Population Growth and Population Projections

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Population Growthand Population Projections
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Birth Intervals
Post partum ovulation time to
conceive birth Amenorrhea
conception
Menarche
Marriage
1st Birth
2nd Birth
3rd Birth

• Issues
• Events out of order (births then marry)
• IVF
• Right censoring
• Multiple births

Menopause
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Population Growth

• P(t1) P(t) B(t) D(t) I(t) E(t)
• For now ignore migration
• Focus on births and deaths together

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Fertility and Population Growth

• TFR
• number of children born into a population
• 2.1 is considered replacement level fertility
• Sex ratio of births
• Number of females in the population
• Gross reproduction rate (GRR)
• Same as TFR except counts only female births
• Usually male births outnumber female births
• TFR GRR x 2.05 (approx)

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Fertility and Population Growth

• Mortality
• To sustain a population, need to know how many
  females survive to reproductive age
• Evolutionary biologists often refer to this is
  reproductive fitness (measured as
• Net reproduction rate (NRR)
• Number of daughters born to a women that controls
  for mortality

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Net Reproduction Rate
Total number of daughters born between 15 and 49
that takes into account survival of mothers. Lx
refers to number of person years lived by a
cohort of women fx refers to the age specific
fertility rate
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NRR

• NRR lt GRR because of mortality
• If NRR GRR, then women are immortal while in
  their reproductive years
• If fertility and mortality rates are constant for
  many years, have a constant growth rate.

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Using the NRR to Predict Growth

• NRR is a cohort measure of growth since it
  assumes a number of daughters over the
  reproductive years
• Most calculate NRR for a single year
• Japan in 1968
• TFR 1.6
• GRR 0.8
• NRR lt 0.8
• Would predict population decline didnt happen

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Geometric and Exponential Growth
Geometric Growth
Assumes additions/deletions happen once a year
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Growth Rates
Population Growth Rates in Urban and Rural Areas,
Less and More Developed Countries, 1975 to 2000
and 2000 to 2025. Derived from United Nations,
World Urbanization Prospects The 1999 Revision
(2000).
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Geometric and Exponential Growth
Exponential Growth
Assumes additions/deletions happen throughout the
year
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In some urban areas in developing countries,
growth rate is .07 or 7 so 70/7 means a
population doubling in 10 years
Many developed countries have very low growth
rates and, as a result, the equation shows
doubling times of hundreds or thousands of years.
But these countries are not expected to ever
double again. Most, in fact, likely have
population declines in their future. Many less
developed countries have high growth rates that
are associated with short doubling times, but are
expected to grow more slowly as birth rates are
expected to continue to decline
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Excel example of geometric growth
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R6.9
R4.2
R3.5
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Annual Growth Rate and NRR

• Link NRR to growth rate
• NRR is a comparison of one generation (mothers)
  to another (daughters)
• Measure the population size after the length of
  one generation (g)
• Note book does not mention gender per se

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Population Structure

• Population pyramids
• Age/sex histograms
• http//www.census.gov/ipc/www/idbpyr.html

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Shapes of Population Pyramids
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HIGHLIGHTS IN WORLD POPULATION GROWTH 1 billion
in 1804 2  billion in 1927 (123 years later) 3 
billion in 1960 (33 years later) 4  billion in
1974 (14 years later) 5  billion in 1987 (13
years later) 6  billion in 1999 (12 years later) 
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Dependency Ratio

• Another measure of the age distribution
• Defined as the number of non-working age persons
  per 100 working age persons

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Stable Population

• Lotka's concept of a stable population (circa
  1907).
• If any population has
• No migration,
• Mortality fertility age-specific rates remain
  constant for a long period
• Then a fixed age structure will develop (called
  stable age structure) which does not depend of
  the initial age structure.
• Population will also increase in size at a
  constant rate.
• Stationary population (which has a zero rate of
  increase) is a special case of stable population

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Stationary Population

• A population with
• No migration
• Constant age specific mortality
• Has birth and death rates that yield a growth
  rate of ZERO
• This is known as a stationary population.
• Its size is constant and its age structure (
  in each age category) is also constant.

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How Many Are There in A Stable Population?
Objective Calculate Ax
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How Many Are There in A Stable Population?
Objective Calculate b, crude birth rate, in a
stable population
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How Many Are There in A Stable Population?
Objective Calculate population x1/2 years ago
The number of births in a stable population that
occurred x 1/2 years ago is simply the crude
birth rate b (which does not change) times the
population x 1/2 years ago. Now, not all those
people survived need to calculate proportion
survived to age x
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How Many Are There in A Stable Population?
(Number born x1/2 years ago) x (survived at age
x1/2) tells you how many people there will be at
age x today in a stable population
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Excel Example
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Population Projections

• Why Do It?
• How To Do It?
• Mathematical models
• Simple
• Works for some circumstances
• Component Method
• Harder
• More extensive data requirements

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Mathematical Models
Implies perpetual growth or ultimate extinction
Assumes there are upper and lower bounds to
population size
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Exponential Growth
GO TO EXCEL
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Logistic Growth
Last line is specified as a regression and can be
estimated as one GO TO EXCEL
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Component Method

• Needs a great deal of data, often at the level of
  detail of single ages.
• The number of components can vary depending upon
  the type of projection needed
• All projections reflect the assumptions you make
  about which components you use, their
  stability/change over time, and how far into the
  future you project

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Component Method
Equations 1 and 2 show m(ale) superscripts
comparable equations for females
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Europe has just entered a critical phase of its
demographic evolution. Around the year 2000,
the population began to generate "negative
momentum" a tendency to decline owing to
shrinking cohorts of young people that was
brought on by low fertility (birthrate) over the
past three decades. Currently, the effect of
negative momentum on future population is small.
However, each additional decade that fertility
remains at its present low level will imply a
further decline in the European Union (EU) of 25
to 40 million people, in the absence of
offsetting effects from immigration or rising
life expectancy.
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Population Momentum
The tendency for population growth to continue
beyond the time that replacement-level fertility
has been achieved because of a relatively high
concentration of people in the childbearing
years. For example, the absolute numbers of
people in developing countries will continue to
increase over the next several decades even as
the rates of population growth will decline. This
phenomenon is due to past high fertility rates
which results in a large number of young people.
As these youth grow older and move through
reproductive ages, the greater number of births
will exceed the number of deaths in the older
populations
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Projection methods and assumptions. The
alternative population projections were carried
out using standard cohort component population
projection methods using software developed by
the authors. Since this analysis aims at
isolating the impacts of alternative fertility
assumptions, in all scenarios only the fertility
component was modified as described in Table 1,
while we assumed that mortality stayed constant
at life expectancies of 81.5 years for women and
75.5 years for men. We also assumed a closed
population without migration.
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Doing Component Methods of Population Projections