf size range declines with tree height, forming well-defined upper and lower boundaries. The vascular system of tall trees that distributes the products of photosynthesis connects distal parts of the plant and forms one of the largest known continuous microfluidic distribution networks. In biological systems, intrinsic properties of vascular systems are known to constrain the morphological freedom of the organism. We show that the limits to leaf size can be understood by physical constraints imposed by intrinsic properties of the carbohydrate transport network. The lower boundary is set by a minimum energy flux, and the upper boundary is set by a diminishing gain in transport efficiency.