生物代谢率与质量的缩放律：从克莱伯定律到WBE分形理论的争论

you give an elephant?

the correct answer is probably none.

it for a scientific experiment?

a top secret project known as MKUltra,

and one of their main

goals was to find out

how drugs like LSD could be

used to change human behavior.

because elephants are

normally quite docile,

but sometimes they just snap.

that this change in

behavior might be triggered

by the release of an LSD-like substance

that naturally occurs in their brains.

to a docile elephant might

reproduce that behavior.

how much LSD should you give

an elephant so that the

dose is large enough

to cause a psychological reaction,

but not so large that it causes harm?

know, LSD had never been given

to an animal that big,

but they did know that

the safe dose in cats

was around 0.3 milligrams.

a thousand times the mass of a cat,

they figured we'll give it

a thousand times the dose.

perform the experiment on Tusko,

an Indian elephant at the

Lincoln Park Zoo in Oklahoma.

with nearly 300 milligrams of LSD.

Tusko trumpeted, collapsed,

fell heavily onto his

right side, defecated,

and went into status epilepticus.

in an attempt to revive him,

but Tusko died shortly thereafter.

that safe drug dosage

scales linearly with mass.

a lot of things like this

that don't scale in the way you'd expect.

smallest mammal by mass,

the Etruscan shrew,

and the largest land mammal,

the African bush elephant.

over the course of its entire life?

around a billion

heartbeats in its lifetime,

and an Etruscan shrew also has a billion

heartbeats in its lifetime.

Also a billion.

A billion again.

what environment they live

in, how large they are,

or even whether they live

for one year or 100 years,

they all get around a billion heartbeats

between the day they're

born and the day they die.

Why not a million?

Why not a thousand?

It's not these other numbers.

part based on the book

Scale by Geoffrey West.

If you want to learn more,

I'll put a link to it

down in the description.

just by knowing a mammal's mass,

you can predict a staggering number

of biological traits from its pulse rate

and reproductive output

to its total lifespan.

If you know the population and location,

that allows you to forecast

everything from average wages

and patent filings to crime

rates, disease prevalence,

and even the literal speed

at which pedestrians walk.

Well, for that, we have

to go back to the case

of Tusko the Elephant.

is proportional to mass.

Double the mass, double the dose.

speed at which an animal

can process chemical compounds

doesn't depend directly on its mass.

It depends more on its metabolic rate.

That is the number of calories it uses

in a given amount of time.

Your heart is pumping, that takes energy.

You're moving food around.

Digestion takes energy.

Keeping your brain going

takes energy, breathing.

Everything that you do requires energy.

they require roughly 250

kilocalories of energy,

used by all of their trillions of cells.

special about a cat's cells.

If you take a cat's cells

and an elephant's cells

and put them under a microscope,

you'll find they're a

similar size, similar makeup,

and they perform the

same sorts of functions.

In other words, the building blocks

of animals are always roughly the same.

a thousand times the mass

has about a thousand times as many cells.

So you'd expect it would need a thousand

times as much energy.

So 250,000 kilocalories per day.

If I'm an organism

and I'm burning up energy all day long,

that energy is radiated out

in the form of body heat.

So we're constantly losing

heat through our surface,

through our skin, to the environment.

let's simplify the problem

and do the standard physicist thing.

Let's assume our animals

are perfect spheres.

for the argument to work,

but it does make everything

a lot easier to follow.

is proportional to its mass,

our 3000 kilogram elephant

has a volume a thousand times

greater than our three kilogram cat.

That's because volume is

proportional to radius cubed.

grows as radius squared.

So the elephant's surface area

only increases by a factor of 100.

while only having a hundred

times the surface area

to radiate it away would end very

poorly for the elephant.

If this were the case,

it would boil alive.

French scientists proposed

a different scaling law.

