This document discusses key concepts related to population growth and dynamics. It defines what a population is and describes demography as the statistical study of populations. Population size, density, and dispersion are identified as key features of populations. Crude density and ecological density are important indexes used to describe populations. Methods for estimating population densities include mark-recapture and minimum known alive techniques. The concepts of growth rate, sources and sinks, and meta-populations are also introduced. Population dispersion patterns like regular, random, clumped and regular clumped are described. Finally, the document discusses age structure and different types of age pyramids in populations.

1. POPULATION
GROWTH
Dr. Anukriti Nigam
Fergusson College (Auto.)
Pune

2. What is a population?
● A group of organism of the same species living in the same
habitat at the same time where they can freely interbreed
Or
● It is a group of individuals of a particular species occupiying a
particular area at a particular time.
Or
● The population that occupies a very small area, is smaller in
size, such a population is called local population.
● A group of such a closely related local population is called
meta-population.

3. What is a Demography?
● It is the statistical study of populations. It is used to
predict how the size of a population will change

4. Population Dynamics
● Three Key Features of Populations
● Size
● Density
● Dispersion

5. Describing a population
1.Size and Density
▪Crude density-density per unit total space.
▪Specific density/ecological/economic -density per unit
habitat space.Graph

7. Important Indexes Used:
1. Crude density: It is the number (or biomass) per unit of total space.
2. Ecological density: Ecological density is the number (or biomass) per
unit of habitat space (area or volume available that can be colonised by
the population)
3. Relative abundance: It is used to denote changing (increasing or
decreasing) population and is time relative. For example, the number of
birds seen on a tree per hour.
4. Frequency of occurrence: Frequency of occurrence is the percentage
of sample plots occupied by a species.
5. Importance value: The importance value of each species are formed
by combining density, dominance and frequency during the descriptive
studies of vegetation.

8. Thus local density provides us with:
(1) Information about the interaction of a population with its environment
(2) Changes in density reflect changing local conditions.
➢The factors that regulate population size can be classified as extrinsic
and intrinsic.
● The populations own response to density is said to be intrinsic, while the
interaction with the rest of the community is said to be the extrinsic
factor.
● Intrinsic factors include intraspecific competition, immigration,
emigration and physiological and behavioural changes affecting
reproduction and survival.
● Extrinsic factors are interspecific competition, predation, parasitism and
disease.

9. Methods for Estimating Population Densities:● Mark-recapture method. This method involves capturing
of a fraction of the population and marking with tags,
paint, radio collars etc. and releasing them back into the
population enough time is allowed for the marked
individuals to recover and mingle with the rest of the
population.
● A second sample is taken, after a certain time period, from
the mingled population.

10. ● The ratio of the marked to unmarked is noted and the
estimate of the population size can be calculated by
the following equation:
● X = nM/N
● where x =the number of marked individuals recaptured,
● N = the total number or size of the second sample, =
● M = the number of individuals marked initially (first
sampling), and N is the total size of the population.
● If the above equation is rearranged, then we get
● N = nM/x

11. Thus, the estimate of the total population density is called
Lincoln index.
The validity of the above equation is based upon the factors
listed:
1. The marking technique has no negative effect.
2. The marked individuals were released at the same site of capture
and were allowed to mix with the population, based on their
natural behaviour.
3.Marking technique does not affect the probability of being
recaptured.
4. The markings should be clear and firmly fixed so that they are
not lost or overlooked.
5. There should not be any significant natality or mortality during
the time interval under study.
6. No significant immigration or emigration of marked or unmarked
individuals during the time interval under study.

12. Problem solving
● Example:
● Supposing 100 deers were radio collared and was
allowed to mix with the population. After a certain
time period 38 deers came to a particular site for
licking salts.
● Of these 38 deers, the numbers of radio collared
animals were 8.
● Thus, the density of deer population is that area is
estimated to be ??????????

13. ● Solution :-
● Supposing 100 deers (M) were radio collared and was allowed to mix
with the population. After a certain time period 38 deers (n) came to a
particular site for licking salts. Of these 38 deers, the numbers of
radio collared animals were 8(x). Thus, the density of deer population
is that area is estimated to be
● N = 38(100)/8 = 475
● However, for bigger carnivore animals the estimate of population is
generally done by the pug mark method eg tigers.
● The other methods generally used are minimum known alive
(MKA) total counts, quadrate or transect sampling, removal
sampling, plotless methods etc.

