- [Instructor] Hi.
This is the first video in a series about biology.
There's a lot to learn in biology.
Most courses start out with water,
then you learn about organic molecules
and then you learn about how those molecules come together
to form living things and you go from there.
And that's all great but we're not going to bother
with any of that, at least not right away.
Instead, we're gonna focus on evolution
because whenever you ask a why question in biology,
the answer always comes back to evolution
and we're going to spend a while on evolution.
It's gonna be 10 to 15 videos.
We're gonna take it slow and we're gonna use simulations
and math to really understand it.
So in the spirit of taking it slow,
let's zoom out and talk about things in general,
including nonliving things.
Why do things exist
You could answer this question in a number of ways
but the answer that we'll use has two parts.
First things, that exist have started existing
or they've been born.
Second, they haven't stopped existing yet
or they haven't died.
It kind of seems like we haven't really said anything,
but breaking it into two parts
does help us look at some patterns.
For example, raindrops.
Why do raindrops exist?
Well, they're good at this first part,
they're good at being born.
They don't last very long but they form pretty often,
often enough where it's not unusual to see them.
A different example is planets or stars.
Unlike raindrops, they don't form very often at all,
but they more than make up for it by lasting a long time.
When we look up in the sky or just at the ground,
we see planets and stars.
They're also common,
even though they do it in a very different way.
Any kind of thing that exists strikes some balance
at being good at one or both of these two things.
So this is all well and good but as promised,
we can make it a lot sharper
by building some simulations and an equation.
This blob creature will be the star of our first simulation.
At each frame in the simulation,
one of these blob creatures will form
and each living creature
will have a one in 10 chance of dying.
For comparison, let's make a second simulation
with this other type of blob creature.
Compared to the first kind,
this blob creature will be more like a planet.
It'll form less often but it will also die less often.
Each frame, there will only be a one in 10 chance
of one of these forming but each blob creature
will only have a one in 100 chance of dying.
After watching for a while,
we can see that even though these two
kinds of blob creatures are quite different,
on average, there's about the same number
of them at any given moment.
You might be able to guess what happens
when a kind of blob creature has a low birth rate
like a planet and also a high death rate like a raindrop.
There just aren't very many of 'em.
At the other extreme, if a kind of blob creature
has a high birth rate like raindrops and a low death rate,
there will be a lot of them.
So why do these simulations seem to stabilize
around a certain number of creatures?
You might already have some intuition for this,
but we can translate that intuition into an equation
which will let us predict equilibrium number
for any birth rate and any death rate.
If the total birth rate is equal to the total death rate,
we'll expect the population size
to stay the same from one frame to the next.
And since each creature individually has a chance of dying,
the total death rate depends
on the current number of live creatures.
Using numbers from our first simulation,
where one creature was born each frame,
and each creature had a one in 10 chance
of dying each frame, we can see that the expected
birth rate and death rates should be equal
when there are 10 creatures
and that's what we saw in the simulation.
But we also saw in the simulation
that the number of creatures fluctuated all over the place.
It didn't just stick at 10.
It's possible for all of the creatures
to get lucky and not die, in which case,
the number of creatures rises to 11 in the next frame
but then the expected death rate
will be higher than the birth rate
and then on average, we'd expect more than one creature
to die in the next frame,
which would push the number back toward 10.
Of course, the creatures could keep getting lucky
but the more creatures there are, the less likely that is.
It's also possible that more than one of them
will get unlucky and die, leaving us with fewer
than 10 creatures but if this happens,
the expected death rate is suddenly lower
than the birth rate, so in the next frame,
we'd expect the population to drift back up toward 10.
The fancy word for a balancing situation like this,
is equilibrium and 10 is the equilibrium number
of creatures for the first simulation.
Going back to the more general version of the equation,
we can shorten it up by using the letter symbols
instead of the full words and we can solve for N
to get a formula we can use
to predict the equilibrium number.
So now if we set up a new simulation
with a birth chance of 80% and a death chance of 2%,
what equilibrium numbers should we expect?
Well, the formula tells us it should be 40,
so let's see what the simulation does.
Looks about right.
All right, so what does this have to do with living things?
From what we said so far,
it kind of seems like we shouldn't exist.
We're too complex to form
spontaneously the way raindrops do.
Imagine all the right atoms and molecules
just happening to come together to form a rabbit.
It's pretty unlikely and we also don't live all that long,
but somehow, living organisms are still pretty common,
so what's going on?
Now would be a good time to pause and think for a second.
All right, ready for the big reveal?
As you may have guessed, living things are special
because we can make more of ourselves.
We have an extra parameter in our simulation,
a chance to replicate.
So let's add replication to our equilibrium equation.
Just like before, we're looking for a situation
where the birth rate is equal to the death rate.
The overall death rate is just like it was before,
it's the number of live creatures,
times the likelihood of each creature to die.
The overall birth rate is different though.
We still have this B, which stands for the likelihood
that a new creature will spontaneously pop into existence
like a raindrop but we also have this extra piece
to account for reproduction.
This works just like the overall death rate.
Each creature has its own chance to reproduce,
so we multiply that chance by the number
of living creatures to get the total number of births
we expect from reproduction, each frame.
The significant thing about this equation
is that N is on both sides.
Before, just the death rate went up
as the number of creatures grew,
but now the birthrate also grows as N gets bigger.
To see this in action, let's solve for N
and look at a simulation.
We'll start our simulation with two creatures.
The spontaneous birth chance each frame will be 10%.
That's a lot higher than it would be for an actual rabbit
but we only have so much time in this video.
And the death chance per creature, each frame, will be 5%.
For now, we'll just leave the replication chance at zero.
Our formula tells us that the equilibrium number
of creatures should be two, though it's a bit hard
to see in this simulation because of the fluctuation.
Anyway, if we bump the replication chance up to 1%,
we see the equilibrium number go up to 2.5.
Not a huge difference but as we push it higher,
the equilibrium number goes up by more and more each time
and we can start to see the effect in the simulation.
And you might notice that we're about to run into an issue.
If we raise the replication chance to 5%,
we'll be dividing by zero
and there won't be an equilibrium at all anymore.
The population will get bigger and bigger without limit
and if the replication chance goes higher
than the death chance, our formula
gives us a negative number for N, which makes no sense
because we can't have a negative number of creatures.
And even if we could, the number of creatures
is clearly going up and up and up
and not getting closer to that negative number.
Reproduction quite literally breaks our equation.
This is why living things are special.
They follow their own set of rules,
which makes it possible for the complexity of life to exist.
The rest of the videos in this series
are going to explore the consequences of this,
which are collectively called the theory of evolution.
See you in the next video.