Since metabolism generates heat

and that heat is radiated

through the surface,

metabolic rate or B,

should scale in proportion

to the surface area, A, instead.

how metabolic rate scales

as a function of mass.

to radius squared,

so we can swap that in,

and if mass is proportional

to radius cubed,

then radius must be proportional

to mass to the one-third.

we find that metabolic rate should scale

with mass to the two-thirds.

come from thinking about cooking.

big turkey for Thanksgiving.

People commonly phrase it as

how long do I need per pound?

But that you realize is linear thinking.

the thickness of the bird

or the roast, because

the heat is coming in

by conduction from the oven

and it's got to do thermal

diffusion into the meat.

like the characteristic length,

which in this case would be

the thickness of the meat.

It'll go like the dimension squared,

whereas volume of the meat is

going to be like length cubed,

and that's proportional to the weight

of the bird or the roast.

you'll get that the characteristic

amount of time needed

to cook the roast will go like its mass

to the two-thirds power.

that weighs twice as much as

another roast, how much longer?

Is that two to the two-thirds the time?

to double the weight,

then you only have to

cook it about 60% longer,

not 100% longer.

according to this scaling,

an elephant that's a thousand

times as heavy as a cat

should only burn a hundred

times as many calories.

So 25,000 instead of 250,000.

would've been just 30 milligrams.

predictions come from different

assumptions about how metabolic rate

scales as a function of mass.

it's just proportional

to mass raised to some power.

are called power laws

and all power laws have

a special property.

of the X and Y values,

you get a straight line.

to the exponent of the power law.

This makes it easy to identify

different types of power laws.

just everyday linear scaling.

If it's less than one,

like the surface law,

that is called sublinear scaling.

And if it's larger than one,

that is known as superlinear scaling.

biologists generally agreed

that the two-thirds exponent

of the surface law was the

correct one for metabolic rate.

biologist, Max Kleiber,

decided to put it to the test.

of different animals from

a small dove at 150 grams

to a large steer at 680,000 grams,

and then he plotted

them against their mass

on a log log plot.

did fall on a straight line.

But the slope wasn't two-thirds.

Instead, it was about three quarters.

double an animal's mass,

metabolic rate goes up by about 1.68,

an increase of 68% instead of the 59%,

which would be predicted by

the two-thirds scaling law.

an elephant burns roughly 178 times

as many calories as a cat,

or about 45,000 kilocalories.

Tusko should have received

was 53 milligrams, which is

around a sixth of the dose

the researchers gave him.

with Tusko The Elephant.

based on a small data set,

primarily made up of mammals.

a larger range of mammals,

as well as for other animals

like birds, reptiles, and fish,

you find that they all follow

roughly the same scaling relationship.

perfectly onto the same line

because the base metabolic rate

for warm-blooded animals is higher

than for cold-blooded ones,

but they all scale according

to the same power law,

mass raised to the three-quarters.

expands all the way down

to single cells and the molecular

machines inside of them.

spanning more than 25 orders of magnitude.

if an elephant has so many more cells

and each cell is a similar size

to a cell in a smaller creature,

and yet it's using

proportionately less energy,

like it's got a lower

metabolic rate per pound

or per kilo or per cell,

that's really saying that those cells

are functioning with much less energy.

efficiency to being big,

and it's hard to understand why.

What is it that the cells

are providing to each other,

somehow cooperating in some way?

100 to the three quarters,

so if you got an organism

that's 100 times bigger,

then according to this, only 31.6

times the metabolic rate.

So it seems like a big savings.

It's a big savings.

It's a biological fact,

but people have been

arguing now for a century

what accounts for this three quarters.

Kleiber's observation,

the mystery only deepened.

brain size also roughly scales

as mass to the three quarters,

and so does an animal's growth rate

and the amount of blood pumped per minute.

as mass to the three quarters.

creature will live, a mammal,

that tends to be proportional to its mass

to the one quarter power.

One over four, not three over four.

double the mass of a mammal,

then on average, its lifespan

is around 19% longer.

Similarly, blood

circulation time also scales

quarter, while breathing rate

and heart rate both scaled

to the negative one quarter.