14. Concept of Growth rate
▪ Growth Rate –ΔN/ Δ t
● Where-ΔN= is the change in
number of organisms.
● Δ t = per time

15. Sources, Sinks and Meta-populations:
● When there is abundant
resources in habitats, more
offsprings are produced by
individuals than required to
replace themselves.
● In such cases, the surplus
offspring may disperse to
other areas.
● Such populations are said to be
source populations .

16. ● The reverse occurs in
case of poor habitats.
● Here, few offsprings are
produced locally, to
replace loss due to
mortality.
● Thus, to maintain the
population, individuals
immigrate from other
habitats. These
populations are said to be
sink populations

17. ➢There are populations that exist
as a set of subpopulations
referred to as meta-populations
by Richard Levins (1970).
➢These meta-populations are
more or less isolated but there
exist some exchange of
individuals (and genes) by way
of dispersal.
➢These concepts of sources, sinks
and meta-populations are
important as they serve as a
framework for studying many of
our threatened and endangered
species.

18. ▪2.Dispersion -Dispersion is the spatial pattern of
individuals in a population relative to one another.
▪In nature, due to various biotic interactions and
influence of abiotic factors, the following four basic
population distributions can be observed:-
▪ Regular
▪ Random
▪ Clumped
▪ Regular clumped

19. (a) Regular dispersion- Here the individuals are more or less
spaced at equal distance from one another. This is rare in
nature but in common is cropland.
● Examples:
monoculture crops, orchard or pine plantation, desert
shrubs etc
(b) Random dispersion: Here the position of one individual is
unrelated to the positions of its neighbours. This is also
relatively rare in nature.
Examples:
Lone parasites or predators show a random
distribution as they are often engaged in random searching
behaviour for their host or prey.

20. (c) Clumped dispersion: Most populations exhibit this
dispersion ,individuals aggregated into patches interspersed
with no or few individuals. Such aggregations may result from
social aggregations, such as family groups or may be due to
certain patches of the environment being more favourable for
the population concerned.
● Examples: Salamanders prefer to live in clumps under logs.
Birds travel in large flocks. Trees form clumps of individuals
through vegetative reproduction.
● D) In regular clumped distribution: Individuals are clumped and
are spaced out evenly from other similar clumps.
Examples: Herds of animals or vegetative clones in plants show
either random or are clumped in a regular pattern.

22. Population Dispersion

23. To determine the type of spacing and the degree of clumping, several
methods have been suggested of which two are mentioned:
1. To compare the actual frequency of occurrence of different sized
groups obtained in a series of samples. If the occurrence of small sized
and large sized groups is more frequent and the occurrence of mid-
sized groups less frequent than expected, then the distribution is
clumped. The reverse is seen in uniform distribution.
2. The distance between individuals are measured and the square root of
the distance is plotted against frequency. The shape of the resulting
polygon indicates the pattern of distribution. A symmetrical polygon
(bell-shaped) indicates random distribution, a slanted polygon to the
right indicates a uniform distribution, and one slanted to the left
indicates a clumped distribution.

24. The Allee principle:
➢Aggregation will subsequently increase competition .
➢This often is counter-balanced by the increased survival of the
group due to its ability to defend itself, or to find resource, or to
modify microhabitat conditions.
➢Thus, both under-crowding (lack of aggregation) and over-
crowding may be limiting. This view was put forward by W. C.
Allee, a Quaker and V. E. Shelford, and was termed as the Allee
effect or Allee principle of aggregation.
➢Allee effect stresses that any optimal function (faster body growth,
increased reproduction, or longer life) takes place at an intermediate
rather than at minimal density.
➢For instance, at low density, a drop in reproductive rate takes place
as some females may go unmated because they were not found by
males or because of an unbalanced sex ratio.

25. 3. Age structure-
• In most types of populations, individuals are of different age.
• The proportion of individuals in each age group is called age
structure of that population.
• The ratio of the various age groups in a population determines
the current reproductive status of the population, thus
anticipating its future.
• From an ecological view point there are three major ecological
ages in any population.
• These are, pre-reproductive, reproductive and post reproductive.
The relative duration of these age groups in proportion to the
life span varies greatly with different organisms.

