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So, let's start with where we were.
We were talking about exponential

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growth in populations.
And, we said we could describe this

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00:00:20,000 --> 00:00:31,000
as one over the dN/dt equals some
growth rate, r.

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00:00:31,000 --> 00:00:40,000
And, in this case,
we're talking about,

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00:00:40,000 --> 00:00:50,000
let me ask that is a question.
As a model for population growth,

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what's wrong with this?  What does
this project?

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00:01:00,000 --> 00:01:06,000
This is N.  This is time.
There's no stopping it.  I mean,

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00:01:06,000 --> 00:01:13,000
we'd be knee deep in everything if
populations grew according to this

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00:01:13,000 --> 00:01:19,000
model, OK, because it just goes off
into infinity in terms of density.

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So, we know that this is inadequate.
In fact, some people describe the

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00:01:26,000 --> 00:01:33,000
entire field of population ecology
as a field that tries to determine

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why real populations can't grow
according to this model.

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00:01:40,000 --> 00:01:45,000
In other words,
the whole field is trying to

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00:01:45,000 --> 00:01:50,000
understand what the mechanisms are
in populations that limit their

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growth.  So, they don't grow
exponentially forever.

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So, in this case, this is really a
maximum growth rate.

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00:02:00,000 --> 00:02:06,000
We can call that r Max.
And in this case, it's a constant.

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00:02:06,000 --> 00:02:12,000
So, when we're talking about
exponential growth,

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the growth rate per unit time is the
maximum growth rate that that

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00:02:19,000 --> 00:02:25,000
population is capable of under those
conditions and it's a constant.

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So, if we want to plot it this way,
one over N, dN/dt, as a function of

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N, is constant.
It doesn't change as density changes.

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So, now we're going to take a
historical look at this.

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00:02:48,000 --> 00:02:58,000
Back in the 1920s, two fellows
named Pearl and Reed wanted to model

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00:02:58,000 --> 00:03:05,000
human population growth.
And they looked at this exponential

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00:03:05,000 --> 00:03:11,000
growth equation,
and they said there's got to be

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00:03:11,000 --> 00:03:16,000
something wrong with that.
We can't just apply that to humans,

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00:03:16,000 --> 00:03:22,000
although if they plotted as a
function of time,

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00:03:22,000 --> 00:03:27,000
and this is humans in the US from
1800 to 1900, and this is the human

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00:03:27,000 --> 00:03:33,000
population size,
if they plotted this on this curve,

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00:03:33,000 --> 00:03:39,000
they got something that looked like
this.

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So, it kind of looked like
exponential growth.

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00:03:46,000 --> 00:03:53,000
But, when they went in it actually
looked at one over ND,

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00:03:53,000 --> 00:04:01,000
dN/dt, which would be the slope
along here, they found that it looks

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00:04:01,000 --> 00:04:07,000
something like this.
In other words,

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00:04:07,000 --> 00:04:11,000
the actual growth rate of the
population was decreasing as the

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00:04:11,000 --> 00:04:15,000
number of humans increased.
And this is called a density

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00:04:15,000 --> 00:04:28,000
dependent response.

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00:04:28,000 --> 00:04:35,000
OK, so if we look at this,
remember from last time that r is

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00:04:35,000 --> 00:04:42,000
equal to the birth rate minus the
death rate, right?

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00:04:42,000 --> 00:04:49,000
So, we can look at,
this is just a simple cartoon

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00:04:49,000 --> 00:04:56,000
drawing of what's going on here.
Density dependent factors regulate

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00:04:56,000 --> 00:05:02,000
population size.
So, if we plot one over ND,

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00:05:02,000 --> 00:05:06,000
dN/dt as either a birth rate or a
death rate, as a function of

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00:05:06,000 --> 00:05:10,000
population density,
when you have density,

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00:05:10,000 --> 00:05:15,000
really the one that's the most
important here is looking at this

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00:05:15,000 --> 00:05:19,000
one, that death rate increases as
population increases,

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and birth rate decreases.
And you have an intersection here

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00:05:24,000 --> 00:05:28,000
where birth rate and death rate are
equal, and your population's going

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00:05:28,000 --> 00:05:33,000
to stabilize there where there will
be no change in population growth.

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00:05:33,000 --> 00:05:39,000
And these density dependent birth
rates and death rates introduce a

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00:05:39,000 --> 00:05:46,000
stabilizing factor.
As N increases, r decreases in the

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00:05:46,000 --> 00:05:53,000
population.  And that's what brings
population back into some sort of

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00:05:53,000 --> 00:06:00,000
equilibrium.  OK, so all
right, forget that.

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00:06:00,000 --> 00:06:06,000
So, let's go back over to Pearl and
Reed.  We're going to stay on the

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board for awhile.
So the question is,

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00:06:12,000 --> 00:06:18,000
how do we modify that equation,
our simple exponential growth

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00:06:18,000 --> 00:06:24,000
equation, so that it more
realistically describes real

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00:06:24,000 --> 00:06:30,000
populations that can't grow totally
unconstrained?

