How evolution shapes the geometries of life: Scientists solve a longstanding biological puzzle

Feb 17, 2014
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. Credit: Loretta Kuo

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 ' 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 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."

Explore further: Metabolism gives a boost to understanding plant and animal nutrient evolution

add to favorites email to friend print save as pdf

Related Stories

Distinctive body type aids long life and predation

Feb 10, 2014

Jellyfish (Cnidarian medusa) have unique body plans that violate a universal law of biology and facilitate their longevity and their propensity to form blooms, according to an international study involving ...

Recommended for you

Rising temperatures can be hard on dogs

7 hours ago

The "dog days of summer" are here, but don't let the phrase fool you. This hot time of year can be dangerous for your pup, says a Kansas State University veterinarian.

Monkeys fear big cats less, eat more, with humans around

11 hours ago

Some Monkeys in South Africa have been found to regard field scientists as human shields against predators and why not if the alternative is death by leopard? The researchers found the monkeys felt far safer ...

User comments : 33

Adjust slider to filter visible comments by rank

Display comments: newest first

MrVibrating
1.3 / 5 (30) Feb 17, 2014
Once again, efficiency = God..
verkle
1 / 5 (27) Feb 17, 2014
Why do both the title and article ascribe these amazing scientific facts to the discredited theory of evolution? It really boggles my mind. Absolutely no shred of proof of evolution in these scientific discoveries.

Please phys.org, report on science and not imaginations.

marko
1 / 5 (9) Feb 17, 2014
This seems like the Bumble Bee Theory all over again.

Obviously nobody told birds and turtles about Kleiber's Law.

The astronaut Neil Armstrong was quoted as saying you only get so many heartbeats in your life, so I am not wasting it on exercise.
animah
5 / 5 (20) Feb 17, 2014
Once again, efficiency = God..

You're the one who put that in though. The explanation conspicuously does not require supernatural intervention.
Absolutely no shred of proof of evolution

Apart from this very artice you mean :-). And the 120 million results Google produces for "evolution evidence"!
cl3186
5 / 5 (17) Feb 18, 2014
Once again, religious nutjobs are present everytime the word 'evolution' is mentioned. If you want to talk about disputing the theory of evolution, please link a peer-reviewed research paper from a reputable journal such as Nature, Cell, ACS Chemical Reviews, APS Reviews of Modern Physics.

I'm sick and tired of these nutjobs crying about the theory of evolution when there are literally zero disputes in any research labs I've been to about this matter. Please link a research paper! Prove us wrong and become one of the greatest scientists of all time by proving the theory of evolution wrong! No one could do it for about 200 years since Darwin published his research.
lengould100
5 / 5 (13) Feb 18, 2014
It's really too bad some apes haven't evolved yet to the level of understanding evolution.
Osteta
Feb 18, 2014
This comment has been removed by a moderator.
thingumbobesquire
1.5 / 5 (4) Feb 18, 2014
Biophysical energy density throughput is fixed by a limit of transmissibility. This limit holds for all life forms in the biosphere with the exception of humanity. Our uniquely noetic powers artificially increase this throughput with no limits excepting our current scientific development. Thus we have moved to ever more dense sources of fuel as we approach the advent of thermonuclear fusion and still even more energy dense matter anti-matter reactions in the not far off future. This is the realm of the noosphere.
MrVibrating
2.9 / 5 (7) Feb 18, 2014
Once again, efficiency = God..

You're the one who put that in though. The explanation conspicuously does not require supernatural intervention.


You don't seem to have understood either the article OR my response - that intricate biological complexity is 'designed' by nothing more than efficiency; ie. as per just about all other examples of complex order, living or inanimate.

Indeed, thermodynamic efficiency can offer just about everything a supernatural creator can, from the nature of human intelligence to the very origins of life itself. More broadly, pretty much everything is the way it is because that's the most efficient way for it to be.

Why is it though that so many readers here who see themselves as enlightened atheists are so militantly incapable of understanding the G-word as a meaningful metaphor? Do you think Einstein was really appealing to the sky fairies when he said "God doesn't play dice", or that the Higgs field is really made of diced deity?
MrVibrating
3.8 / 5 (5) Feb 18, 2014
Examples of efficiency as 'grand designer' (with no woo implied):

- under nothing more than gravity's influence, disparate amorphous matter spontaneously takes spherical forms - and further, these stars and planets automatically sort their own jumbled ingredients into neatly stratified layers by order of mass / energy density

- living organisms do much the same thing - churning lifeless dust into functional organic machinery

- Snow flakes spontaneously take on intricate yet randomly varying patterns, all following a perfect six-plane symmetry borne of the H bond angle

- etc... here, Kleiber's law is just yet another example of spontaneously-emergent order from chaos, and like just about every other example you'll be able to think of, all these are different manifestations of 'design' by blind thermodynamic efficiency

As an atheist of any merit, this principle should be the central message of your gospel!

animah
5 / 5 (4) Feb 19, 2014
MrVibrating, this is an interesting point: Evolution iteratively designs efficiency.