They're not all three quarters power laws,

but they are all multiples of a quarter.

So the question on everyone's mind was

where are these quarter power

scaling laws coming from?

(mellow music)

Brian Enquist was studying

for an undergraduate degree in biology.

classes then that you take,

you learn about the Krebs Cycle

and then you have to memorize

all the different parts

of a flower and then all...

They have a different

terminology for everything.

he took a zoology class

where they showed him those

quarter power scaling plots.

I was like, "You got to be kidding me."

You know, this is kind of

like something fundamental

that's kind of like underlying

biological diversity.

And there I knew immediately that I wanted

to kind of quit my specialized

kind of plant physiology research

and do something associated with scaling.

(mellow music)

studying for his PhD,

under Professor James Brown,

who had been thinking about

scaling laws for years.

So they knew that often

when power laws appear,

there's some form of self-similarity

in the underlying system.

So they wondered, what could

that self-similarity be?

And they suspected that it

might have something to do

with the way resources are

transported through the body,

specifically the networks that do this.

They had the biological intuition,

but to get a complete theory,

they needed a formal

mathematical framework.

In other words, they

needed a mathematician

or a theoretical physicist.

with the Santa Fe Institute,

and he started asking around with,

is there anyone up here

that's interested in these

biological scaling relationships?

And then the president at the

time said, "You know what?

I know of this physicist

who's up at Los Alamos

who was talking about biological

scaling relationships."

And so we met Geoffrey and

it was like immediately,

it's like we'd been talking

about the same things

for like years.

It's like, you know, finding,

someone who's been like

speaking your language,

but no one could understand you.

and Enquist teamed up

to try and find a compelling

explanation for Kleiber's Law.

three simple premises.

The first premise is that the networks

that distribute resources

are space-filling,

since they need to reach

every cell in the body.

The second premise is

that the terminal units

of those networks, the thinnest segments

on the outer periphery

of the delivery system,

have the same width regardless

of the size of the organism.

That is the outermost blood

vessels that carry nutrients

to an elephant's skin

cells are about as thick

as the ones in a mouse.

The elephant just has many more of them.

And the third premise is that over time,

evolution has driven

these transport networks

toward an efficient design.

So what should such a network look like?

(mellow music)

fuel from one place to another

as efficiently as possible,

you want the path to be

as short as possible.

So basically a straight line.

But because fuel needs to

reach every part of the body,

you would also need many different paths.

And as you go to larger

and larger organisms,

the networks inside need to

reach a larger and larger volume.

One way to do this is

to stretch all the paths

and match the growth of the animal.

In this case, the volume of the animal

should scale as these

internal path lengths cubed.

Or if we rearrange that,

internal path length should scale

as volume to the one-third,

just like the overall

length of the animal does.

Take these two regions.

The two vessels that

are bringing blood here

go through almost the

same path in the body,

and they only split up just

before they reach their destinations.

If instead we had just one

vessel up to this point

and split it only when the

paths needed to diverge,

we could serve the two regions

using a lot less vessel material

and a lot less blood to fill the vessels.

Of course, you can extend this logic

for all the blood vessels in the body,

and you end up with a

much more efficient design

of branching blood vessels.

because each branching point

provides an opportunity

for some of the blood to

bounce back, that is reflect.

If you have many reflections,

that would mean it

costs significantly more

energy to pump blood around.

So next, they argue that

nature should favor structures

that minimize reflections.

And as it turns out, this happens

if the cross-sectional area of the vessels

stays the same before

and after the branching.

So if you've got a cross-sectional area

of two centimeters squared

for the main vessel,

then each of the two

branches need to have an area

of one centimeter squared each,

for large vessels at least.

For smaller ones, daughter

branches can be a bit thicker

to allow blood to slow down

and exchange resources with

the tissue it's reaching.

If you keep repeating this

pattern across the network,

you end up with this, a

branching self-similar fractal.

And if you look at the actual shape

of the circulatory system,

it has this geometry.

So it seemed like they

were onto something.

to quarter power scaling laws?