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00:06:30,000 --> 00:06:44,000
So what Pearl and Reed did,
how do we modify the exponential

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00:06:44,000 --> 00:06:59,000
growth?  So, here's what we want the
characteristics to be of this

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00:06:59,000 --> 00:07:14,000
equation.  We want one over N,
dN/dt, to go to zero as N gets large.

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00:07:14,000 --> 00:07:19,000
And we want it to go to our max,
the maximum growth rate, when N

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00:07:19,000 --> 00:07:24,000
approaches zero.
In other words, at really,

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00:07:24,000 --> 00:07:29,000
really low population density is,
you can effectively have exponential

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00:07:29,000 --> 00:07:34,000
growth because nothing's
limiting you.

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00:07:34,000 --> 00:07:41,000
When the density gets very,
very large, you want this growth

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00:07:41,000 --> 00:07:48,000
rate to go to zero.
So, they came up, so let's plot

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00:07:48,000 --> 00:07:56,000
this N.  This is T,
and here's our exponential growth

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00:07:56,000 --> 00:08:06,000
equation.
And they came up with a function

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00:08:06,000 --> 00:08:19,000
that looks like this.
So, this would be one over N,

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00:08:19,000 --> 00:08:32,000
and to describe this, we have this
equation.

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00:08:32,000 --> 00:08:37,000
And this is called the logistic
equation for reasons that are

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00:08:37,000 --> 00:08:42,000
historically obscure.
This is a French term that has

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00:08:42,000 --> 00:08:47,000
something to do with,
anybody know, who speaks French?

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00:08:47,000 --> 00:08:52,000
It has to do with something
military.  Anyway,

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00:08:52,000 --> 00:08:57,000
I've never been able to figure out
why they call this the

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00:08:57,000 --> 00:09:05,000
logistic equation.
But it doesn't matter what it's

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00:09:05,000 --> 00:09:15,000
called, this is what it is.
And K here is the carrying capacity

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00:09:15,000 --> 00:09:26,000
of the environment.
It's the maximum number of

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00:09:26,000 --> 00:09:37,000
organisms were the population
levels off, OK?

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00:09:37,000 --> 00:09:44,000
All right, so let's look at this.
Let's replot this, because it's

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00:09:44,000 --> 00:09:52,000
easier to analyze the features.
We're going to plot one over N,

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00:09:52,000 --> 00:10:00,000
dN/dt as a function of N.  If we
want to rewrite the equation,

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00:10:00,000 --> 00:10:08,000
one over N, dN/dt equals our max.

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00:10:08,000 --> 00:10:20,000
We're just rearranging that equation
to make it easier to visualize.

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00:10:20,000 --> 00:10:32,000
OK?  So that we have a line that we
can put that on,

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00:10:32,000 --> 00:10:45,000
such that K is the X intercept,
and what's this?

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00:10:45,000 --> 00:10:57,000
Our max, exactly.
So, you can see these features over

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00:10:57,000 --> 00:11:07,000
here at this plot, right?
So, as this goes to zero,

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00:11:07,000 --> 00:11:13,000
or as N is very large, one over N,
dN/dt goes to zero.  And, when N is

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00:11:13,000 --> 00:11:19,000
very small, one over N,
dN/dt is near our max.  You're

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00:11:19,000 --> 00:11:25,000
basically growing.
You're over here where the

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00:11:25,000 --> 00:11:31,000
exponential growth curve and the
logistical curve are essentially the

95
00:11:31,000 --> 00:11:37,000
same thing.  Yeah?  Do I
have something wrong?

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00:11:37,000 --> 00:11:47,000
Oh, very good,
very good, very good.

97
00:11:47,000 --> 00:11:57,000
Thank you.  Absolutely right.
OK, so the slope here is going to

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00:11:57,000 --> 00:12:09,000
be minus r max over K.  .
OK, so here we have a nice density

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00:12:09,000 --> 00:12:23,000
dependent response.
OK, let's analyze some more

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00:12:23,000 --> 00:12:35,000
features of this.
Just looking at the exponential and

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00:12:35,000 --> 00:12:45,000
the logistic, just to summarize,
one over N, dN/dt as a function of N,

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00:12:45,000 --> 00:12:55,000
and if we just look at the dN/dt as
a function of N,

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00:12:55,000 --> 00:13:06,000
for exponential we already said that
this is a flat line, right?

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00:13:06,000 --> 00:13:14,000
It's a constant,
but the actual change in numbers as

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00:13:14,000 --> 00:13:22,000
a function of time is a straight
line, whereas for the logistic,

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00:13:22,000 --> 00:13:31,000
one over N, dN/dt as a function of N,
what does this look like?

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00:13:31,000 --> 00:13:38,000
We just did it,
so we are summarizing here.