26. Age pyramids
▪ Young population (Triangular)-It indicates a
high percentage of young individuals. In rapidly growing
young populations birth rate is high and population growth
may be exponential as in yeasty house fly, Paramecium,
etc
▪ Stable population (Bell)-It indicates a stationary
population having an equal number of young and middle
aged individuals.
▪ Declining population (Urn)-It indicates a low
percentage of young individuals and shows a declining
population

29. Population Growth:
The size of a population for any species is not a
static parameter, it keeps changing with time.
It depends on the following factors:
(i) Food availability
(ii) Predation pressure
(iii) Weather

30. 4. Natality
● It is simply a broader term covering the production of new
individuals by birth, hatching, by fission, etc.
● The natality rate may be expressed as the number of
organisms born per female per unit time.
● In human population, the natality rate is equivalent to the
birth-rate.
● Increases population size
● Each species will have its own maximum birth rate
● Maximum birth rates are seen when conditions are ideal
● This can lead to exponential growth
1. MAXIMUM NATALITY/FECUNDITY
2. ECOLOGICAL NATILITY/FERTILITY RATE

31. (a) Maximum natality:
Also called as absolute or potential or physiological natality, it is
the theoretical maximum production of new individuals under ideal
conditions.
It is a constant for a given population. This is also called fecundity
rate.
(b) Ecological natality:
Also called realized natality or simply natality, it is the
population increase under an actual, existing specific condition.
Thus it takes into account all possible existing environmental
conditions. This is also designated as fertility rate.

32. ● Natality is expressed as
● ∆Nn/∆ t = Absolute Natality rate (B)
● ∆Nn/N ∆ t = Specific natality rate (b) (i.e., natality rate
per unit of population).
● Where N = initial number of organisms.
● n = new individuals in the population.
● t = time.

33. 5. Mortality
● Mortality reduces population growth
● It operates more when conditions are not ideal
● Overcrowding leading to competition, spread of
infectious disease
TYPES
1. MINIMUM /SPECIFIC/POTENTIAL MORTALITY
2. ECOLOGICAL/REALISED MORTALITY

34. ● (a) Minimum mortality:
● Also called specific or potential mortality, it represents the
theoretical minimum loss under ideal or non-limiting
conditions. It is a constant for a population.
● (b) Ecological or realised mortality:
● It is the actual loss of individuals under a given
environmental condition. Ecological mortality is not
constant for a population and varies with population and
environmental conditions, such as predation, disease and
other ecological hazards.

35. Vital index and survivorship curves
● A birth-death ratio (100 x births/deaths) is called vital index.
● For a population, the surviving individuals are more significant
for a population than the dead ones.
● The survival rates are generally expressed by survivorship curves.
● A survivorship curve is a graph of the survival rate of a group
of organisms. In making a survivorship graph, a cohort is
used; in this case, a group of individuals who were born at
roughly the same time.
● This cohort is then graphed with the number of surviving
individuals on the y-axis and the age of the cohort on the x-axis.
● Generally, a species will have one of three types of survivorship
curves.

36. Survivorship
● Survivorship is the percentage of newborn individuals in a
population that can be expected to survive to a given age.
● It is used as another way to predict population trends.
● To predict survivorship, demographers study a group of
people born at the same time and notes when each member
of the group dies.

37. Survivorship
● Wealthy developed countries such
as Japan and Germany currently
have a Type I survivorship curve
because most people live to be
very old.
● Type II populations have a similar
death rate at all ages.
● Type III survivorship is the
pattern in very poor human
populations in which many
children die.
● Both Type I and Type III may
result in populations that remain
the same size or grow slowly.
The results of these studies are then plotted
on a graph and might look like one of the
types of survivorship graphs

39. Age, years (x)
Probability of surviving to age x
(lx)
No. of female offspring born to a
mother of age x (mx)
0 1.000 0.000
1 0.845 0.045
2 0.824 0.391
3 0.795 0.472
4 0.755 0.484
5 0.699 0.546
6 0.626 0.543
7 0.532 0.502
8 0.418 0.468
9 0.289 0.459
10 0.162 0.433
11 0.060 0.421
6. LIFE TABLES- Information on mortality , natality in
different ages and sexes can be combined to form life table.
Example-Consider a sheep population which is censused once a year
immediately after breeding season

40. TYPES OF LIFE TABLES:-
▪Cohort or age-specific or dynamic life tables: -data are
collected by following a cohort throughout its life. This is
rarely possible with natural populations of animals.
▪ Note: a cohort is a group of individuals all born
during the same time interval.
▪Static or time-specific life tables:- age-distribution data
are collected from a cross-section of the population at one
particular time or during a short segment of time, such as
through mortality data.
▪Composite :- data are gathered over a number of years
and generations using cohort or time-specific techniques.

41. Factors that affect density
1. Immigration- movement of individuals into a population
2. Emigration- movement of individuals out of a population

42. The density of a population in a given habitat during a given period, fluctuates due to the four basic
processes:
● (a) Natality refers to the number of
births during a given period in the
population that are added to initial
density.
● (b) Mortality is the number of deaths in
the population during a given period.
● (c) Immigration is the number of
individuals of the same species that have
come into the habitat from elsewhere
during the time period under
consideration.
● (d) Emigration is the number of
individuals of population who left the
habitat and moved elsewhere during a
given period of time.