Well, mathematician Felix

Hausdorff discovered

that self-similar fractals

have an interesting property.

(mellow music)

Take a straight line segment.

It's completely one-dimensional

and not a fractal at all.

Hausdorff assigned this

line segment a value of 1.0.

But now imagine adding a few bends

and more bends to those bends.

If you keep doing this,

the line becomes more

and more fractal-like.

Eventually, if you keep applying

the right kind of contortions,

that one-dimensional line segment fills up

an entire region of the 2D plane.

Hausdorff assigned these

space-filling fractal curves

a value of 2.0, corresponding

to their dimensionality.

The same ideas apply to a 2D surface.

Two-dimensional.

All then the fractal network

is doing is crumpling up

that sheet of paper,

and it effectively fills

a ball of volume.

So you can now describe

that sheet of paper

as a sphere instead of a

two-dimensional sheet of paper.

right pattern of folds

at smaller and smaller

scales, and a 2D surface

fills more and more of a 3D volume.

In the mathematical limit,

it becomes space filling

with Hausdorff dimension of 3.0.

"Well, what does that mean?"

That enables an organism for a given size

to pack in more of these

metabolic surface areas

than would be expected.

And it's because of this

fractal-like structure

that enables you then to pack

in and have all of these folds

and convolutions and on top of each other

to pack in an enormous

amount of membrane surfaces.

dimension of the surface

of the circulatory

system is roughly three,

meaning its surface area doesn't scale

as its length squared,

but it's length cubed.

And since the metabolic rate hinges on

how fast resources can be

exchanged across the surface area,

well, it must also

scale like length cubed.

But remember, West, Brown and Enquist

wanted to explain Kleiber's Law.

So they needed to know how

metabolic rate scales with mass.

(mellow music)

Since every cell needs to

be served by the network,

this means that the volume

around the network should be proportional

to the animal's mass.

And since volume is just

surface area times length

and surface area is

proportional to length cubed,

that means both volume and mass

must be proportional to

length to the fourth,

which can be rewritten to show

that length is proportional

to mass raised to the one quarter.

And if you plug that into the equation

for the metabolic rate,

you find that the metabolic rate

must be proportional to

mass to the three-quarters,

exactly as Max Kleiber had found.

West, Brown and Enquist

published their work in 1997,

and it soon came to be known

as WBE Theory, after their initials.

It makes very specific predictions.

This is good science.

Okay?

This is sticking your neck out,

and it's an incredibly beautiful theory.

(mellow music)

from Geoffrey West's book.

These are the scaling

exponents WBE theory predicts,

including many that are

not multiples of a quarter,

but all follow from the same theory.

For example, the radius

of an animal's aorta

should scale with its mass

to the three-eighths or .375.

And the area of its lungs

should scale with mass

to the 11-12ths or about 0.92.

In total, this chart makes

26 different predictions.

Now, these are the observed data.

Radius of the aorta, 0.36.

Lung area, 0.95.

about what they did.

They had a table with

something like, I don't know,

20 or 30 predictions of exotic exponents,

and that's what you

really see in the data.

So this one theory accounts not only

for the three-quarters

power of metabolism,

but for literally dozens of other things

that biologists have measured.

laws are easy to explain

once you've got the

three-quarters law for metabolism.

Take a mammal's heart rate, for instance.

Heart rate is equal to the blood flow rate

over the amount or volume

of blood in every beat.

(mellow music)

The volume of blood

per beat has been found

to scale in direct proportion

to an animal's mass.

So that's just M.

And the blood flow rate?

Well, remember that

metabolism is all about

how nutrients get

distributed around the body.

So most biologists agree metabolic rate

and blood flow rate are directly

proportional to one another.

So heart rate should scale

as metabolic rate over mass.

Swapping in the scaling

law Kleiber had found,

that gives us M to the minus one quarter,

meaning bigger animals should have slower

heartbeats than smaller ones.

And this is exactly what

we observe in nature.