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00:13:38,000 --> 00:13:45,000
But here's one that I want you to
think about.  What does the dN/dt

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00:13:45,000 --> 00:13:52,000
look like as a function of N if
something's growing according to the

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logistic equation?
Like this?  Yes, there you go,

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00:13:59,000 --> 00:14:06,000
like that.  Right.
Because there is an inflection point

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00:14:06,000 --> 00:14:14,000
here, right?  So,
this is what's sometimes called the

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00:14:14,000 --> 00:14:21,000
optimum yield,
and believe it or not,

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00:14:21,000 --> 00:14:29,000
this model is actually used in
fisheries conservation for years.

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00:14:29,000 --> 00:14:36,000
Now we know that it's so much more
complicated than that that you can't

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00:14:36,000 --> 00:14:43,000
just set the model is.
But one could argue that if you are

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00:14:43,000 --> 00:14:50,000
managing a population that you want
to harvest, that you try to keep

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00:14:50,000 --> 00:14:57,000
them at the density at which the
dN/dt, the production of organisms,

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is maximal.  So, you try to maintain
a population there at that point.

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One of the features of the logistic
equation is that it assumes

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00:15:22,000 --> 00:15:40,000
instantaneous feedback of the
density on growth rate.

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00:15:40,000 --> 00:15:45,000
In other words,
it says in a population of a certain

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density, the results in terms of
offspring will be instantaneous.

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And we know that's not true.  So,
this is an oversimplification.  Even

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in the simplest organisms,
even microbes in a culture,

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say you suddenly starve them up some
substrate that they're using.

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It takes a while for their
biochemistry to readjust before that.

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They might have one generation
that's still at the same growth rate

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00:16:14,000 --> 00:16:18,000
as it was before,
before the biochemistry readjusts

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and says, whoa,
we can't keep going at this rate.

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Slow down.  And then for higher
organisms, you might have a whole

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generation before that sets it in.
Plants that make seeds, etc.

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So we know that there's a problem
here.  So, people have tried to

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introduce time lags into the
equation, and we don't have time.

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I mean there's lots of really neat
things that you can do with this.

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00:16:43,000 --> 00:16:48,000
If this was an advanced ecology
course, you'd be modeling it on your

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00:16:48,000 --> 00:16:53,000
computer, and putting time lags in,
and see what happens and all that

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kind of stuff.
So we don't have time to do any of

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that.
I show you this more as a way,

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I want you to learn how population
ethologists think,

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00:17:09,000 --> 00:17:16,000
not that this is actually the most
important model that ever existed.

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So how do we introduce time lags
into the logistic?

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00:17:22,000 --> 00:17:28,000
Well, the simplest way is to
introduce time.  So, we're

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00:17:28,000 --> 00:17:37,000
going to say dNt/dt.
Let me just make sure that's not

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00:17:37,000 --> 00:17:48,000
ambiguous.  dNt/dT,
is equal to r max times N at that

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time t times K minus
Nt minus tao.

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In other words,
the density at some time,

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00:18:05,000 --> 00:18:10,000
tao hours or days or whatever,
earlier than t, divided by K.  So,

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00:18:10,000 --> 00:18:16,000
what this says is that the growth
rate of the population is a function

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of the density up a little bit
earlier, or some amount earlier than

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00:18:21,000 --> 00:18:27,000
the time at which we're measuring
the growth rate.

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So t or tao is the time lag between
sensing environments, and

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change in growth rate.
So let's look at what that means in

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00:19:03,000 --> 00:19:10,000
terms of, this brings us to another
level of complexity.

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So let's look at the possibilities
here.  So, with no lag,

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we have our logistic equation,
right?  The population just reaches

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00:19:24,000 --> 00:19:31,000
the carrying capacity
and levels off.

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With a very short lag,
and of course you have to play with

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this to understand what I mean by
short, long, and medium because you

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have to change all the different
parameters.  But if you have a short

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lag, what you get is an actual
overshoot of the carrying capacity

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in the near term because the
feedback hasn't kicked in.

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But then, it will come back and it
will level off at the carrying

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capacity.  If you have a medium lag,
you will often see something like

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this where you get a couple of
oscillations in here.

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But it levels off at the same
carrying capacity.

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And, a long lag,
you can end up with behavior that

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ultimately ends up in the population
crashing.  And we don't have time to

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analyze this, but at the end of the
lecture I'm going to come back to

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why this is so important in terms of
human population growth.

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And for those of you who are
interested in complex systems and

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00:21:04,000 --> 00:21:07,000
chaos theory, the logistic equation
in its discrete form actually will

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00:21:07,000 --> 00:21:10,000
go chaotic for certain parameter
values.  And for a long time,

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for those of you who don't know what
I'm talking about,

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00:21:13,000 --> 00:21:16,000
just ignore me.  And for those who
are interested ought to spend

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00:21:16,000 --> 00:21:21,000
a minute on it.
For a long time,

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this equation goes into a state of
sort of chaotic oscillations,

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but that can be described
mathematically.