43. ● Out of these four, natality and immigration contribute an
increase in population density while mortality and emigration
contribute to the decrease in population density.
● So, if N is the population density at time t, then its density at
time t +1 is
● Nt+1 = Nt + [(B + I) – (D + E)]
● Where, N = Population density
● t = Time,
● B = Birth rate,
● I = Immigration,
● D = Death rate,
● E = Emigration
From the above equations, we can see that population
density will increase if, (B + I) is more than (D + E).

44. Immigration
Emigration
Natality MortalityPopulation
+
+
-
-
Factors That Affect Future
Population Growth

45. KEY FEATURES OF POPULATIONS, con’t
Population size is limited by:
density-dependent factors
● Disease
● Competition
● Predators
● Parasites
● Food
● Crowding
● The greater the population,
the greater effect these
factors have.
● Ex. Black plague in the
Middle Ages – more deaths
in cities
density-independent factors
● Volcanic eruptions
● Temperature
● Storms
● Floods
● Drought
● Chemical pesticides
● Major habitat disruption (as
in the New Orleans flooding)
● Most are abiotic factors

46. Other factors that affect population growth
Limiting factor- any biotic or abiotic
factor that restricts the existence of
organisms in a specific
environment.
●EX.- Amount of water
Amount of food
Temperature

47. Phases of population growth
Phase 1: Log or exponential phase
● Unlimited population growth
● The intrinsic rate of increase (r)
● Abundant food, no disease, no predators etc
Phase 2: Decline or transitional phase
● Limiting factors slowing population growth

48. Phase 3
Plateau or stationary phase
● No growth
● The limiting factors balance the population’s capacity
to increase
● The population reaches the Carrying Capacity (K) of
the environment
● Added limiting factors will lower K
● Removing a limiting factor will raise K

49. Factors affecting the carrying capacity
● Food supply
● Infectious disease/parasites
● Competition
● Predation
● Nesting sites

50. Many
organisms
present
Few
organisms
present
Few
organisms
present
None None
Limiting Factor- Zone of Tolerance

51. Carrying Capacity- the maximum
population size that can be
supported by the available
resources
There can only be as many
organisms as the environmental
resources can support
Other factors that affect population growth

52. Carrying Capacity
Carrying Capacity (k)
Nu
m
b
e
r
Time
J-shaped curve
(exponential growth)
S-shaped curve
(logistic growth)

54. PREDICTING POPULATION GROWTH
● Model:
● A hypothetical population that has key characteristics of
the real population being studied.
● Used by demographers to predict how a population will
grow.

55. PREDICTING POPULATION GROWTH, con’t
● Nearly all populations will tend to grow exponentially
as long as there are resources available.
● Two of the most basic factors that affect the rate of
population growth are the birth rate, and the death rate.
● r(rate of growth)=birth rate – death rate

56. Growth Models
● Studying about the behaviour and pattern of different
animals can help us to learn a lesson on how to control
the human population growth.
● There are following two models of population growth:
● Exponential Growth:
● Logistic Growth:

57. ● Availability of resources (food and space) is essential for the
growth of population.
● The unlimited availability results in population exponential.
● The increase or decrease in population density (N) at a unit time
period (t) is calculated as (dN/dt)
● Let dN/dt = (b – d) N
● Let (b-d) = r, then, dN/dt = rN
● Where, N is population size,
● b is birth per capita
● d is death per capita,
● t is time period
● r is intrinsic rate of natural increase.
● r, is an important parameter that assess the effects of biotic and
abiotic factors on population growth. It is different for different
organisms.

58. Figure 35.3A
Exponential Growth Curve

59. Logistic Growth:
● Practically, no population of any species in nature has
unlimited resources at its disposal. This leads to
competition among the individuals and the survival of
the fittest.
● Therefore, a given habitat has enough resources to
support a maximum possible number, beyond which
no further growth is possible.
● This is called the carrying capacity (K) for that species
in that habitat.

60. When N is plotted in relation to
time t, the logistic growth show
sigmoid curve and is also called
Verhulst-Pearl Logistic Growth
and is calculated as
dN/dt = rN (K – N/K)
Where, N is population density at
time t
K is carrying capacity
r is intrinsic rate of natural increase.
This model is more realistic in
nature because no population
growth can sustain exponential
growth indefinitely as there will
be completion for the basic needs.
Human population growth curve
will become S-shaped, if efforts are
being made throughout the world to
reduce the rate of population growth
and make it stationary.

61. Thanks.