Typically, the taller the tree, the smaller its leaves. The mathematical explanation for this phenomenon, it turns out, also sets a limit on how tall trees can grow.
Think this leaf is big? (Image: George Steinmetz/NGS)
Kaare Jensen of Harvard University and Maciej Zwieniecki of the University of California, Davis, compared 1925 tree species, with leaves ranging from a few millimetres to over 1 metre long, and found that leaf size varied most in relatively short trees.
Jensen thinks the explanation lies in the plant's circulatory system. Sugars produced in leaves diffuse through a network of tube-shaped cells called the phloem. Sugars accelerate as they move, so the bigger the leaves the faster they reach the rest of the plant. But the phloem in stems, branches and the trunk acts as a bottleneck. There comes a point when it becomes a waste of energy for leaves to grow any bigger. Tall trees hit this limit when their leaves are still small, because sugars have to move through so much trunk to get to the roots, creating a bigger bottleneck.
Jensen's equations describing the relationship show that as trees get taller, unusually large or small leaves both cease to be viable (Physical Review Letters, doi.org/j6n). The range of leaf sizes narrows and at around 100 m tall, the upper limit matches the lower limit. Above that, it seems, trees can't build a viable leaf. Which could explain why California's tallest redwoods max out at 115.6 m.