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### Human Population Growth and Food Requirements

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Today we move forward with our discussion on Human Ecology and in this lecture we
will look at Human population growth and food requirements, especially the theory of
Thomas Robert Malthus.
(Refer Slide Time: 00:23)

We had seen Thomas Malthus in our first module in the lecture on the history of ecology.
He was an English cleric and scholar who lived between 13th February 1766 and 23rd of
December 1834. And in 1798 he wrote a book “An Essay on the Principle of Population”
and this book has had a very deep impact on the study of population ecology. What did he
write in this book?

(Refer Slide Time: 01:03)

Basically the tenets of Malthusian growth models are these. The first point is that
population grows in geometric progression roughly doubling every 25 years. Now this 25
years is a time frame that he noted from his particular times, but then later on we will see
that this 25 years no longer holds valid.
But, more or less what he said was that the population grows in geometric progression. So,
if you have say 1 million people somewhere so, from 1 million in 25 years that will become
2 million, then in the next 25 years it will become 4 million then 8 million and then 16
million and 32 million and so on. So, if we see that this one is 25, 50, 75, 100, 125; so in
125 years it has moved from 1 to 32.
However, if we look at the food supplies they do not increase in geometric progression,
but they increase in arithmetic progression. So, in this period; in 125 years, it will go from
1 to 2, 2 to 3, 3 to 4, 5 and 6. So, suppose in the beginning, we had 1 million people and
say 1 million kg of cereals so, at the end of 125 years we will be having 32 million people
and only 6 million kgs of, tons of cereal. So essentially it says that, the population tends to
overrun food supply.
Suppose, you try to increase the food production for some particular point of time so, in
that period because the population is dependent on the food. So, the population will
increase very fast and even if you start with a larger amount of food, in a very short time

the population will overrun the food supply. So, this creates an imbalance so, you have
more number of people and less number of resources.
If you remember our talks on Darwinism, that also said a very similar thing that every
organism tends to over produce, but then the resources are limited and so, there is a
struggle for existence. Now, in the struggle for existence, there are some organisms that
die out.
(Refer Slide Time: 03:33)

When you have overpopulation; so, suppose you have 10000 individuals of any particular
species, let us say that we are considering a Chital population. Now you have 1000
individuals, but the carrying capacity is say 700 individuals. In this case, 300 individuals
will die off, why would they die off? Because you have limited amount of resources, more
number of individuals, everybody is fighting and so in that case there would be some
individuals who will be dominant and some individuals who will be not so dominant or a
bit recessive.
The dominant individual is able to get more amount of food because it is able to drive
everybody away. For instance, things that we talked about in the case of intra specific
competition, so, there will be competition and there will be some individuals in any
population that will be able to drive off the other individuals. When you have this driving
off of other individuals, so there will be some individuals in this population precisely 300
individuals who do not have access to sufficient amounts of food; so they will suffer from

malnutrition, maybe they will suffer from some diseases and slowly and steadily they will
die off. Ultimately, we will come to a situation where you have only 700 individuals left
which is equal to the carrying capacity. Now, these are the tenets of Darwinism.
Here, what we are talking about is an intra-specific competition. In the case of Malthus,
what he says is that here also you have a population that grows very fast, you have a food
supply that is growing not so fast, now in this case the food supply we can correlate it with
the carrying capacity of the environment. In the case of Darwinism the carrying capacity
was more or less fixed, but in this case Malthus saw that the food supply is increasing; so
he stated that it goes on increasing in an arithmetic progression. But here is well you will
have a situation in which the population tends to overrun the food supply and when that
happens then nature would bring in some sorts of checks and balances.
Malthus also said that this imbalance is corrected by positive checks. So, these deeds of
people he is referred to as positive checks. And he said that these positive checks are vice,
misery, famine, war, disease, pestilence, floods and other natural calamities. He said that
in his theory, we are not talking about intra specific competition and some people who are
able to drive off others, but then he says that the nature’s way of solving this issue is to
You will have some famine or maybe you will have some floods or you will have some
diseases that are going to wipe out a major portion of the population. And once that
happens the population which reduces to a level that is beings that can be sustained by the
level of agricultural productivity. But then Malthus said that these positive checks are not
a good way of checking the population because here we are talking about human beings
and we do not want to have a situation of floods or families or diseases or pestilence.
Then he said that as human beings, we have this other option that we can correct this
imbalance, the imbalance between the number of people and the food supply using
preventive checks. Now, preventive checks are foresight, late marriage, celibacy, moral
restraint and so on. Essentially, he said that even though in nature’s plan is that we are
going to increase our population in a geometric progression, but then we as human beings
we can use our foresight or there could be some individuals who can let go of producing
offspring. So, they are not producing any offsprings, they are living a celibate life or there
could be people would opt for a late marriage.