The world's smallest

mammal, the Etruscan Shrew,

has an extraordinary heart

rate of 1200 beats per minute.

That's 20 beats per second.

Whereas the biggest land mammal,

the African bush elephant,

has a typical heart rate of

only 30 beats per minute.

similar for lifespan.

One of the leading theories is

that an animal's lifespan is based on

the accumulation of metabolic damage.

That is, as each chunk

of tissue in an organism

processes nutrients over time,

this causes damage to accumulate,

and that over time

causes the animal to die.

So the rate at which an

animal accumulates damage

is its metabolic rate per unit of mass,

and its lifespan should be

the inverse of that rate.

If damage accumulates

faster, it dies sooner.

If it accumulates slower, it lives longer.

So lifespan is proportional to M over B,

or substituting in Kleiber's

Law, M to the one quarter.

So lifespan should increase with mass.

And you do see this in nature.

(mellow music)

A shrew only lives for one

to two years in the wild

while a mighty African elephant

can live up to 70 years.

So if you're a small mammal,

you have many heartbeats per minute,

but you live a relatively short life.

Conversely, if you're a larger mammal,

your heart beats much slower

and you live a lot longer.

live fast and burnout

and die young, right?

Or spend it frugally and

live a really long life.

noticed something else.

Heart rate scales as B over M.

So it equals B over M times some constant.

And lifespan scales as M over B.

They're inverses of each other.

They scale in equal and

opposite directions.

Now, the total number of

heartbeats in an animal's life

is just the heart rate

multiplied by the lifespan.

So when you multiply these

two terms, they cancel out,

leaving you with just a constant.

So that suggests that no matter

what mammal you're talking about,

it should have roughly the

same number of heartbeats.

You can find that number by

just plugging in some examples.

Let's start with the Etruscan Shrew.

The shrew's 1200 beats per

minute multiplied by a lifespan

of around 1.5 years gives you

around 950 million heartbeats

in the course of the shrew's life.

Meanwhile, an African

elephant's 30 beats per minute

multiplied by a lifespan

of around 65 years

gives you a little over

a billion heartbeats.

And we could keep going.

(upbeat music)

But for nearly every mammal you look at,

you keep landing at the same figure of

around a billion heartbeats.

This is why nearly every

mammal from a tiny field mouse

to a gazelle, from a

cheetah to a hippopotamus,

they all get around a billion heartbeats

between the day they're

born and the day they die.

But there is one major outlier, one mammal

that gets significantly more

than a billion heartbeats.

And that is us, humans.

(mellow music)

We are the lucky ones.

Three centuries ago,

humans were much closer

to the standard value of

one billion heartbeats.

But around the mid 1800s, germ theory

and better sanitation

methods became widespread,

causing a stark decrease in

the number of child mortalities

and deaths from disease.

So life expectancy began to climb up.

And with it, the average number

of heartbeats in a lifetime.

If you look closely, you can

also see some significant drops

like this 1918 dip from

the Spanish flu pandemic

or over here, what appears to be

the impact of the Second World War.

But overall, the trend is clear.

We have systematically

been increasing the number

of heartbeats we get in

our lifetime to the point

where now the average human

gets nearly three billion

heartbeats before they die.

I don't know if there's a

better argument for science

and technology than this.

It has literally given the average human

more than a full extra life.

And it's not just humans.

Other mammals have been observed

to have much longer lives in

captivity when they're away

from the hazards they would

naturally encounter in the wild.

Or if you look at it purely

from the number of years we get,

we now have the lifespan

of a much larger mammal,

somewhere between an elephant and a whale.

But there is one curious

thing about this trend.

(mellow music)

Take a look at this graph.

It looks surprisingly similar

to the graph from before.

In fact, if you overlay them,

they look remarkably similar.

Now I want you to take a

guess at what this graph is.

Have you got your answer?

It is the number of

people living in cities.

For these two charts,

we're using data from parts

of the United Kingdom

where the record keeping

goes back several centuries,

but the rest of the world

has followed similar trends.

