(slow music) - [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.