So, if you have a late marriage, in that case the rate of population growth will come down
because in place of having population that is doubling every 25 years maybe you will have
a population that is doubling every say 30 years. So, he said that late marriage is also a
way in which we can use a preventive check and things like moral restraint and so on.
So, this is in short, the Malthusian growth mode. The population increases in a geometric
progression, food increases in an arithmetic progression. That leads to an imbalance and
there are positive checks and there are preventive checks. So, this is in short the Malthusian
model.
(Refer Slide Time: 08:49)

If we look at the world population growth rate, so, we can say that, yes, it does increase
exponentially, so there is some amount of this geometric progression thing that is working.
So, the population is increasing at a very fast rate.

(Refer Slide Time: 09:06)

Now, if we put the Malthusian theory in terms of mathematics, we can say that if P(t)
denotes the population at a time t,
Then, the rate of increase of the population is denoted as

dP
dt = kP
where k is a constant and P is the population.
(Refer Slide Time: 09:50)

Essentially what this thing is saying is that, you have a population that is increasing now;
the rate of increase of the population will be proportional to the population that is present
at that particular point of time.
So, essentially if you have a situation in which you have 1 million people, so, in that case
you will have many more births as compared to a situation in which you only have say
100,000 people; so in this case you have less number of births. Because in the case of a
smaller population, you have a lesser number of females that are pregnant at an important
of time or are producing the offsprings, because the females of any population that are
very young or that a very old will not be producing the offsprings, only those females that
are in the reproductive age are going to produce the population or are going to produce the
offsprings. In that case, we can say that the change in population with respect to time is
proportional to the population P.
dP
dt
∝ P
dP
dt
= k P, where k is a constant.
Integrating the above equation,
P(t) = Po e
k t
, where Po denotes population at time t0.

So, here we are saying that the population at any time t is equal to some constant value
which is the population at time point 0 multiplied by e to the power k into t where k is this
constant that we had derived here and t is the time period. So, this would say that we have
a population that is increasing exponentially.

(Refer Slide Time: 11:34)

And from here we can define this term called as the doubling time. Now, doubling time or
td is defined as the time that is required to double the population size. So, suppose we
started with 1 million people, so, how much time does it take for the population to increase
from 1 million to 2 million or from 2 million to 4 million or from 4 million to 8 million,
that time t d is called the doubling time. So, here we can say that in time td we have the
population at time td is twice the original population or the population at time point 0.
(Refer Slide Time: 12:18)

So, we know that the population at any time t is given by the equation P(t) = Po e k
and we
are saying that the population at time td is equal to twice the original population, which is
represented as P(td) = 2P0
The population at any time t is given by the equation P(t) = Po e k........................................ (1)
The population at time td is represented as P(td) = 2P0............................................................ (2)
Replacing t as td in equation (1),
2P0 = Po e k t
d
2 = e k t
d
Taking natural logarithm on both sides,
ln 2 = ln e k t
d
ln 2 = k td
Rearranging the equation,
td =
1
k
ln 2, where td is a constant,
Now, in this particular case because ln 2 is a constant and k is also a constant so, we can
say that td is constant or essentially when you are having an exponential increase, there
will be a fixed time period td which is known as the doubling time in which you will see
that the population is increasing in a geometric progression so, this is what Malthus said.
So, essentially this is a formula that we can remember td =
1
k
ln 2, but then, is this theory

correct? Is this what we actually see out there in nature?
It turns out that, if you have a population that is increasing exponentially and you have the
food supply that is increasing in an arithmetic manner, then we should have had a number
of famines, a number of floods, a number of pestilences, but then we are not seeing all of
these today which brings us to the criticisms of this model. So, there are some things in
this model that are not quite correct.

So, the first criticism is that the population growth is not as suggested. The population
growth is not completely exponential. In our results we had seen that this term td is a
constant which Malthus said that it would be 25 years.
(Refer Slide Time: 14:47)

But then, if we look at the actual doubling time, so, on this x axis we have the years, on
the y axis we have the number of years it takes to double the population. So, if we look at
this point 1543 so, it took 697 years for the world population to double from 0.25 billion
in 637 to 0.5 billion in 1543.
So, it took as many as 697 years or close to 700 years to move from 0.25 billion to 0.5
billion. And if we look at a time point later on so, if we look at this year 1928; in 1928, the
world population had reached 2 billion and it had taken only 125 years to move from 1
billion to 2 billion. So, the t d is not constant, it can vary from as much as say around 700
years to as little as 37 years. So, if you look at this point so, in 1987 the world population
was 5 billion and it had taken only 37 years to move from 2.5 billion to 5 billion. What we
are saying here is that even though the Malthusian model says that your t d is a constant,
but then in actuality we are saying that t d is not a constant.

