Of π Day, Plants, and Paleoclimates

March 14, 2013 by Drew Kerkhoff 1 Comment

Happy π Day! After not posting anything on Darwin Day, I decided that I could not let another geek holiday go by without a post. So let’s talk about the importance of π in the global biogeocoenosis.

Now you may say, “But π is just about geometry! That’s not biology!” Or maybe if you’ve blocked out 10^th grade math, you may say, “But pie is just for dessert!” Allow me to retort:

WRONG!

Biology is all about structure and function and the mathematics of structure (and to some extent, function too, come to think of it….) is geometry. Much of evolutionary biology is concerned with the history, diversification, and development of biological form. On some level, most evolutionary biologists study changes in the geometry of organisms and why it matters. Also, pie makes an excellent breakfast.

So because π relates the diameter of a circle and its circumference, we need to think about the important circles of life. I like trees and the cross-section of a tree trunk is roughly circular, so that seems like a productive place to start! Imagine a beautiful sugar maple like the ones local farmers here in Knox County tap to make maple syrup early every spring. My checker at Wal-Mart told me that just last weekend her husband had really smoked up her house boiling down the last of their haul of sap for this season.

So where does that sap come from? The tree stores starch in its roots and early in the season, the roots start moving the starch into the sap to fuel the production of leaves way up in the canopy. The sap flows through little tiny tubes just under the bark of the tree, which is why we can tap into the sap. These tubes, collectively called the xylem system, stretch continuously through the body of the tree, from the tiniest tips of the roots to the veins of every leaf. But how does the sap flow? Are there little pumps down in the roots that push the fluid up? Does it simply “climb” up the little tubes by capillary action? For a long time, this was one of the major mysteries of botany: how do plants, which have nothing resembling a heart, get water from the soil to their leaves, fighting all the while against gravity?

The answer, which has only become fully established over the past few decades, turns out to be a little crazy. The water in the little tubes is not being pushed, but pulled up the tubes. The water molecules form long, continuous strands from the roots to the leaves, stuck together by the electrochemical force of cohesion. And all those tiny strands of water are under tension – they are being stretched like minuscule rubber bands. And the crazy part is that they are being stretched by the air! The underside of leaves are pocked by tiny pores called stomata, and as the water evaporates, it pulls just a bit on the strand of water behind it, all the way down to the roots. So simply because it is drier than the plant’s tissues, the air “sucks” water up from the soil, perfusing all of the plants cells along the way. Plant xylem is one of the wonders of engineering accomplished by evolution. In a single large tree, the xylem can move hundreds of gallons of water over large distances without any direct input of energy on the part of the organism. Talk about efficiency!

About now, you may be wondering, “What about the π?”

To find the importance of π here, we just need to consider the circles in the picture. Not just the big circle of the trunk, but all of the tiny circles that make up the tubes of the xylem. And how tiny they are matters, because the same forces that hold the water molecules together in strands also make it stick to the side of the tubes. In bigger tubes, less of the water is in contact with the wall, so it flows faster. Back in the mid 19^th century, scientists figured out that the flow rate (Φ) through a pipe could be described by the following equation:

So there! There is my favorite pi in biology!

The πr⁴ term, where r is the radius, has to do with the cross sectional area of the pipe and how much fluid is in contact with the wall of the pipe. What is so important about it is not so much the π (sorry, but such is the life of a constant) but the fact that the radius is raised to the fourth power. That means that if you double the radius of a tube, all else equal, you actually increase the flow by a factor of 2⁴ or 16-fold! So plants with bigger tubes can move more water, more quickly.

It turns out that this simple fact has terrific importance for both plant evolution and perhaps even for the history of Earth’s climate. Back in the Cretaceous, 65.5-145 million years ago, Earth’s vegetation was dominated by conifers and ferns. No Triceratops ever munched on a sugar maple. The lineage of flowering plants that are so common today were only just beginning to evolve, and evolutionary biologists have long marveled at their rather explosive (in geological/evolutionary terms, at least) diversification and rise to dominance. Darwin himself called it, “an abominable mystery.” What were the secrets to their success?

Almost certainly, some of them were physiological, and one of the most notable differences between flowering plants and their cousins was in the xylem. Flowering trees had not just discovered flowers and animal pollination (another of the secrets to their success), they had also found a way to make the tubes bigger than those of conifers. And not just a little bigger, a LOT bigger: up to fifty times wider! And because of the πr⁴ term, even though one of these humongous vessels takes up as much space as 2,500 smaller tubes, the flow rate increases more than 6 million fold! At the same time, the leaves of flowering plants were changing too. The density of leaf veins increased enormously during the Cretaceous, bringing more of the water and soil nutrients in the sap closer to the sites of photosynthesis, and releasing much more water vapor into the atmosphere. The evolutionary relationship between these innovations, their relative order and mutual influence, remain uncertain, but together they changed the world. In fact, they sped it up.

Provided with more water and nutrients, the photosynthetic machinery of the leaves went into overdrive. Vegetation became more productive, capturing more carbon from the atmosphere, though it released more through respiration as well. Those faster living leaves also died younger, speeding up the cycling of nutrients through decomposition. And after the cataclysmic transition from the Cretaceous to the Paleocene, whole forests of flowering trees became dominant over large swaths of the continents, and they even began to make their own rain. With their huge vessels and richly veined leaves, theses trees collectively accelerated the hydrological cycle, moving water into the atmosphere that eventually had to return to the ground as rain. Even erosion may have increased. Recent modeling studies suggest that if Amazon rainforests were constrained to more ancient conifer-style rates of water transport, the dry season would lengthen by up to 80 days, well beyond the tolerance of most rainforest species.

And in making their own world here on Earth, the flowering plants have made our world. No primate ever knew a world without them. Even our climate is a product of their evolution. And we could not understand it without understanding that the ratio of the circumference to the radius of a circle is a transcendental constant.

π for now.

Evolutionary research on the vascular innovations of flowering plants is incredibly exciting right now. Two recent interesting papers (which I drew on for this post) include:

C. Kevin Boyce and Maciej A. Zwieniecki. 2012. Leaf fossil record suggests limited influence of atmospheric CO2 on terrestrial productivity prior to angiosperm evolution. Proceedings of the National Academy of Sciences of the USA.

Taylor S. Feild, Timothy J. Brodribb, et al. 2011. Fossil evidence for Cretaceous escalation in angiosperm leaf vein evolution. Proceedings of the National Academy of Sciences of the USA.