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And for a long time,
ecologists kept looking at

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populations trying to see whether,
indeed, they were growing according

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00:21:45,000 --> 00:21:51,000
to this chaos theory and it hasn't
really developed to anything,

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00:21:51,000 --> 00:21:57,000
but it was interesting.  Chaos
theory first started coming to

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00:21:57,000 --> 00:22:03,000
light; the sea collision was one of
the first that people started

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00:22:03,000 --> 00:22:09,000
looking into, coincidentally.
But just because an equation has

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00:22:09,000 --> 00:22:13,000
certain properties,
it doesn't mean that thing it's

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00:22:13,000 --> 00:22:18,000
trying to model has those properties.
So that was a really interesting

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00:22:18,000 --> 00:22:23,000
development.  OK,
so let's go back to Pearl and Reed.

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Where did they go?  Oh, they're up
there.  OK, so this was

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00:22:27,000 --> 00:22:33,000
all a digression.
So Pearl and Reed were looking at

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00:22:33,000 --> 00:22:40,000
the human population data,
and trying to model it.  And they

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00:22:40,000 --> 00:22:47,000
showed that they had this density
dependent response.

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00:22:47,000 --> 00:22:53,000
They developed this equation in
order to describe it.

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00:22:53,000 --> 00:23:00,000
And then, they looked at the data
again using this graphical

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00:23:00,000 --> 00:23:07,000
formulation.
So, let's look at that.

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00:23:07,000 --> 00:23:14,000
We're just going to use the graphic
method, because it's easier to

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00:23:14,000 --> 00:23:22,000
illustrate.  And now,
we're looking at the human

197
00:23:22,000 --> 00:23:29,000
population in the US,
and this is one over N,

198
00:23:29,000 --> 00:23:36,000
dN/dt, and this is N in millions.
And so, they have some data points

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00:23:36,000 --> 00:23:44,000
that they put on here.
This is 1800 to 1810.  So,

200
00:23:44,000 --> 00:23:51,000
they have different data points for
different intervals,

201
00:23:51,000 --> 00:23:59,000
and their last point here was 1900
to 1910, an average of

202
00:23:59,000 --> 00:24:06,000
the population size.
And so, they projected down here

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00:24:06,000 --> 00:24:12,000
there were 100 million people then.
So, they said, so they asked the

204
00:24:12,000 --> 00:24:19,000
question: OK, we're modeling this
population, we're saying it grows

205
00:24:19,000 --> 00:24:25,000
according to the logistic equation,
we can predict what the carrying

206
00:24:25,000 --> 00:24:32,000
capacity in the United States for
humans by simply doing a regression

207
00:24:32,000 --> 00:24:39,000
through this, and seeing
where it intercepts.

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00:24:39,000 --> 00:24:50,000
So, that should be the carrying
capacity.  And they predicted that

209
00:24:50,000 --> 00:25:02,000
we'd have 197 million when we reach
the carrying capacity.

210
00:25:02,000 --> 00:25:08,000
And that was in the year 2030.
So that was a prediction of their

211
00:25:08,000 --> 00:25:15,000
model back in the 1920s,
that the carrying capacity of the US

212
00:25:15,000 --> 00:25:22,000
for humans was 197 million,
and that that would be reached in

213
00:25:22,000 --> 00:25:29,000
2030.  Well, they missed it by a lot.
So, let's look at the data,

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00:25:29,000 --> 00:25:37,000
which is not surprising.
Here's 1965.  We reached 200 million

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00:25:37,000 --> 00:25:47,000
way before 2030.
1990, 250 million,

216
00:25:47,000 --> 00:25:56,000
and actually today, at 10:45 this
morning, because I looked it up on

217
00:25:56,000 --> 00:26:06,000
my trusty population
clock on the Web,

218
00:26:06,000 --> 00:26:13,000
we had 295,979,
38 people.  This is also done by

219
00:26:13,000 --> 00:26:20,000
modeling, we're not counting people
one at a time.

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But this website is keeping track
based on various models.

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And, based on the models that we
have today, in 2030 we should have

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about 345 million.
But these models are based on

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00:26:41,000 --> 00:26:47,000
something entirely much more complex
now than the simple logistic

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00:26:47,000 --> 00:26:53,000
equation.  OK,
so the contribution of Pearl and

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Reed was to be yet to get people to
start thinking about the feedback

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00:26:59,000 --> 00:27:05,000
mechanisms, how to model population
growth, and think about the feedback

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00:27:05,000 --> 00:27:11,000
mechanisms in that model.
You don't have that in your handout,

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00:27:11,000 --> 00:27:18,000
but it's not important.  It's not on
the web, but if you care about it,

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there is the website that keeps
track of human population in the US.

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So, here's the total population
number that I got this morning at

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00:27:31,000 --> 00:27:37,000
10:14 and 17 seconds off the web.
And these are just some interesting

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00:27:37,000 --> 00:27:43,000
statistics for the US,
and I have them for the last three

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00:27:43,000 --> 00:27:48,000
years: one birth every eight seconds,
one death every 13 seconds,

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00:27:48,000 --> 00:27:54,000
one migrant every 26 seconds,
and a net gain of one person every

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00:27:54,000 --> 00:28:00,000
12 seconds.  So they're keeping
close track here.