Of course, that doesn't mean

cities cause people to live longer,

but it goes against the

perception of cities

as being full of pollution and

breeding grounds for disease.

Already in 1889, a medical doctor wrote,

"The poisonous germs and

pollutions of the city,

it's impure air and water, bad sewage,

and endless nuisances."

So how do you reconcile these two views?

Or more specifically, is

there any quantitative data

on how smaller cities

compare to larger ones?

• It turns out this is something

that Geoffrey West pursued

after his work with Brown and Enquist.

He and collaborators like

Luis Bettencourt and others

have looked at scaling laws in cities.

(mellow music)

• [Host] They looked at

how different properties

like the amount of crime scale

as the population of the city increases,

and what they found is that if you plot

serious crimes on a log log plot,

the data clusters around a straight line

with a slope of 1.15,

meaning crime grows faster

than linear or super linear.

So for every doubling

of a city's population,

you get around 2.2 times

as many criminal cases

or around 120% more crime

as opposed to the 100%

you might naively expect.

To make matters worse, researchers found

that the same general pattern

holds for the amount of wastewater

and even the number of AIDS cases.

The exact exponents vary a little,

but overall, as cities grow larger,

you systematically get more of each.

So it seems like that medical

doctor was onto something.

And you might think life on

earth would be better off

if we all lived in small towns instead,

but that might not be the case.

(mellow music)

In 2006, Dirk Helbing, Christian Kuhnert,

and Geoffrey West looked at how the number

of gas stations scales as

a function of population.

• If a city is twice as

big, does it need twice

as many gas stations?

Because, you know, we have to

supply not exactly nutrients,

but energy, gas, for all those cars.

• [Host] The naive expectation is that

if you double the number of cars,

you're going to need to

double the amount of fuel,

so double the gas stations.

To find out whether this was true,

they plotted the data on a log log plot

and found a straight line.

But the exponent wasn't

one, it was about 0.8.

This means that for every

doubling, you only need around 74%

more gas stations, which

is a decent savings.

(mellow music)

The amount of roads and electrical cables

also scale in roughly the same way.

The rough figure that

West gives in his book

is that they all have scaling

exponents of around 0.85.

• It is interesting

that some of the things

that we can share, like you can drive

on the road, but so can I.

When it's shared resources, yes,

cities can be surprisingly green.

The argument is that

cities can be even greener

than you might think than living out

in the middle of nowhere.

• But cities have even bigger benefits.

Things like total wages, GDP,

and the number of patents

all scale superlinearly,

with exponents that cluster

somewhere around 1.15,

meaning that for every doubling in size,

you get around 120% more of each.

All of this becomes especially significant

when you compare a small

town of say 50,000 people

to a city 100 times its size

because infrastructure needs

only need to go up by a factor

of about 50 while total wages,

GDP, patents and inventions,

they all go up by a factor of 200.

Unfortunately, disease

and crime also go up

by the same factor.

Or look at it this way,

on a per person basis,

you'd only need about

half the infrastructure,

while you get double all

the socioeconomic factors.

So cities far from being

detrimental to the world,

they might actually be

one of our best inventions

and an indirect driver

of a lot of scientific

and technological progress.

Perhaps this is also why people often say

that life in the city feels faster.

A feeling that seems justified

because researchers looked at

how fast people walk in

cities of different sizes.

And they found that

people literally do walk

faster in larger cities.

• That turns out to depend on city size.

It's not just that the

sidewalks are congested or not.

It's just like the vibe

gets people amped up.

They move faster in cities.

• So the pace of life

seems to be increasing,

but that may come at a cost

because as one person put it,

"everything nowadays is ultra.

Everything is being

transcended continually

in thought as well as in action.

No one knows himself any longer.

Young people are stirred

up much too early in life

and then carried away in

the world of the times.

Wealth and rapidity are

what the world admires".

Could it be that life

is accelerating so fast

that humans won't be able to keep up?

Well, probably not

because this quote was written in 1825

by Wolfgang von Goethe.

