Surface Area to Volume Changes
Thus, cell volume dictates the metabolic demand of supply for those materials. So, surface area-to-volume relationships are extraordinarily important. If you're an aquatic organism that requires materials from the external environment and you do that by means of passive diffusion or active transport, your surface area has to be magnified with respect to your volume. So what an evolutionary biologist can do is to conduct a hypothetical search through this universe for light interception and for passive diffusion.
Here, you just see the ability to intercept sunlight plotted against wavelengths of light. Here, you see this ability for spheres of different sizes, very small spheres and progressively larger spheres to this size. You see the same ability plotted for a small sphere, a cylinder, an M&M like shape and a very large sphere. You can see that there are advantages to being small. You can intercept a lot more light when you're very small. If you have to get bigger, you can see that you might want to become cylindrical as opposed to remaining spherical.
The curious thing about this is now we can test these predictions. Here you see cell surface plotted as a function of cell volume for real cells. I actually have data, these magenta or violet colored points, are data collected from the literature. You can see that there is a very nice mathematical relationship amongst the data. The slope of this relationship, shown here, is .7. This agrees precisely with what the computer would say would be the best way to change cell geometry or cell shape as cells get larger. You can see that the simulation, shown here by means of little black points, coincides precisely with what plants actually do.
Can plants read?
I don't think this coincidence is fortuitous. I think plants have read the book and I think they're doing precisely what they ought to do as they increase in size. They alter their geometry and they alter their shape. They do it by essentially progressing from very, very small spheres to very long, very thin, cylindrically shaped cells. That's exactly what the computer says they ought to do. It's precisely what they do. Incidentally, the hypothetical slope, if cells weren't changing shape or geometry, is roughly .667. That's what happens if a sphere continues to increase in size and doesn't change its geometry or shape which of course a sphere can't do as it gets larger. Curiously, plants have changed their geometry and their shape as cells get larger by amplifying their surface area with respect to volume.