(Refer Slide Time: 16:35)

We cannot say that the population is actually growing exponentially, even though it looks
like an exponential growth. Because when we are plotting the population versus time; it
does look like we are increasing the population like this, but then if we look into the
intricacies we find that t d is not a constant here.
(Refer Slide Time: 16:51)

And it turns out that actually the population grows by this demographic transition.
What do we mean by a demographic transition?

(Refer Slide Time: 17:05)

Consider a society; in the first case, you have a society, that is a primitive society and in
this primitive society you have a high birthrate and a high death rate. Now, you have a
high birthrate, because there are no methods of contraception that are available and
because people are reproducing as much as possible. So, that because in this society you
have a higher death rate. So, every parent wants that at least some of it is offsprings are
able to survive to it is own maturity.
Remember, we are again talking about fitness. Now fitness is the situation in which you
are able to produce your offspring and your offsprings are such that they are also able to
produce their own offsprings. Now this primitive society has a high death rate. Now, why
does it have a high death rate? Because you do not have modern medicine that is available.
If there is any communicable disease, if you have any infection, there is a very huge
possibility that you might die. Also, sanitation is not there so, people are suffering from
diseases like cholera, you do not have good houses, so you might have huge amounts of
say plague or diseases that come up when you are not living in a sanitary environment and
so on.
So, there is a huge death rate. You do not have sufficient access to food, there is widespread
malnutrition, even your theories of nutrition have not been developed. So, you do not know
if somebody is getting, say, scurvy or somebody is getting beri-beri. So, you do not know
why are they getting these diseases or that you can prevent scurvy by giving some amount

of lime or some amount of citrus fruits. So, you do not have all of these information and
in the absence of all these information you have a very high death rate.
If you have a high death rate the society compensates by having a high birth rate. So, for
instance, if you know that out of every 6 children 5 children are going to die in their infancy
so, you have say an infant mortality rate of 5 out of 6. So, if you... as parents, if you want
to have at least one progeny that lives to its maturity; so, you would want to have at least
say 6 children because you know that 5 out of 6 are going to die anyway. So, a high death
rate leads to a high birth rate.
In these societies with a very high birth rate and a very high death rate, both the high birth
rate and the high death rate cancel out each other. So, the rate of population growth is very
less, because the number of individuals that are born into this society a number of them
die off. So, this is the first stage in the transition in which you have a high birth rate and a
high death rate.
The second stage in demographic transition is where you are reducing the death rates. So,
you have shifted from a high death rate to a low death rate. Now, how are you able to
reduce the death rate? By providing more amount of nutrition, by providing modern
medical facilities, by having more amount of information about what somebody should
eat, how to prevent diseases, how to treat diseases, if they are there.
In this level of society, you have now a low death rate. But then a low death rate does not
automatically transition into a low birth rate. Why? Because parents who were in the
previous generation producing say 6 offsprings, they will not shift from say 6 offsprings
to one offspring in an instant. So, you have the society in which you have a low death rate
because of the medical facilities and because of the advances in science and technology,
but you still have a high birthrate.
If that is the situation, you have a low death rate and a high birthrate so, in that case you
have a number of individuals that have been born in this population, but because the death
rate is low so, a number of them are also able to survive and reproduce further.
When that happens, you see the classical case of an exponential rate of population increase.
So, this is population versus time and you have individuals that are being added into this
population again and again and the more number of individuals that you have in this

population the more number of offsprings that are produced. So, this cycle supports itself
and the population booms, that is the second stage.
The third stage in this demographic transition is when you have a very huge amount of
population. So, now the society tries to reduce the birthrate as well.
(Refer Slide Time: 22:17)

