Hi. It’s Mr. Andersen and this is environmental
science video 12. It is on population ecology. One of the greatest conservation stories in
biology is the story of the whooping crane. They used to number 10,000 in the U.S. but
by 1938 their numbers had dropped to only 15 individuals. So scientists had to figure
out where are they, where are they breeding, how do we protect those areas and you can
see the population is starting to rebound. But the health of the population is dependent
upon the size of the population. How do we increase the size of a population? Through
births and immigration. New individuals coming into the population. Likewise, how do we decrease
it? Through deaths and emigration. These things contribute to what is called the intrinsic
growth rate. Is it increasing? Or is it decreasing? It is not the only characteristic. We also
have the density and distribution. We have the sex ratio and the age structure as well.
But what other factors, outside of this intrinsic growth rate can affect their growth? Well
we break that into two groups. Density dependent and independent. Density dependent factors
are factors that limit growth based on the density of the population. So if you think
about it as the population’s density increases, if there is not enough food or water or shelter,
we call those limiting resources. And what happens to the population? It will eventually
level off. It hits something called the carrying capacity or K. It is the maximum number of
individuals an area can support. We also have density independent. And those are going to
be things just related to chance. So a flood or a fire could be examples that limit the
size of a population. So in population ecology we are studying these factors. And scientists
come up with models that help to describe what is going on in a population. So a famous
model is the exponential growth model. What we are looking at is this growth rate and
how it is increasing the population over time. And then we have a logistic model. It is also
showing exponential growth but eventually it is reaching what is called a carrying capacity
or this limit of population growth. Scientists also study strategies that species have. Some
are what are called K selected. That means their population size will increase until
it gradually hits a carrying capacity. And those who live more of a boom or bust cycle,
that are r selected. And we can look at how long individuals survive and that tells us
a little bit about which strategy they are using. And so the population size is incredibly
important. So if we have these rabbits, so we have 9 rabbits and their N value at this
point would be 9. If we lose 2 of them our N value is 7. If we gain 3 now our N value
is going to be 10. It is the set number we have. But also density is important. That
is the number of individuals we have in a given area. And so we could call this one
density but we would call this greater density. We could also look at their distribution.
I would say that these rabbits are now randomly distributed. But they could be distributed
uniformly. Or they could be just clumped in their distribution. And we could also look
at their sex ratio. So how many are males and how many of them are going to be females.
And we could expand that to look at what is called their age structure. Not only what
is their gender but also how old are they. So we could organize them like this where
this is going to be our first year female rabbits, second year and third year. And we
can do the same thing with males. But when it comes to the health, the population size
is incredibly important. It is dictated by births, deaths, immigration and emigration.
And so we have a formula that allows us to look at that. And the calculations are very
simple. You can do them just in your head. And so let’s say we have a population of
10. So our N naught is going to be 10. That is our initial population. Here is our equation.
So it is really simple. The change in N is going to be the births minus the deaths plus
the immigration minus the emigration. So let’s look at this population over here and see
what happens. So this rabbit gave birth to 3 other rabbits. And so if we write this out
what is our births going to be? It is going to be 3. Now let’s watch the population
again. So you can see 1 of the rabbits died. And so we are going to be put a 1 here in
the deaths. We could look at immigration, how many come in. It looks like just 1. So
we would put a 1 right here. And then how many emigrate? It looks like 2 left. And so
we would put a 2 right here. And so the delta N or the change in N is simply going 3 minus
1 plus 1 minus 2, or 1. That is the change. Or we have seen an increase in 1. Now what
is the growth rate? The growth rate is going to be the change divided the initial population.
So 1 divided by 10 gives us a 10 percent growth rate of 0.1 is our growth rate. We call that
the intrinsic growth rate. And as long as we have no other factors outside that population,
that will remain constant over time. And you could solve a really hard problem. We could
have a million people in an area. 100,000 are born. 10,000 die. If you are given the
immigration and emigration you should be able to calculate r for that population. So if
we study a group of rabbits over time their population will increase. But it will eventually
level out at some point. Now that leveling out point is called the carrying capacity
or the K. Now why is a population going to level out? It is because they are running
out of something. They are running out of food or water or shelter. And so we call all
of those things limiting resources. Disease could be another limiting resource. The more
rabbits we have the more disease. And so it is eventually going to level it off. Now it
will not look perfect like that. The normal population is going to have over shoots and
it is going to have a lot of die off. But we are going to have the average that we eventually
hit. These are density dependent factors because they are based on the density of the population.
We can also have density independent. So imagine that these rabbits over on this side are killed
in a forest fire. That is just chance. It is just chance taking over and so it is not
based on the density of rabbits that we had. So if we start to use models to explain how
this works, a really important model is the exponential growth model. And so the equation
looks like this. It is a little scary but it is really not that bad. N sub t is going
to be the population at any time into the future. N sub O is going to be the initial
population. So let’s say we start with a population of 10. r is going to be the growth
rate. That is that intrinsic growth rate. And t is going to be time. So the only thing
that you really do not know in this equation is e. e is going to be the mathematical constant.