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00:28:00,000 --> 00:28:04,000
OK, all right,
so now are going to move on to

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global population growth,
humans on the earth, the whole shoot

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00:28:08,000 --> 00:28:12,000
and match.  And,
there's this wonderful book for

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00:28:12,000 --> 00:28:17,000
anyone who's interested by Joel
Cohen, called,

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00:28:17,000 --> 00:28:21,000
How Many People Can the Earth
Support?  And,

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00:28:21,000 --> 00:28:25,000
it's a great book for MIT students
because it's a wonderfully nerdy

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00:28:25,000 --> 00:28:30,000
account.  I'm a nerd,
so I can say that.

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00:28:30,000 --> 00:28:35,000
I'm a total nerd.
But it's just a wonderful account,

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00:28:35,000 --> 00:28:40,000
analysis, if you analyze human
population growth,

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00:28:40,000 --> 00:28:45,000
and at the same time looking at the
phenomenon in a totally objective

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00:28:45,000 --> 00:28:50,000
way.  He's a theoretical ecologist.
So, this is in your textbook.  But,

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00:28:50,000 --> 00:28:55,000
it's from this book.  And, it's from
10,000 B.C. up to here we are today,

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00:28:55,000 --> 00:29:01,000
the population on Earth in billions.

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00:29:01,000 --> 00:29:06,000
And, this is back in the hunter
gatherer era.  We had 4 million

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00:29:06,000 --> 00:29:11,000
people.  And this was a small
revolution at the time,

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00:29:11,000 --> 00:29:16,000
the introduction of the agriculture
and domestication of animals allowed

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00:29:16,000 --> 00:29:21,000
for higher birth rates,
and so had a little blip,

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00:29:21,000 --> 00:29:26,000
went up to 7 million here.
And then for a long time, there was

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00:29:26,000 --> 00:29:32,000
just no change in human
population on Earth.

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00:29:32,000 --> 00:29:38,000
And so then, here you start to get,
I'm not sure what started this up

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00:29:38,000 --> 00:29:44,000
rise.  Maybe when we see the next
slide we'll see.

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00:29:44,000 --> 00:29:51,000
No, I'm not sure what started that.
We'll have to look into that.

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00:29:51,000 --> 00:29:57,000
Maybe just the accumulation of
people that you can't see on this

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00:29:57,000 --> 00:30:04,000
scale, here's the bubonic
plague, a decrease.

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00:30:04,000 --> 00:30:08,000
Here's the beginning of the
Industrial Revolution and the

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00:30:08,000 --> 00:30:13,000
introduction of modern medicine,
which greatly reduced mortality.  So,

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00:30:13,000 --> 00:30:18,000
you see this incredible,
and here's fossil fuel, increase in

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00:30:18,000 --> 00:30:23,000
the population of humans on Earth.
So, if you look at this curve, you

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00:30:23,000 --> 00:30:28,000
think, oh my God,
we're in the middle of this

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00:30:28,000 --> 00:30:33,000
incredible exponential increase.
And, the reality is this doesn't fit

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00:30:33,000 --> 00:30:37,000
at all in an exponential model at
all.  I mean, if you tried to fit

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00:30:37,000 --> 00:30:42,000
that to our simple exponential,
it does not fit.  We are going to

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00:30:42,000 --> 00:30:47,000
explain what's happening here in a
minute.  So here we are at 6 billion

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00:30:47,000 --> 00:30:51,000
people.  And we hit 6 billion in
1999.  And here we are with a steady

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00:30:51,000 --> 00:30:56,000
increase.  I've just got the last
three years.  This marks the

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00:30:56,000 --> 00:31:01,000
lectures that I've given
in this class.

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00:31:01,000 --> 00:31:05,000
Every year I check in and see where
we are.  It's kind of a living

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00:31:05,000 --> 00:31:09,000
document.  And,
we're now projected to reach 9

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00:31:09,000 --> 00:31:13,000
billion and level off.
When I first started teaching about

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00:31:13,000 --> 00:31:17,000
human population growth,
the projections were at 12 billion.

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00:31:17,000 --> 00:31:21,000
And I'm not that old.  This number
keeps changing,

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00:31:21,000 --> 00:31:25,000
and luckily it's changing in the
right direction.

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00:31:25,000 --> 00:31:29,000
We keep predicting fewer and fewer
humans before it will level off.

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00:31:29,000 --> 00:31:33,000
But it's still 3 billion more humans
than we have now,

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00:31:33,000 --> 00:31:38,000
and many people think now were
already beyond the carrying capacity

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00:31:38,000 --> 00:31:42,000
of the Earth.  So,
I'm not saying not to worry,

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00:31:42,000 --> 00:31:47,000
I'm just saying that at least it's
going in the right direction.