In this case you have a low death rate and you shift from a high birth rate to a low birth
rate. Now, how can you have a low birth rate? By say having more access to contraceptions
or say by having an increased age at which people want to have offsprings or maybe in
this society, now people just do not want to have any offsprings or they just want to have
only one off springs. So, in place of having a norm of say 6 or 7 babies, now the norm is
shifted to just 1 baby.
In this case you have a low death rate and a low birth rate. So, again the birth rate and the
death rate are able to counter each other. So, the net increase in the population will be very
small. So, the population is now stabilized. So, in place of having your population that was
increasing like this, now you have a population that is now moving towards stability. So,
in this case the population will become stable in a very short period of time; because now,
again you have a low birthrate that is being compensated by a low death rate.
The fourth stage in the transition could be of a stage in which you continue to have a low
death rate, but you have an even lower birth rate, so, we had talked about the replacement

level fertility. A replacement level fertility is a situation in which you have 2 people in the
parental generation and they are able to replace themselves in the next generation. So, for
instance you have a mother and a father so, 2 people in one generation and then in the next
generation you also have 2 kids. So, that is the replacement level fertility. What if you
have 2 individuals and the parental generation and less than 2 individuals in the next
generation.
Suppose, on an average you have say 1.7 babies or say even just 1 baby. So, in that case
the population will now go on decreasing itself. So, in place of having this population that
was just stabilizing itself, now you can have a situation in which the population has started
to decrease. So, that can be another mode in which the demographic transition occurs.
What we are observing here is that you have the birth rates and the death rates. In the very
first instance, you have a high birth rate and a high death rate. So, the birth rate is this
green colored curve and the death rate is this blue colored curve. Now, in this stage, when
you have a high birth rate and a high death rate, the population does not increase, the
population remains more or less constant.
Then, in the second stage, when you have a falling death rate and the birth rate has
remained stable so, in this case the population has started rising. In the third stage, you
have a falling death rate that continues and the birth rate has started to decrease, but here
again we see that, we are increasing in the population, but then it is now becoming more
and more stable and this is the stage where they actually are today. Now, in a short while
when we reach this stage in which your birth rate and the death rates both are low, so, in
this case we will observe flatness in the total population.
This yellow curve is the total population and then, when you have reached this flatness,
the fifth stage can be a stage in which your birth rate starts rising again or maybe the birth
rate becomes even lower than the death rate and in both the cases you will have different
results. So, if birth rates increase then you will see a further increase in the population or
else you will start seeing a decrease in the population.
These stages can also be represented in terms of the population pyramids. In the case of a
population pyramid, what we are seeing here. A population pyramid looks like this.

(Refer Slide Time: 26:43)

Here you have the number of men in the population, here you have the number of women
in the population and then this is the age of different cohorts. Let us say that in the case of
an age group between 0 to 5 years, you have a number of babies, some of which are male
babies, some of which are female babies.
In the case of 5 to 10 years, you have a lesser number of individuals that are here. Then
progressively it reduces, 15, 20, 25, 30 and maybe 35. Now, this is a population where we
are saying that you have a life expectancy of around 35 years plus if we consider the
population that is there in the reproductive age, let us say bit more than say 18 to 35 years.
So, here we have less number of individuals that are there, but then the number of children
that are being born are very large.
In this case, this is representing a population with a high birth rate and a high death rate.
Now, this has a high death rate because if you look at any particular rung; so, in this
particular rung here we have so many children, but then out of these children only these
many are able to reach to the next rung and then only these many are able to reach the next
In this pyramid, we are seeing a high birth rate and a high death rate and this is represented
here. So, this is a population in which you have a high birth rate so, the bottom is very
large, a high death rate so, it is tapering very fast and this is representative of the first stage;
a high birth rate and a high death rate.

(Refer Slide Time: 29:03)

In the case of the second stage, you have a reduction in the death rates. When you have
more death rates, so, suppose you have a population in which you have a very steep death
rate. Now, if you reduce the death rates so, these many individuals that were dying off, so,
now they will survive and maybe your death rate will reduce. In this case, the curve will
become something like this.
So, it is now becoming more and more triangular; it still has a very large sized base because
you have a number of children that are being born, so, these are the number of children
being born, but if you look at the number of children that are there at the age of 5 years.
So, earlier we had only these many children, but now, because you are able to reduce infant
mortality and you are able to reduce under 5 child mortality, so, the number of children
that are able to survive that has increased. Now, this curve in place of looking like this, it
now looks more like a triangle. So, this is the second population pyramid that we observe.
Here you have a high birth rate, but death rate that is now lowering. Now, when you have
a stage in which your birth rate also starts to slow down. In this case, earlier we had this
large taper; now the taper will start to reduce; so that is the third stage.