To your 2nd point, nature is indeed breathtaking on its own. No supernatural required. This is what makes scientific journeys so fulfilling. Scientific involvement empowers, I think, a very personal connection to nature.

The scientific method is not a gospel though - it is constantly refined by its practitioners. Gospel can by definition not be work in progress :-)
TheGhostofOtto1923
4.3 / 5 (7) Feb 19, 2014
Once again, efficiency = God..
Examples of inefficiency as 'grand designer' (with woo exposed):
http://oolon.awar...OGGM.htm

-I'll mention just one... 99.9% of all the species that ever lived are extinct. How long before god gets it right?

Ok a few more... humans are born premature because if they were brought to full term their heads would not fit through the birth canal. They come out upside down and so need assistance to ensure a safe birth.

These brains consume 3-4 times as much energy as the next animal. They are prone to damage, disfunction, and genetic deformity. They reach peak function shortly after adolescence and then quickly begin to decline, leaving us with substandard performance for the bulk of our lives.

Godders would blame all this on original sin, but are quick to claim 'gods efficiency' when somebody mentions the occasion where he apparently cocked up and got something right.

Hey we used to live 100s of years - ask noah.
MrVibrating
4 / 5 (2) Feb 20, 2014
Er no i said "efficiency is God", not "God is efficient"..!

And all the 'inefficiencies' you give are borne of compromises to efficiency - ie. bipedalsm is more efficient for us despite the reproductive difficulties it brings. Having high processing power makes us more efficient in spite (and indeed because) of its energy requirements.

Your obsessive proclivity to see the hand of 'Godders' everywhere says it all ... (ie. you having doubts?) ;)
TheGhostofOtto1923
3.8 / 5 (4) Feb 20, 2014
Er no i said "efficiency is God", not "God is efficient"..!
Whats the difference? Are you saying that the hand of god-who-made-all is only present in efficient things?

If we are created in his image then is god a jumble of compromises as well?
Your obsessive proclivity to see the hand of 'Godders' everywhere says it all ... (ie. you having doubts?) ;)
I have no doubts that the omniscient, omnipotent god you worship doesn't exist because we know that the things and events and people he describes in his book never existed ;)

And yes, I am as obsessive about exposing this FACT as you religionists are of keeping it hidden and pretending it's not true.
Having high processing power makes us more efficient in spite (and indeed because) of its energy requirements.
We are already able to design more efficient and more powerful systems. Did god need us to do this for him?
TheGhostofOtto1923
4 / 5 (4) Feb 20, 2014
MrVibrating, this is an interesting point: Evolution iteratively designs efficiency
Evolution doesn't design anything. It selects for fitness. This often results in inefficiencies as evolution is forced to work with what it has.

Humans can design from scratch. For instance we do not have to force an animal brain to function beyond the capacities of its original configuration; we can begin with a plan for adequate energy distribution, processing power, storage capacity, general robustness, modularity, and expandability.

If we were created along with the animals, why did god need to, as mrVibrator says, compromise anything? Why are we plagued with animal architectures and animal vestiges? Is god plagued with these things as well?
matt_roadhouse
3 / 5 (2) Feb 20, 2014
Why is evolution always referred to as something the chooses, designs, innovates. Actions, that in any other circumstances, refer to intelligence. Just being an atheist doesn't mean you are immune to Critical Thinking processes. I realize your opposition rarely use Critical Thinking either!

It's because everyone already believes that this is not some random event. Mathematics, Physics and Chemistry (Chirality) has proved that none of this comes from jamming all the raw materials together. We can't reproduce anything without adding organic chemistry techniques. Let alone use 10,000 transistors to make something on the level of a honeybee with flight, language, sight, memory ..(that's how few neurons make up their brains)

The Einstein quote can only be refuted by multiple universes where it the one in x trillion 'rolls of the dice' that provided the exact laws of physics to have matter exist, the 'perfect' ambient temp in space, where a frozen water state decreases density, etc
matt_roadhouse
5 / 5 (1) Feb 20, 2014
Fitness means nothing if there isn't another driving force. natural selection is very random.

