A change in topic... to trees

Yeah, yeah, I know. I've basically abandoned this blog after my kid was born. Well, I'm back. I may continue working on the toast problem, but in the mean time, here are some random thoughts I had a little while ago.

I was on an elliptical machine recently, bored out of my mind because nothing good was on TV. (This experience only reinforced my desire to exercise only outside, and never to watch TV.) I was staring out the window, I looked straight into a medium sized tree. I decided to use this tree to entertain me, and since I’m not one for poetry, I decided to calculate how many leaves were on it. Calculate, not count. I wasn’t going to count them, because 1. I don’t know how I could keep count of such a thing, and 2. I wasn’t that bored. Instead, I was going to calculate it.

Here’s what I decided to do. First, I’d imagine a model for how the leaves are distributed. Then, I’d use that model to calculate how many leaves are on the tree. Looking the tree, it occurred to me that most of the leaves are on the outer-most branches. When you climb a tree, you scramble up the thickest branches and don’t have much trouble with leaves where you want to put your hands and feet. This makes sense, the leaves grow on the outermost branches in the sun, and they shade the thick trunk and main branches near the center. Therefore, the center branches don’t get much sun direct sunlight and have no need for leaves. There’s probably a name for this organization, but I haven’t studied enough biology to know what it is called.

First, I calculated the surface area of the tree. My tree was tall and somewhat skinny. I estimated it had a diameter (d) of about 3 meters (about 10 feet) and height (h) of 6 meters (about 20 feet). I approximated this as the outer surface of a cylinder, with an area of πdh. (πd is the circumference of a circle, often written 2πr, where the radius is half the diameter, so 2r=d.) Using my numbers above, I got about 54 m2 area.

Each leaf was about 2 cm by 3 cm, for an area of 6 cm2, or 0.0006 m2. (Notice that 1 m2 = 10,000 cm2, even though 1 m = 100 cm. This is something I remember getting wrong in high school. 1m times 1 m is 1 m2, but this is the same thing as 100 cm (= 1 m) times 100 cm = 10,000 cm2.) Therefore, if the outer surface was covered with a single layer of leaves, it would take 54 m2 / 0.0006 m2 / leaf = 90,000 leaves to cover it.

Looking at the center of the tree from where I was standing, it seemed like there were two or three leaves blocking my view of the center of the tree. It makes sense that there are more than one, because if that one leaf were to get eaten by insects, the tree would miss out on the sun shining in that area. However, there isn’t any need for 50 leaves in one area, because that would be too many extra leaves in that one spot. The probability of 49 leaves getting eaten and only one being left behind is too low to make 50 leaves per location necessary. The true number is probably somewhere between 1 and 10, so I multiply my “single layer” value of 90,000 leaves by 3, and get an estimate of 270,000 leaves.

A small tree with big leaves might have considerably less than this – maybe only 30,000 leaves. Meanwhile a big tree with small leaves could probably have millions of leaves. There are some types of trees that are HUGE and grow tiny leaves, the weeping willow is one, and perhaps they grow tens of millions (maybe a hundred?) million leaves. Next time I see a weeping willow, I can make some measurements and calculate.

OK, so was I right? I don't have any books about tree biology, and I don't know if they would contain such trivial info if I did. So, I turned to the lazy person's answer book: the internet! Answers I found ranged from unsupported but purportedly authoritative statements of "an oak tree has about 200,000 leaves" , to estimates based on ground coverage. Both of these agree with my estimate, but I'd like a more biologically derived response. How many leaves should a tree grow. I tried using google scholar and found that there are too many other uses for tree (information theory, computer science...) and couldn't find any biology papers. I guess verification of my model has left me stumped, no pun intended.