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00:31:47,000 --> 00:31:51,000
So, in Cohen's book, he analyzes
this, sort of the history of humans

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00:31:51,000 --> 00:31:56,000
on Earth as having four major
evolutionary changes where you have

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00:31:56,000 --> 00:32:00,000
the dramatic change in population
growth.  You have local agriculture

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00:32:00,000 --> 00:32:05,000
in 8000 B.C.
And, the doubling time of the

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00:32:05,000 --> 00:32:11,000
population before and after those
evolutions went from what he

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00:32:11,000 --> 00:32:16,000
estimates to be 40,
00 to 300,000 years for a population

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00:32:16,000 --> 00:32:21,000
to double down to 1000 to 3000 years
for the population to double.

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00:32:21,000 --> 00:32:27,000
In other words, this is an
incredibly faster growth rate,

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00:32:27,000 --> 00:32:32,000
because this is doubling times.
And then, with global agriculture in

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00:32:32,000 --> 00:32:37,000
the 1700s, again you have a
shortening of the doubling time of

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00:32:37,000 --> 00:32:42,000
the population.
And then in the 50s with the

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00:32:42,000 --> 00:32:47,000
introduction of real public health
across the world,

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00:32:47,000 --> 00:32:52,000
another reduction,
and luckily in the 70s,

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00:32:52,000 --> 00:32:57,000
with the introduction of fertility
control, at least in the developed

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00:32:57,000 --> 00:33:03,000
countries, is the first time you
actually see a shift.

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00:33:03,000 --> 00:33:08,000
We've gone from growing faster,
and faster, and faster to actually

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00:33:08,000 --> 00:33:14,000
growing more slowly.
The doubling time is extending.

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00:33:14,000 --> 00:33:20,000
So, the good news is we're not in
some kind of runaway population

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00:33:20,000 --> 00:33:26,000
growth that's going to continue
forever.  We've already peaked out

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00:33:26,000 --> 00:33:32,000
as a globe, and we are going to
level off in terms humans.

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00:33:32,000 --> 00:33:37,000
And the real big question is when we
level off, will we be above the

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00:33:37,000 --> 00:33:43,000
carrying capacity of the Earth?
Have we overshot K?  And we don't

305
00:33:43,000 --> 00:33:49,000
know yet because these feedback
mechanisms haven't come back.

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00:33:49,000 --> 00:33:55,000
So, let's now analyze this a little
bit more before we look at it in

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00:33:55,000 --> 00:34:01,000
that context, because this
is an important thing.

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00:34:01,000 --> 00:34:05,000
First of all, before we do that,
I want to remind you that all of

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00:34:05,000 --> 00:34:09,000
these lectures are tied together
because remember this from lecture

310
00:34:09,000 --> 00:34:14,000
20 when we were talking about
biogeochemical cycles?

311
00:34:14,000 --> 00:34:18,000
And, here's the same population
size and billions on Earth,

312
00:34:18,000 --> 00:34:23,000
the brown curve.  It's smoothed over,
and these are the greenhouse gases,

313
00:34:23,000 --> 00:34:27,000
concentration of greenhouse gases in
the atmosphere.  This is

314
00:34:27,000 --> 00:34:32,000
the human footprint.
This is how we've changed the

315
00:34:32,000 --> 00:34:38,000
metabolism of the Earth,
by this explosive growth of humans.

316
00:34:38,000 --> 00:34:44,000
And one more slide just showing you
that this is another way to look at

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00:34:44,000 --> 00:34:49,000
it, showing that the growth of the
global population has peaked.

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00:34:49,000 --> 00:34:55,000
So, over here, each of these is the
population in billions,

319
00:34:55,000 --> 00:35:01,000
and it basically shows you the
number of years necessary

320
00:35:01,000 --> 00:35:06,000
to add a billion.
And you could see that it's taking

321
00:35:06,000 --> 00:35:11,000
longer and longer to add a billion.
You can see that there is an

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00:35:11,000 --> 00:35:16,000
inflection point here.
So, using the tools that we've

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00:35:16,000 --> 00:35:22,000
developed to analyze populations,
let's look at why this growth is

324
00:35:22,000 --> 00:35:27,000
leveling off.  What caused the
growth to begin with,

325
00:35:27,000 --> 00:35:32,000
and why it's leveling off?
And the really important feature

326
00:35:32,000 --> 00:35:38,000
here is what's called a demographic
transition.  This is what we are

327
00:35:38,000 --> 00:35:44,000
going through on the Earth right now
in terms of human population growth.

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00:35:44,000 --> 00:35:50,000
And, the way we look at this, we
are planning birth rates here,

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00:35:50,000 --> 00:35:56,000
which is the pink one, and death
rate here, which is the green one.

330
00:35:56,000 --> 00:36:02,000
And, when birth rates and death
rates are both uniformly high,

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00:36:02,000 --> 00:36:08,000
which is the way it was back in the
early days when we didn't have

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00:36:08,000 --> 00:36:14,000
fertility control,
and we didn't have modern medicine.

333
00:36:14,000 --> 00:36:17,000
So, you had a lot of babies and a
lot of people dying.

334
00:36:17,000 --> 00:36:21,000
And growth rate, and so this is the
total population.