One overly snowy winter can decrease all populations of bird that are too dark colored (due to predation). Changes in available food, mating habits, predation all can 'select' a species that plain sucks in another scenario. Next year it's brown backgrounds and all the white birds get eaten. Its a zero sum situation.

"Beneficial" is far too subjective. Honestly, even a species that seems to have an upper hand could not breed, and pass along those genes. Disease, predation, climate are all outside of this. Diversity is why things survive. Life evolves to have maximum diversity. One can state that with certainty, but not 100% of evolutionary theory is sound.
TheGhostofOtto1923
3 / 5 (2) Feb 20, 2014
Why is evolution always referred to as something the chooses
"Natural selection is the gradual process by which biological traits become either more or less common in a population as a function of the effect of inherited traits on the differential reproductive success of organisms interacting with their environment. It is a key mechanism of evolution."
Next year it's brown backgrounds and all the white birds get eaten. Its a zero sum situation
So in matts made-up perfect world natural events are timed to cancel out natural selection.

But in the real world, environments change over time. Populations will adapt and diverge and, over time, form new species. Thats the way it work.
matt_roadhouse
5 / 5 (1) Feb 20, 2014
Its not some made-up perfect world. It's an example of how natural selection can be extremely narrow and not all that beneficial. Something to make you think about your quoted definition.

So what genes get favored in pigment then?

Didn't seem to make you ponder it though. Guess my time is typically wasted here.

Your quoted definition is very correct, and stand-alone is perfect. Of course whatever gets to reproduce will pass on it's genes. May as well define the word cell. Does nothing to show or prove any sort of deeper mechanics
TheGhostofOtto1923
3 / 5 (2) Feb 20, 2014
example of how natural selection can be extremely narrow and not all that beneficial
Its an example of an exceedingly rare and improbable occurrence in the real world. But that doesnt seem to matter to you in the formation of your opinion. Could it be because your opinion is pre-formed and immune to evidence and reason?
what genes get favored in pigment?
What are you saying? Are you saying that genes dont regulate pigmentation? Or are you asking me to name the specific ones?
Does nothing to show or prove any sort of deeper mechanics
I am getting the opinion that you wouldnt know if it did or not. Should I copy/paste a few more paragraphs for you, or do you care to do the research yourself? Or do you think you already know all that you need to know about it?

Fruitfly pigmentation

"At least nine genes are directly involved in the synthesis of pigment, together with a number of others that indirectly affect the pattern of pigmentation."

-Hope this helps-
MrVibrating
5 / 5 (1) Feb 20, 2014
Whats the difference? Are you saying that the hand of god-who-made-all is only present in efficient things?

If we are created in his image then is god a jumble of compromises as well? I have no doubts that the omniscient, omnipotent god you worship doesn't exist because we know that the things and events and people he describes in his book never existed ;)

And yes, I am as obsessive about exposing this FACT as you religionists are of keeping it hidden and pretending it's not true. We are already able to design more efficient and more powerful systems. Did god need us to do this for him?


There's nothing dualistic about efficiency - it's just the manifestation of the laws of thermodynamics. I don't 'worship' it, or anything else.

If you consider me or anything i've said to be 'religious' then it's either English or basic physics you have problems with, not me...
TheGhostofOtto1923
1 / 5 (1) Feb 20, 2014
Whats the difference? Are you saying that the hand of god-who-made-all is only present in efficient things?

If we are created in his image then is god a jumble of compromises as well? I have no doubts that the omniscient, omnipotent god you worship doesn't exist because we know that the things and events and people he describes in his book never existed ;)

And yes, I am as obsessive about exposing this FACT as you religionists are of keeping it hidden and pretending it's not true. We are already able to design more efficient and more powerful systems. Did god need us to do this for him?


There's nothing dualistic about efficiency - it's just the manifestation of the laws of thermodynamics. I don't 'worship' it, or anything else.

If you consider me or anything i've said to be 'religious' then it's either English or basic physics you have problems with, not me...
Ah I see. You were being clever. I suggest you use semi-quotes to indicate sarcasm.
Whydening Gyre
5 / 5 (3) Feb 20, 2014
It's really too bad some apes haven't evolved yet to the level of understanding evolution.

