http://www.sciencedaily.com/releases/2014/02/140217161106.htm
How evolution shapes the geometries of life
New research suggests 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 Law (metabolism equals mass to the
three-quarter power) and applying it separately to the geometry of plants
and animals, researchers were able to show that plants and animals display
equivalent energy efficiencies.
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.
To nourish its mass, an animal needs fuel. Burning that fuel generates
heat. The animal has to find a way to get rid of excess body heat. The
obvious way is surface cooling. But because the tiger's surface area is
proportionally smaller than its mass, the surface is not up to the task.
The creature's hide would get blazing hot, and its coat might burst into
flames.
So as animals get larger in size, their metabolism must increase at a
slower rate than their volume, or they would not be able to get rid of the
excess heat. If the surface area were the only thing that mattered, an
animal's metabolism would increase as its size increased, at the rate of
its mass to the two-thirds power. But Kleiber's Law, backed by many sets of
observations, says the actual rate is mass to the three-quarters power.
Clearly there's a missing factor, and scientists have pored over the data
in an attempt to find out what it is. Some have proposed that the missing
part of the equation has to do with the space occupied by internal organs.
Others have focused on the fractal, or branching, form that is common to
tree limbs and animals' blood vessels, but added in new assumptions about
the volume of fluids contained in those fractal networks.
The UMD and University of Padua researchers argue a crucial variable has
been overlooked: the speed at which nutrients are carried throughout the
animals' bodies and heat is carried away. So the team members calculated
the rate at which animals' hearts pump blood and found that the velocity of
blood flow was equal to the animals' mass to the one-twelfth power.
"The information was there all along, but its significance had been
overlooked," said hydrologist Andrea Rinaldo of Italy's University of Padua
and Switzerland's Ecole Polytechnique Federale. "Animals need to adjust the
flow of nutrients and heat as their mass changes to maintain the greatest
possible energy efficiency. That is why animals need a pump -- a heart --
and trees do not."
Plugging that information into their equation, the researchers found they
had attained a complete explanation for Kleiber's Law.
"An elegant answer sometimes is the right one, and there's an elegance to
this in the sense that it uses very simple geometric arguments," said
physicist Amos Maritan of the University of Padua. "It doesn't call for any
specialized structures. It has very few preconditions. You have these two
lineages, plants and animals, that are very different and they arrive at
the same conclusion. That is what's called convergent evolution, and the
stunning result is that it's being driven by the underlying physics and the
underlying math.”
====================================================================================================================
The whole problem with the world is that fools and fanatics are always so
certain of themselves, and wiser people so full of doubts.
--- Bertrand Russell
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/groups/opt_out.