For the past 200 years

and probably longer,

almost every generation has

felt like life was accelerating.

And yet every generation has managed.

So I think it's likely we can continue

to adapt indefinitely.

And as cities continue to grow in size,

all of us will continue

to reap the benefit

of economies of scale in much the same way

that mammals benefit from being larger.

But while WBE Theory seems to predict

where the exponents in

biological scaling laws come from,

for cities, there is no widely accepted

explanatory theory yet.

Trying to explain where

those exponents of 0.85

and 1.15 come from is one of

the big goals for theorists.

Although even WBE Theory is

not universally accepted.

For one, the fact it

predicts the right exponents

doesn't necessarily mean the

theory itself is correct.

There are a few other

theories that predict

some of the same scaling exponents,

and there are also some other critiques.

• There's a lot of discussion.

It may look convincing.

And personally, I tend to

think it is very impressive.

But I have very good

colleagues like Peter Dodds

at University of Vermont,

and he thinks that a

lot of the data analysis

is either not done exactly right

or that the data are so noisy

that you shouldn't really

take this so seriously.

• Dodds even argues that Kleiber's Law

itself might not be true.

(mellow music)

• In the 1960s, there's a

symposium on energy metabolism,

some name like this in animals,

and at the end of it, they vote 29 to zero

that it's going to be

three quarters, right?

Because, you know, you

got to set some rules.

If you go back and look at the data,

which no one is really

doing anymore, right,

the data does not work.

Like it doesn't work.

(mellow music)

• [Henry] This is a

graph of metabolic rate

as a function of mass based on a study

that looked at 391 species of mammals,

much larger than Kleiber's range.

And it looks like the three-quarter

slope fits quite well.

But this is just the

top part of the chart,

the biggest mammals.

If you zoom out, you see that

the rest of the mammals appear

to fall on a line that's

closer to two-thirds.

And in recent studies of bird metabolism,

you also find a slope that appears closer

to two-thirds than three-quarters.

Could it be that those French scientists

from centuries ago were right,

that metabolic rate really does

just scale with surface area?

Well, not so fast.

(mellow music)

For one, many recent studies

of cold-blooded animals find slopes

that are significantly

higher than two-thirds.

The bigger problem is that measuring

metabolic rates is difficult.

It generally involves putting

animals in a container

and taking very precise measurements

of their heat production

or oxygen consumption,

all while ensuring that the

animal is in an unstressed,

low activity resting state.

Unsurprisingly, this is

particularly difficult

to pull off with large animals.

And as a result, many studies

have found scaling exponents

where the error bars include both

two-thirds and three-quarters.

Today, the research community is split.

Many uphold Kleiber's Law and

the three-quarter scaling,

while others think it's two-thirds.

But a growing number suspect

that there is no

universal scaling exponent

across all of life.

In fact, it may very well be the case

that the metabolic rate of larger mammals

scales as their mass

to the three-quarters,

while for smaller ones, it's

their mass to the two-thirds.

• You know, it's like

everything in science

that there are people

arguing, and that's good.

• I guess the bigger exhortation

would be someone to really measure it,

measure things beautifully.

You know, we're in 2026,

has to be not just one

elephant at one zoo,

it needs to be measured again really well.

• [Host] What everyone does agree on

There's often in real life

departures from proportionality,

and you have to be aware of it.

Sometimes things punch above their weight,

and as you get bigger,

you get more efficient.

Sometimes there are detriments to size.

efficiency perspective,

animals benefit from being larger.

Similarly, all of us potentially stand

to gain from having more

people living in larger cities.

It could lead to more

discoveries and inventions,

and in doing so, improve

the standard of living

for all of us, which

might even give us more

heartbeats in our lifetimes.

Kleiber's law to WBE theory,

how metabolic rate scales with mass

has been one of biology's

biggest debates for centuries.

By collecting better data

and analyzing it carefully,

there's a good chance

that the next generation of

researchers could be the ones

to finally put this debate to rest.

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