Understanding evolves...:-)
cl3186
4 / 5 (1) Feb 21, 2014
@matt_roadhouse

The biggest misconception among the people who are uneducated on biology is that they think the mechanism of evolution is random. There have been countless times where biologists states that the natural selection is the OPPOSITE of random. An evolutionary biologist Professor Dawkins famously said that evolution is "like automatic, not random". There are random elements in mutation at the genetic level, but it is a precisely driven mechanism as a whole.
antialias_physorg
5 / 5 (4) Feb 21, 2014
There have been countless times where biologists states that the natural selection is the OPPOSITE of random.

Erm: The selection isn't random. It is very much dependent on the environment. The mutation part of evolution is random. Evolution is mutation AND selection.

If selection were random you would see no evolution happening at all.

but it is a precisely driven mechanism as a whole.

Careful: it's neither driven nor directed. Only the selection is confined. The distinction is important because evolution is a PASSIVE process that takes away the unfit - not an ACTIVE process that promotes the fit.

'Ajax' on bash.org put it most succinctly::
"Some people...have the idea that evolution is a fucking system of...'oh i need flippers, i'd better grow some' type bullshit.
It's more like 'Oh shit look at that freak over there with the flippers hahaha OH SHIT I AM DROWNING OH GOD SAVE ME FLIPPER BOY'."
MrVibrating
4 / 5 (2) Feb 21, 2014
I suggest you use semi-quotes to indicate sarcasm.


LOL no i wasn't being sarcastic - again, if being an atheist means my vocabulary has to be so impoverished as to preclude any hint of a reference to Him Upstairs then i'll happily admit right now to being High Priestess of the Great Lord Anumpti Nunu's Toothbrush (as is my birthright as king of the Potato People).

Whatever. It's a word - whether or not you believe it was the first - a universal synonym for the Fates, providence, the Prime Mover, the Divine, the sum of all unknowns and unknowables. The transcendant, the three 'omni's (if only rhetorically); the notional First Cause, the Grand Clockmaker, an appeal to humility, an expression of the profound.

It's a perfectly valid and useful word and, contrary to what anyone else (including He Himself) may say, i steadfastly reserve the right to use it as inappropriately and frequently as i see fit.

God God God God God. GOD.

There, i said it. I 'went there'. Sue me.
Skepticus
5 / 5 (2) Feb 22, 2014
It's really too bad some apes haven't evolved yet to the level of understanding evolution.

I would say even that is a real insult to the entire ape clan!
freeiam
5 / 5 (1) Feb 23, 2014
This seems like the Bumble Bee Theory all over again.

Obviously nobody told birds and turtles about Kleiber's Law.

The astronaut Neil Armstrong was quoted as saying you only get so many heartbeats in your life, so I am not wasting it on exercise.


Strange enough Armstrongs quote has disappeared, all the better because it shows complete ignorance of basic physiology: training actually causes a slower average heartbeat!
freeiam
5 / 5 (1) Feb 23, 2014

LOL no i wasn't being sarcastic - again, if being an atheist means my vocabulary has to be so impoverished as to preclude any hint of a reference to Him Upstairs


Your right ofcourse, cursing is also really expressive sometimes and doesn't require to be a member of a scientific sect to be effective.

If I can make a suggestion, being an Atheist isn't radical enough because RIAEP (religion is an explained phenomenon).
MrVibrating
3.5 / 5 (2) Feb 23, 2014

LOL no i wasn't being sarcastic - again, if being an atheist means my vocabulary has to be so impoverished as to preclude any hint of a reference to Him Upstairs


Your right ofcourse, cursing is also really expressive sometimes and doesn't require to be a member of a scientific sect to be effective.
Yep, for cursing, or just as a punchy metaphor for definitions i've listed above; in this case, i was obviously merely stating the obvious conclusion, that blind efficiency alone can produce elaborate designs, without cause to appeal to any higher powers..

If I can make a suggestion, being an Atheist isn't radical enough because RIAEP (religion is an explained phenomenon).

Quite, hence my devotion to His Serene Highness's holy dental sundries (May All His Flossings Be Blessed).
Smithder
not rated yet Feb 24, 2014
Examination of growth rates in young Fir trees gives an exponential rate of 2.7.

Small dogs typically live ca 13 years, while large breeds only see 6 to 7 years.

Seems like you have to be very careful to pick your life form in order to be sure that it will agree with Kleiber's Law - not a very good law it seems.
11791
not rated yet Feb 24, 2014
the cult of the flying spaghetti monster is bigger than your floss guru
Smithder
5 / 5 (2) Feb 26, 2014
"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."

What utter rubbish !! Both trees and animals have pumps - they are just different sorts of pump.
Andragogue
not rated yet Mar 02, 2014
And yet small dogs outlive larger breeds. And that's a crying shame.