335
00:36:21,000 --> 00:36:24,000
So, you don't have much population
growth.  Then,

336
00:36:24,000 --> 00:36:28,000
what happens, you get to a place
where you have a very

337
00:36:28,000 --> 00:36:32,000
high birth rate.
Birth rate continues to stay high,

338
00:36:32,000 --> 00:36:38,000
but with the introduction of public
health, and modern medicine,

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00:36:38,000 --> 00:36:43,000
we were able to keep people alive a
lot longer.  And,

340
00:36:43,000 --> 00:36:49,000
that came in advance of fertility
control.  So, what happens,

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00:36:49,000 --> 00:36:54,000
when these two curves deviate from
one another, you have explosive

342
00:36:54,000 --> 00:37:00,000
growth, and that's what this big
exponential shoot is.

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00:37:00,000 --> 00:37:04,000
But then, if you then reduce the
birth rates through fertility

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00:37:04,000 --> 00:37:09,000
control to match the death rates,
you then have low birth rates and

345
00:37:09,000 --> 00:37:14,000
low death rates.
Then you have no population growth,

346
00:37:14,000 --> 00:37:19,000
OK? So, it's very simple and
intuitive when you understand what's

347
00:37:19,000 --> 00:37:24,000
going on, but I don't think that
most people really have come to the

348
00:37:24,000 --> 00:37:29,000
point of thinking about
it like that.

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00:37:29,000 --> 00:37:37,000
And where we are on Earth today is
the developed countries have gone

350
00:37:37,000 --> 00:37:46,000
through their demographic transition.
And you have a sense of that just

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00:37:46,000 --> 00:37:55,000
from looking at family size in these
countries.  So,

352
00:37:55,000 --> 00:38:04,000
if we look at, this is Sweden as an
example of a developed country.

353
00:38:04,000 --> 00:38:10,000
And this was 1800.
And this is 2000.  You see

354
00:38:10,000 --> 00:38:16,000
something like this.
This is just an approximation.

355
00:38:16,000 --> 00:38:22,000
This is the birth rate and this is
the death rate,

356
00:38:22,000 --> 00:38:28,000
and the population growth rate looks
something like this.

357
00:38:28,000 --> 00:38:36,000
The populations leveled off whereas
if you look at a country like Egypt

358
00:38:36,000 --> 00:38:44,000
over the same time frame,
and you can get these curves off the

359
00:38:44,000 --> 00:38:52,000
web easily, it looks something like
this.  You have a high

360
00:38:52,000 --> 00:38:59,000
birth rate.
And death rate has gone down,

361
00:38:59,000 --> 00:39:05,000
but they're not matching each other
at all.  So, population look

362
00:39:05,000 --> 00:39:11,000
something like this.
It hasn't even begun to level off.

363
00:39:11,000 --> 00:39:17,000
So the real trick is, in terms of
trying to level off at someplace

364
00:39:17,000 --> 00:39:23,000
lower than 9 billion,
is to get the birthrates in the

365
00:39:23,000 --> 00:39:29,000
developing countries to drop
as fast as we can.

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00:39:29,000 --> 00:39:35,000
And that will determine the level at
which humans will level off on Earth.

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00:39:35,000 --> 00:39:41,000
So, let's just briefly,
let me go back over here,

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00:39:41,000 --> 00:39:47,000
and let's go back over this carrying
capacity.  And this is basically

369
00:39:47,000 --> 00:39:53,000
what Joel Cohen's book is about,
where he says, how many people can

370
00:39:53,000 --> 00:39:59,000
the Earth support?
He's asking, what's the carrying

371
00:39:59,000 --> 00:40:05,000
capacity of the earth for humans?
And here are the possibilities.

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00:40:05,000 --> 00:40:13,000
And of course, I'm simplifying the
most complex system that we know

373
00:40:13,000 --> 00:40:20,000
into a simple two-dimensional graph,
but I think it's a good way to think

374
00:40:20,000 --> 00:40:28,000
about it.  Here's the way we've been
living on Earth.

375
00:40:28,000 --> 00:40:34,000
We have been growing like this.
Granted, we're starting to level

376
00:40:34,000 --> 00:40:40,000
off, but we've been growing like
this.  And what we've been assuming,

377
00:40:40,000 --> 00:40:47,000
is that the carrying capacity will
grow with us, OK?

378
00:40:47,000 --> 00:40:53,000
We can handle as many humans as we
want to put because we,

379
00:40:53,000 --> 00:41:00,000
smart people, with technology can
increase the carrying capacity.

380
00:41:00,000 --> 00:41:05,000
If we don't have enough grain,
we'll genetically engineer to make

381
00:41:05,000 --> 00:41:10,000
more grain.  We can fix it; we can
fix it, so let's just go with the

382
00:41:10,000 --> 00:41:15,000
flow.  And indeed,
technology has greatly increased the

383
00:41:15,000 --> 00:41:20,000
carrying capacity of the earth for
humans.  There's no doubt about it.