So it is a number. It is just like pi. It is going to be 2.718. It just keeps going
like that. So for our purposes we just think of it as 2.71. And so let’s say we want
to figure out what is going to happen to the population in year 1. So if we want to figure
out, we started at 10, what is going to be the population probably at year 1? We just
use this equation. So e is going to be the same. So what is going to be our r value?
Our r value will always be 0.5. That is that intrinsic growth rate. What is our t value?
Our t value is going to be time. What is our initial population? It is going to be 10.
So if I expand that a little bit or simply multiply 1 times 0.5, 1 year times that growth
rate. And so that is going to be 10 times 2.71, again that is e, raised to the 0.5 power.
So that is really like taking the square root of 2.71. And so that is 1.64. So if we work
that out that is going to be around 16 rabbits after 1 year. So let me graph that. And let’s
go to year 2. So same thing. We are going to plug in r value of 0.5 but now our t value
is going to be 2. Still have that same initial population. And so now it is going to be 2.71
raised to the 1 power. So what is that? That is simply 2.71. So if we work this out now
we are going to have 27 rabbits in that next year. You can see the population is increasing.
We are starting to see that exponential growth. Let’s go for year 3. So if we figure out
year 3, again our intrinsic growth rate is still 0.5. 3 is going to be the year we are
at. Still have that same initial. And so this is going to be 2.71 raised to the 1.5 power.
You probably need a calculator to do this. We now get 44.6 or, let’s say 45 rabbits.
So if we graph it, you can see that the population is increasing like that. We have what is called
a j-shaped curve. And it is going to increase rapidly over time. We are going to, the whole
world would be filled with rabbits if we keep following this model. And so we know that
is not what occurs. And so not only intrinsic growth rate is important but K, that carrying
capacity. So if you are given a problem like this could you graph what is going to happen
over time if K is 70? Well you are going to get something that looks like this. It is
going to be j for awhile but is eventually going to curve off and we are going have a
s shaped curve. This is a logistic growth model. There is also a mathematical model
we will not work through. I will put a link to another video where I do that down below.
And so scientists, now that they have models, they can start to apply that to nature. So
what we have found is that species kind of fall into one of two camps. We have what are
called K selected species. Those are going to be species that their population increases
and then it will eventually hit a carrying capacity and it stays there. What are some
characteristics of species like that? They are going to give a lot of parental care to
their offspring. They are just going to have a few offspring. And so the whooping crane
would be an example of that. Humans are an example of that. We do not just go up and
down in our population. r selected are going to do that. So an arctic hare is an example
of that. A famous study was looking at the pelts that were collected by the Hudson Bay
Company. And they found from 1850 to 1930 that the population of arctic hare just went
up and down and up and down. And so hares are going to be groups of individuals that
have lots of offspring. They do not get tons of parental care and their population is going
to increase and then it will crash. So we have this boom and bust cycle. Now what is
interesting is that there is another species. And so the arctic hare are fed on by the Canada
Lynx. And if we look at their population, their population goes through a boom and bust
as well. We have what is called a predator prey relations where as the arctic hare population
increases then we can have more lynx feeding on it. But as they crash then the lynx are
going to crash as well. Now a way to look at which strategy species are using is figuring
out their survivorship. And so we have time on the bottom and then we have the survivors
on the side. So if we look at humans as a type 1 survivorship curve, what that means
is when we are born almost all of the humans survive. And then throughout their lifetime
they all die right at the end. And so we give a lot of parental care to our offspring. Almost
all of them survive and then when we get into our 80s, 90s, then we all die off. We could
also have a type 2 survivorship curve. Songbirds are an example of that. From the moment they
are born they are dying off at a constant rate. Or we could look at type 3. Those are
individuals like the acorns from a tree. Almost all of them die but a few of those survive
and those make up the plants that we have. And so could you link that to K or r selected
species? Well type 1 individuals are generally going to be those K selected species. And
the type 3 are generally going to be those r selected species. But there are so many
examples that are in the middle. So if you think about a sea turtle for example, they
have lots of offspring. They do not give them much parental care, but they live a long time.
And so it is not as simply as are you r or are you K? It is somewhere in the middle.
But they are applying these different strategies in life. And so did you learn the following?
Could you pause the video at this point and fill in the blanks? If not, population size
is determined by immigration and birth. That increases it. Decreased by emigration and
deaths. We have other characteristics, density, distribution, sex ratio and age structure.
There are density independent and dependent factors. Density independent remember are
related to chance. Density dependent lead to what is called a carrying capacity or K.
We use models to study it. Exponential models are built on the growth rate. Logistic models,
also built on the growth rate but include carrying capacity. And then we have different
strategies in species. K selected, r selected. Remember we are K selected. And then we have
survivorship curves that we can study to get that. That is a lot. I hope it made sense.
And I hope that was helpful.