(Refer Slide Time: 30:39)

In the third stage, what is happening is that in place of having the curve that was looking
like this. Now, the society is trying to reduce the number of children that it is having.
Probably, in place of having a steep slope like this, probably it will look like this, because
the individuals that have already have been born, but then the society can only reduce then
the children that are being born now or in the future.
In this case, in place of having these many children that were being born, now the society
is trying to reduce this number to this much; which is why we are observing that this curve
is now starting to lose out these two corners that were there in this triangle.
In the fourth stage, when you have a low birthrate and a low death rate, what is happening
is that, after having this particular shape of the curve. Now, what the society is trying to
do is to convert it into a shape that looks like this.

(Refer Slide Time: 31:52)

Now you are trying to reduce your birth rates, but because the death rate is also low. Any
individual that is born is going to survive for a very long period and then slowly you will
start seeing the death at a very old age. Here again you have the age and here you have the
number of women and the number of men, or the male and the female population that is
there.
In this case what we are seeing is that, for till say a particular age; till the age of, say 45 or
50, there is hardly any death that we are observing in this particular population. So, there
is hardly any deaths that we are observing till this particular age, let us say that this age is
say 45 years or say 50 years. And even after this year, this age, because the society is
having access to modern medical facilities. So, even the deaths after this age are very low
in numbers and so it very slowly it becomes to the top and then this is the life expectancy
of this particular population or this particular society. So, this is how we represent that
society in the case of a population pyramid.
Later on, it is possible that the society might try to reduce the birth rates even further and
when that happens, you will see a society that will start looking like this. So, the number
of children that have been born or that are being born, that the society would try to reduce
that even further. So, from having these many number of children, probably the society
will start to think about having these many number of children or it is also possible that
the society might find that now the population has a number of old individuals and

probably we need number of children to support ourselves. So, it is also possible that you
might have a curve that will start to bulge out in the bottom.
This is what is represented here in the case of the fifth stage. So, this is the fifth stage of
the society that has a low birthrate, a low death rate, but then the birth rate is slightly more
than the death rate. So, that was the first criticism of Malthus that what he had projected is
not exactly correct because it also depends on the level of affluence of the society, it also
depends on what stage of demographics stage you are there in the society.
The second criticism of Malthus is that agricultural growth is not as he had suggested.
Malthus had suggested that agricultural growth goes as an arithmetic progression 1 to 2, 2
to 3 and so on.
(Refer Slide Time: 35:04)

And that is possible when we are looking at a short period of time. For instance, here we
are seeing that the growth rate is increasing in an arithmetic progression.

(Refer Slide Time: 35:17)

But then, if we look at longer time scales, we find that here also we are observing an
exponential increase in the yields of a number of crops. So, here we are saying the long
term cereal yields in the case of United Kingdom, on the x axis we have the time so, it
starts from 1270 and goes till 2014 and on the y axis we are seeing the yields; how many
tonnes per hectare of cereals are being produced.
Here we are looking at the red color is barley, the blue one is oats and the green one is
wheat. Now, if you look at the very early stage productivity, we see that the productivity
was close to say 0.5 tonnes per hectare, but now the productivity is as high as 8 tonnes per
hectare in the case of wheat. So, from 0.5 tonnes per hectare to 8 tonnes per hectare, in this
period we saw more or less in arithmetic progression, but then in this period what we are
observing is a geometric progression or an exponential increase.
What Malthus had predicted in the case of agricultural productivity or agriculture supply,
that is also not correct. It might move as a geometric progression or it might even move as
an exponential growth or a geometric progression. Malthus also did not consider that with
time we can even incorporate more land into our agricultural sector.
If we look at the amount of land that has been used for different sectors; let us consider
this diagrammatic representation of the amount of land that is there in different sectors.
Here we can see that this pink area is the amount of land that we have diverted to the crops.
This is the cropland area. Then the red portion is the amount of area that has been diverted
to livestock.
We can see that roughly around say between one forth and one third of the total area of the
earth has been diverted to agriculture. It is either a cropland or it is a land that is used for
livestock or a land that is being used for grazing. What about the other lands? The green
one is showing us the area that is under the forest, the blue one is showing roughly the
amount of area that we have under built up area, the brown one is showing us the amount
of area that is barren land and this dark brown area is showing us the amount of area that
is a shrub land and this blue area is the total amount of fresh water.
If you add up all the fresh water that is there in the world, if you add up all the lakes, all
the ponds, all the rivers, it would be roughly the size of Mongolia. And if you add up all
the cropland, it would be roughly the size of China plus Japan plus some other countries
of Southeast Asia. And this proportion has not remained constant with time.