Why does a mouse’s heart beat about the same number of times in its lifetime as an elephant’s, although the mouse lives about a year, while an elephant sees 70 winters come and go? Why do small plants and animals mature faster than large ones? Why has nature chosen such radically different forms as the loose-limbed beauty of a flowering tree and the fearful symmetry of a tiger?
These questions have puzzled life scientists since ancient times. Now an interdisciplinary team of researchers from the University of Maryland and the University of Padua in Italy propose a thought-provoking answer based on a famous mathematical formula that has been accepted as true for generations, but never fully understood. In a paper published the week of Feb. 17, 2014 in the Proceedings of the National Academy of Sciences, the team offers a re-thinking of the formula known as Kleiber’s Law. Seeing this formula as a mathematical expression of an evolutionary fact, the team suggests that plants’ and animals’ widely different forms evolved in parallel, as ideal ways to solve the problem of how to use energy efficiently.
If you studied biology in high school or college, odds are you memorized Kleiber’s Law: metabolism equals mass to the three-quarter power. This formula, one of the few widely held tenets in biology, shows that as living things get larger, their metabolisms and their life spans increase at predictable rates. Named after the Swiss biologist Max Kleiber who formulated it in the 1930s, the law fits observations on everything from animals’ energy intake to the number of young they bear. It’s used to calculate the correct human dosage of a medicine tested on mice, among many other things.
But why does Kleiber’s Law hold true? Generations of scientists have hunted unsuccessfully for a simple, convincing explanation. In this new paper, the researchers propose that the shapes of both plants and animals evolved in response to the same mathematical and physical principles. By working through the logic underlying Kleiber’s mathematical formula, and applying it separately to the geometry of plants and animals, the team was able to explain decades worth of real-world observations.
“Plant and animal geometries have evolved more or less in parallel,” said UMD botanist Todd Cooke. “The earliest plants and animals had simple and quite different bodies, but natural selection has acted on the two groups so the geometries of modern trees and animals are, remarkably, displaying equivalent energy efficiencies. They are both equally fit. And that is what Kleiber’s Law is showing us.”
Picture two organisms: a tree and a tiger. In evolutionary terms, the tree has the easier task: convert sunlight to energy and move it within a body that more or less stays put. To make that task as efficient as possible, the tree has evolved a branching shape with many surfaces – its leaves.
“The tree’s surface area and the volume of space it occupies are nearly the same,” said physicist Jayanth Banavar, dean of the UMD College of Computer, Mathematical, and Natural Sciences. “The tree’s nutrients flow at a constant speed, regardless of its size.”
With these variables, the team calculated the relationship between the mass of different tree species and their metabolisms, and found that the relationship conformed to Kleiber’s Law.