384
00:41:20,000 --> 00:41:25,000
But there's got to be a limit.  So,
is this the model that we want to go

385
00:41:25,000 --> 00:41:30,000
by?  So, some people argue,
so, the climate, we'll fix that with

386
00:41:30,000 --> 00:41:35,000
technology.
We can fix any of this with

387
00:41:35,000 --> 00:41:40,000
technology, and if things get really
bad, we'll go to Mars; we'll

388
00:41:40,000 --> 00:41:45,000
terraform Mars.
We'll colonize planets.

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00:41:45,000 --> 00:41:49,000
That's not that far-fetched,
so why should we worry about all

390
00:41:49,000 --> 00:41:54,000
these humans on the Earth?
We'll just figure out, we'll go out

391
00:41:54,000 --> 00:41:59,000
and find new places.
So that's one model.

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00:41:59,000 --> 00:42:04,000
Another model is, if we're going to
do this, here's what I call the

393
00:42:04,000 --> 00:42:12,000
optimistic model.
Well, I guess this is the super

394
00:42:12,000 --> 00:42:22,000
optimistic model.
This one assumes that it'll do

395
00:42:22,000 --> 00:42:33,000
something like this that we may
overshoot.  And then birth rates,

396
00:42:33,000 --> 00:42:37,000
and if you want to you can easily
describe a scenario that says that

397
00:42:37,000 --> 00:42:42,000
we have overshot,
that this whole environmental

398
00:42:42,000 --> 00:42:46,000
movement, the measurement of toxins
in our environment,

399
00:42:46,000 --> 00:42:51,000
the global change, all of that is
really overshooting the carrying

400
00:42:51,000 --> 00:42:56,000
capacity.  And we wouldn't be
worrying about things that we're

401
00:42:56,000 --> 00:43:00,000
worrying about if we hadn't overshot
it, but that if we get

402
00:43:00,000 --> 00:43:07,000
our act together,
we won't have eroded the Earth's

403
00:43:07,000 --> 00:43:15,000
natural system so much that we can
come back to a stable level.

404
00:43:15,000 --> 00:43:23,000
And then, of course, the
pessimistic scenario is that,

405
00:43:23,000 --> 00:43:31,000
indeed, we've overshot, and we've
overshot so much that we have eroded

406
00:43:31,000 --> 00:43:38,000
the carrying capacity,
and that we will level off at some

407
00:43:38,000 --> 00:43:44,000
level that the Earth will no longer
be able to support the level of

408
00:43:44,000 --> 00:43:50,000
humans that it can even support now,
that we have lost so much topsoil,

409
00:43:50,000 --> 00:43:56,000
and modern agriculture won't be able
to overcome that,

410
00:43:56,000 --> 00:44:02,000
that our water will be polluted,
that the climate will change so

411
00:44:02,000 --> 00:44:08,000
dramatically, the fisheries will be
eliminated, yada, yada, yada.

412
00:44:08,000 --> 00:44:13,000
I shouldn't say yada,
yada, yada.  Those are catastrophic

413
00:44:13,000 --> 00:44:19,000
things.  Erase that from the tape!
Every once in a while,

414
00:44:19,000 --> 00:44:25,000
I remember I'm being taped.
So, those are bad things, not to be

415
00:44:25,000 --> 00:44:30,000
yada, yada, yada'd.
So, anyway, this is what some people

416
00:44:30,000 --> 00:44:35,000
are worried about,
that we are, indeed right now,

417
00:44:35,000 --> 00:44:40,000
in your lifetime and in fact mostly
in your lifetime,

418
00:44:40,000 --> 00:44:45,000
you are inheriting this,
notice the time frames on this graph.

419
00:44:45,000 --> 00:44:50,000
I mean, this is just this little
snippet of time in the history of

420
00:44:50,000 --> 00:44:55,000
life on Earth where all these
dramatic things are happening.

421
00:44:55,000 --> 00:45:00,000
And we just happen to be living in
it.

422
00:45:00,000 --> 00:45:04,000
Just think if you're living back
here, and thousands and thousands of

423
00:45:04,000 --> 00:45:08,000
years went by,
and nothing changed.

424
00:45:08,000 --> 00:45:12,000
OK, so we don't have any answers,
but this is a way to think about it,

425
00:45:12,000 --> 00:45:16,000
and a lot of people are putting a
lot of energy into modeling the

426
00:45:16,000 --> 00:45:20,000
systems, and try to figure out where
we are the scariest trajectories.

427
00:45:20,000 --> 00:45:24,000
So, the next two lectures Professor
Martin Polz, who is a professor in

428
00:45:24,000 --> 00:45:28,000
civil and environmental engineering,
and the microbiologist is going to

429
00:45:28,000 --> 00:45:33,000
come in and talk to you about,
again, its population economy.

430
00:45:33,000 --> 00:45:37,000
He'll talk to you about population
genetics, and some really exciting

431
00:45:37,000 --> 00:45:42,000
work that's going on in the field
now using genomics to decipher

432
00:45:42,000 --> 00:45:46,000
evolution and population biology.
And then I'll be back with some

433
00:45:46,000 --> 00:45:49,000
really neat DVD clips.
So, come back.