This document discusses various methods for population forecasting, including arithmetical increase, geometrical increase, incremental increase, simple graphical, master plan, and logistic curve methods. It provides examples of calculating future populations using the arithmetical, geometrical, and incremental increase methods. The logistic curve method models population growth as an S-shaped curve, and the document gives the logistic curve equation and shows working through an example problem to determine saturation population and expected population in the next decade.

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SUSTAINABLE
DEVELOPMENT
(OPEN ELECTIVE)
Course Instructor : Dr. Vikas B. Varekar
Civil and Environmental Engineering Department,
Veermata Jijabai Technological Institute
CE4106S
Population
Population
• Worlds Population
• 7.5 billion as of July 2017
Population Growth ….????
Factors affecting on population growth
Biotic factors
food, disease, competitors, and predators
Abiotic factors
rainfall, floods, and temperature
Population Growth
Factors affecting changes in population are:
• increase due to births
• decrease due to deaths
• increase/ decrease due to migration
Forecasting of Population
1) Arithmetical Increase Method
2) Geometrical Increase Method
3) Incremental Increase Method
4) Simple Graphical Method
5) Graphical Comparison Method
6) Master Plan Method
7) Logistic Curve Method
8) Apportionment Method

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ARITHMETICALINCREASE METHOD
7
• It is assumed that the population is increasing at
constant rate, i.e.
dP/dt = C
• Therefore, Population after nth decade will be
Pn= P + n.C
where, Pn is the population after ‘n’ decades
and ‘P’ is present population, C is the average
increment for the decades
• Suitable for large and old city with considerable
development.
• If it is used for small, average or comparatively
new cities, it will give lower population estimate
than actual value.
Arithmetical Increase Method
Solution
• Calculate average increment for the decades
• Estimate the population for the given year
Solution
Solution Solution

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Problem
• The population data for a town is given below. Find out
the population in the year 2051, and 2061 by arithmetical
increase method
GEOMETRICALINCREASE METHOD
• In this method the per decade percentage increase or
percentage growth rate is assumed to be constant
• The increase is compounded over the existing population
every dacade, this method also known as uniform
increase method.
• The geometric mean is defined as the nth root of
the product of n numbers
• should be applied for a new industrial town at the
beginning of development for only few decades
GEOMETRICALINCREASE METHOD
• The population at the end of nth decade ‘Pn’ can be
estimated as:
Pn = P (1+ IG/100)n
Where, IG = geometric mean of percentage increase
P = Present population
N = no. of decades.
• IG = (r1 X r2 X r3 X….X rm)1/m
• r growth rate in percentage
GEOMETRICALINCREASE METHOD
• Problem
Solution Solution

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Solution Solution
• Calculate geometric mean
• Estimation of population
Solution Solution
Problem
• The population data for a town is given below. Find out
the population in the year 2021, 2031and 2041 by
geometrical increase method
327,500; 429,025; 562,023
Incremental Increase Method
• In this method per decade growth rate is not assumed to
be constant as in arithmetic / geometric mean method
• But is progressively increasing or decreasing depending
upon weather the average of the incremental increase in
the past data is positive or negative
• Suitable for an average size town under normal condition
where the growth rate is found to be in increasing order.

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Incremental Increase Method
• Population after nth decade is can be estimated as,
Pn = P+ n.X + {n (n+1)/2}.Y
where, Pn = Population after nth decade
X = Average increase
Y = Incremental increase
Incremental Increase Method
Solution
• Increase in population
• Incremental increase in population
• Estimate population for nth decade
Incremental Increase Method
Incremental Increase Method Incremental Increase Method

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Incremental Increase Method SIMPLE GRAPHICAL METHOD
• In this method, the populations of last few decades are
correctly plotted to a suitable scale on graph.
• The population curve is smoothly extended for getting
future population.
• This extension should be done carefully and it requires
proper experience and judgment.
SIMPLE GRAPHICAL METHOD Population Forecasting
• First four methods based on the assumption that,
• Factors and conditions which are responsible for
population increase in the past will continue in future also.
• But the assumption may or may not be satisfied
• City may suddenly impose immigration restrictions
• Compulsory family planning for eligible couples
• Develop enhanced medical facilities thereby reducing
death rates
MASTER PLAN METHOD
• The big and metropolitan cities are generally not
developed in haphazard manner, but are planned and
regulated by local bodies according to master plan.
• The master plan is prepared for next 25 to 30 years for
the city. According to the master plan the city is divided
into various zones such as residence, commerce and
industry.
• The population densities are fixed for various zones in the
master plan.
• From this population density total water demand and
wastewater generation for that zone can be worked out.
LOGISTIC CURVE METHOD
• This method is used when the growth rate of population
due to births, deaths and migrations takes place under
normal situation and it is not subjected to any
extraordinary changes like epidemic, war, earth quake or
any natural disaster, etc.
• If the population of a city is plotted with respect to time,
the curve so obtained under normal condition looks like S-
shaped curve and is known as logistic curve.

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LOGISTIC CURVE METHOD LOGISTIC CURVE METHOD
• the curve shows an early growth JK at an increasing rate
i.e. geometric growth or log growth,
dP/dt ∝ P
• The transitional middle curve KM follows arithmetic
increase i.e.
dP/dt=C
• For later growth MN the rate of change of population is
proportional to difference between saturation population
and existing population, i.e.
dP/dt ∝ (Ps - P)
LOGISTIC CURVE METHOD
• A mathematical solution for this logistic curve JN,
which can be represented by an autocatalytic first
order equation, is given by
where,
LOGISTIC CURVE METHOD
P = Population at any time t from the origin J
Ps= Saturation population
P0= Population of the city at the start point J
m & n = Constants
t = Time in years
Problem

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Problem
• In three consecutive decades the population of a town is
40,000; 100,000 and 130,000. Determine: (a) Saturation
population; (b) Equation for logistic curve; (c) Expected
population in next decade.
Solution
Q.3. (a) Saturation population: 137,500
(b) Equation for logistic curve: m = 2.437; n = -0.187;
(c) Expected population in next decade: 136,283population
in next decade.