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K. Jensen/Harvard University and M. Zwieniecki/UC Davis

Wide variety.
The leaves of angiosperm trees vary wildly in size, but the range of size narrows among taller trees.

Simple Physics May Limit the Size of Leaves

By: 
Adrian Cho
2013-01-04 12:10

Leaf growth may not be as complicated as it seems. When compared, species to species, shorter trees exhibit a greater variety of leaf sizes than taller ones, with the tallest trees all having leaves that measure 10 to 20 centimeters in length, a biophysicist and a biologist report. The narrow size range may have a simple explanation in the inner plumbing of trees, they say. If it's correct, the analysis would also explain why the tallest trees top out at about 100 meters.

"It's a very simple observation," says Kaare Jensen, a biophysicist at Harvard University, who presents, along with Maciej Zwieniecki of the University of California, Davis, the analysis in a paper published today in Physical Review Letters. "We were fortunate that others hadn't made it before."

Jensen and Zwieniecki considered only flowering plants, or angiosperms, such as maples and oaks, but not gymnosperms, such as pines and redwoods. Reviewing existing data for 1925 species, they found that among angiosperms shorter than 30 meters, leaf length varies enormously, from the 3-centimeter curlicues of the lacebark elm to the 60-centimeter flaps of the bigleaf magnolia. The range narrows as tree height increases, with the tallest angiosperms all sprouting leaves that are 10 to 20 centimeters long.

The two explain this trend in terms of the flow of sap and energy through the tree. A leaf of an angiosperm produces a sugary sap that flows into a network of pipelike cells called the phloem, which transports the sap down the tree's trunk and through the roots. Along the way, the tree metabolizes the sugar. Such flow is driven by a difference in the concentration of sugars, which generates "osmotic pressure."

Jensen and Zwieniecki modeled a tree as a pair of cylindrical tubes: a short, permeable tube (the phloem in the leaf) attached to a long, impermeable tube (the phloem in the trunk). Sap diffuses into the leaf phloem and travels down the trunk phloem. The longer the permeable leaf tube is, the more surface area it has, so the more easily sap can enter. Things are different in the trunk phloem: There, the longer the tube is, the more frictionlike resistance it offers to flow. (They modeled the "sink" in which sap seeps out of the phloem as a third, permeable cylinder, but assumed that it is so long that it provides negligible resistance and can be ignored.)

The researchers then considered how the total flow of sap and energy varies with leaf length. If the leaves are big, then resistance from the trunk limits the flow. In fact, making the leaves bigger than a certain maximum length yields no additional flow or benefit. On the other hand, if the leaves are very small, their resistance limits the flow. And if a leaf is shorter than a certain minimum length, then the sap would flow through the phloem more slowly than it could simply diffuse through the tree. At that point, the phloem plumbing would become useless.

In fact, these limits neatly fit the observed pattern of leaf sizes, the researchers report. And as tree height increases, the two limits converge and cross at roughly 100 meters: the height of the tallest angiosperms. That means trees taller than 100 meters simply could not produce leaves that obey both length limits, setting a limit for tree height, Jensen says.

Not everybody buys the explanation. "I love the approach, but I just think it's too much of a stretch," says John Sperry, a plant physiologist at the University of Utah in Salt Lake City. The super-simple model leaves out several factors that ought to drastically change the mathematics, Sperry says. For example, he says, there is not a one-to-one relationship between leaves and phloem tubes in the trunk, as the tubes merge. As for the uniformity of leaf size among the tallest trees, Sperry notes that such trees grow in the mildest environments and that similar conditions may lead to similar leaf sizes for other reasons.

However, C. Kevin Boyce, a paleontologist at the University of Chicago in Illinois who specializes in plant evolution, says he finds the argument for the limits plausible. "Articulating the pattern itself is an important step," he says. "And if you're the first person to recognize a pattern you also get first crack at explaining it." The theory could be further tested by seeing if the pattern of leaf sizes is the same for different families within the angiosperm group, he says.

Jensen has a different idea for testing the theory. The mathematics provides a simple equation for how the flow speed varies with the height of a tree and the length of its leaves. That speed could be measured in different species of tall trees, he says, although that might require taking an MRI machine up into the rain forest canopy.

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