This document discusses population growth models, including exponential and logistic growth. Exponential growth occurs when resources are unlimited and the population grows rapidly in a J-shaped curve. Logistic growth occurs when resources are limited, causing the population to initially grow rapidly then slow down, reaching an asymptote as the carrying capacity is approached. Key factors that influence population growth are birth rates, death rates, immigration, emigration, food availability, and competition for limited resources. Governments have implemented controls to limit unsustainable human population growth.

1. Population Growth.
Growth models:
Exponential growth
Logistic growth

2. The size of a population for any species is not a static
parameter
• Population keeps changing with time.
• Population changes depending on various factors.
• food availability,
• predation
• Atmospheric pressure
• adverse weather.

3. The population changes in a given habitat
due to changes in four basic processes:
• Natality
• Mortality
• Immigration
• Emigration
• Natality and Immigration: increase population density..
• Mortality and emigration decrease population density..

4. • Natality refers to the number of births in the population
during a given period.
• Mortality is the number of deaths in the population
during a given period.

5. • Immigration is the number of individuals of the same
species that have come into the habitat from elsewhere
during the time period.
• Emigration is the number of individuals of the
population who left the habitat and gone elsewhere
during the time period under.

7. • Nt+1 = Nt + [(B + I) – (D + E)]
• N is the population density at time t,
• then its density at time t +1 is

8. • Population density will increase if the number of births
+ immigrants (B + I) is more than the number of deaths
+ emigrants (D + E).
• For instance, if a new habitat is just being colonised,
immigration may contribute more significantly to
population growth than birth rates

9. Growth Models :
• Exponential growth:
• Logistic growth:

10. Exponential growth:

11. Exponential growth:
• Resource (food and space) availability is essential for
the growth of a population.
• When resources in the habitat are unlimited, each
species has potential to grow in number:
• Observed by Darwin while developing his theory of
natural selection.

12. • When food and space are available the population of
species grows in an exponential or geometric fashion.
• Darwin showed how even a slow growing animal like
elephant could reach enormous numbers in the
absence of checks.

13. • If in a population of size N.
• b = the birth rates
• d = death rates
• Increase or decrease in N during a unit time period t
• dN/dt = (b – d) × N
• (b–d) = r
dN/dt = rN

14. • The “r” in this equation is called the ‘intrinsic rate of
natural increase’
• “r” values, for the Norway rat is 0.015.
• The flour beetle it is 0.12.
• In 1981, the “r” value for human population in India
was 0.0205..

15. when we plot N in relation to time results in a
J-shaped curve..

16. • The integral form of the exponential growth equation as
• Nt = N0 ert
• Nt = Population density after time t
• N0 = Population density at time zero
• r = intrinsic rate of natural increase
• e = the base of natural logarithms (2.71828)

17. • Paramecium starting with just one individual and
through binary fission, doubling in numbers every day,
• Then imagine after 64 days the population size (food
and space remain unlimited)

18. Logistic growth
or
Verhulst-Pearl Logistic Growth

19. • A population growing in a habitat with limited resources
show initially :
• lag phase,
• acceleration
• deceleration
• and finally an asymptote (Zero).

20. A plot of N in relation to time (t) results in a sigmoid curve.

21. • =dN/dt= rN (K-N/K)
• N = Population density at time t
• r = Intrinsic rate of natural increase
• K = Carrying capacity
• K= In a given habitat has enough resources to support a
maximum possible number, beyond which no further growth
is possible..

22. No population of any species in nature has its disposal
unlimited resources to permit exponential growth".
• This leads to competition between individuals for
limited resources.
• Only the ‘fittest’ individual will survive and reproduce.

23. • The governments of many countries have also realised
this fact..
• and introduced various restraints (controls) with a view
to limit human population growth..

24. Harinatha Reddy Aswartha
Assistant Professor
Department of Microbiology
biohari14@gmail.com