EDS 1102: Population, poverty and the Environment
Topic: Population Ecology
Population Ecology
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•
A group of interbreeding
individuals (individuals of
the same species) living
and interacting in a given
area at a given time is
defined as a population.
Population ecology is the
study of how individuals
of a particular species
interact
with
their
environment and change
over time.
Theories of population growth
Malthusian model of population
growth
Demographic transition theory
Malthusian Model of Population growth
Malthusian Model of Population growth
Demographic transition theory
“Demographic transition refers to a population cycle that begins with a fall
in the death rate, continues with a phase of rapid population growth and
concludes with a decline in the birth rate”-E.G. Dolan.
According to this theory, economic
development has the effect of
bringing about a reduction in the
death rate.
According to the theory of demographic
transition, population growth will have to
pass through these different stages during
the course of economic development
Stages
Stage 1
Stage 2
High and fluctuating birth and death
rate (slow population growth)
High birth rate and declining death
rate (rapid population growth)
Stage 5
Stage 3
Stage 4
Declining birth and low death rate
(declining the population growth)
Low birth and death rate slow
population growth
Birth and death rate is approximately equal
(zero population growth)
Population Growth Models
Populations change over time and
space as individuals are born or
immigrate (arrive from outside the
population) into an area and others
die or emigrate (depart from the
population to another location).
Populations grow and the age and
gender composition also change
through time and in response to
changing environmental conditions.
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•
Exponential Growth
Logistic Growth
Exponential Growth
Charles Darwin, in his theory of
natural
selection,
was
greatly
influenced by the English clergyman
Thomas Malthus. Malthus published a
book (An Essay on the Principle of
Population) in 1798 stating that
populations with unlimited natural
resources grow very rapidly. According
to the Malthus’ model, once
population size exceeds available
resources,
population
growth
decreases dramatically.
Figure : The “J” shaped curve of exponential growth for a hypothetical population
of bacteria. The population starts out with 100 individuals and after 11 hours
there are over 24,000 individuals. As time goes on and the population size
increases, the rate of increase also increases (each step up becomes bigger). In
this figure “r” is positive.
Exponential Growth
This type of growth can be represented using a mathematical function
known as the Exponential growth model:
G = r x N.
In this equation
G is the population growth rate, it is a measure of the number of
individuals added per interval time.
r is the per capita rate of increase (the average contribution of each
member in a population to population growth; per capita means “per
person”).
N is the population size, the number of individuals in the population at a
particular time.
Exercise 1
At the beginning of the year, there are 7650 individuals in a population of
beavers whose per capita rate of increase for the year is 0.18. What is its
population growth rate at the end of the year?
Solution:
Given that the population size (N) is 7650 and the per capita rate of increase
(r) is 0.18, we can plug these values into the formula to calculate the
population growth rate (G):
Exponential growth model: G = r x N
G=0.18×7650=1377
So, the population growth rate at the end of the year is 1377 individuals. This
means that, based on the given per capita rate of increase, the beaver
population is expected to increase by 1377 individuals over the course of the
year.
Per capita rate of increase (r)
In exponential growth, the population growth rate (G) depends on
population size (N) and the per capita rate of increase (r).
r = (birth rate + immigration rate) – (death rate and emigration rate).
If r is positive (> zero), the population is increasing in size;
this means that the birth and immigration rates are greater than death and
emigration.
If r is negative (< zero), the population is decreasing in size;
this means that the birth and immigration rates are less than death and
emigration rates.
Per capita rate of increase (r)
Suppose, birth rate of Nurpur village is 6.5 and
immigration rate 5.9 , death rate 7.3 and emigration
rate is 4.7. what will be the value of ‘r’?
Solution:
We know,
r= (Birth rate+ immigration rate)- (death rate + emigration rate)
Given that,
Birth rate= 6.5
Immigration rate=5.9
Death rate=7.3
And emigration rate=4.7
Then, r= (6.5+5.9)-(7.3+4.7)
=12.4-12
=0.4
The value of r is greater than zero and this indicates that the population size is increasing.
Logistic Growth
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•
Exponential
growth
cannot
continue
forever
because
resources (food, water, shelter)
will become limited.
When resources are limited,
populations
exhibit
logistic
growth. In logistic growth a
population
grows
nearly
exponentially at first when the
population is small and resources
are plentiful but growth rate slows
down as the population size nears
limit of the environment and
resources begin to be in short
supply and finally stabilizes (zero
population growth rate) at the
maximum population size that can
be supported by the environment
(carrying capacity).
Figure: Shows logistic growth of a hypothetical bacteria population.
The population starts out with 10 individuals and then reaches the
carrying capacity of the habitat which is 500 individuals.
Logistic Growth
The mathematical function or logistic growth model is
represented by the following equation:
G= r x N[1-N÷K]
K is the carrying capacity – the maximum population size
that a particular environment can sustain (“carry”).
Exercise 2
Suppose, population size of the city ‘X’ was 1200000 in
June, 2021 and the per capita rate of increase was 1.58
and the carrying capacities was 1300000. what was
the growth rate of the population of the city ‘x’.
We know that,
Population growth, G=r x N(1-N÷K)
Here, r= per capita rate of increase
N= population size
K= carrying capacities
Given that, r=1.58
N= 1200000
k= 1300000
So, G=1.58 x 1200000 (1-1200000÷1300000)
= 1.58 x 1200000 (1-0.92)
=1.58 x 1200000 x 0. o8
= 151680