Population Dyanmics

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Population Dyanmics
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Outline

• Population Growth
• Exponential Growth incremental steps
• Exponential Growth Formula
• Prediciting the Worlds Population
• Doubling Times
• Factors Affecting the Dynamics of Population
  Growth
• Role of Technology
• Two Demographic Worlds
• Population Growth Factors
• Future of Population Growth

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POPULATION GROWTH

• For most of human history, humans have not been
  very numerous compared to other species.
• It took all of human history (1804) to reach 1
  billion.
• 150 more years to reach 3 billion.
• 12 years to go from 5 to 6 billion. (October 12,
  1999)
• Human population tripled during the twentieth
  century.

Image from Cunningham Cunnigham, 2004
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Populations are Dynamic, not static

• Dynamic implies that the number of individuals in
  a population change over time.
• Static implies an equilibrium or not changing
• Simple population formula Nt N0 (B D) (I
  E)
• N number of individuals
• B Births,
• D Deaths
• Need only worry about I and E when dealing with a
  particular location
• I immigrants
• E emigrants

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Nt N0 (B D), not the whole story

• Formula says as long as B gt D, Nt will increase.
• But how is it increasing?
• What is the growth rate?
• Exponential Growth?

Figure from Botkins and Keller, 2003,
Environmental Science.
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What is Exponential Growth?

• Population Growth
• Exponential Growth - Growth as a percentage of
  the whole.
• dN/dtrN
• dN change in population
• Dt change in time
• r rate of growth or increase (or decrease)
• Sometimes called Biotic Potential - Potential
  of a population to grow in the absence of
  expansion limitations.

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Another Chance to Show off Excel

• Calculate exponential population growth
• Think of population growth as occurring in steps.
• Example is for r 1.25 growth (1 to keep adding
  previous population, growth rate 25)
• Time increments can any unit, days, years, 100s
  of years

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Graph of 25 Growth
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Lets Look at Some Real Numbers

• World population in 1965 was 3.2 billion
• Annual growth rate (r) was 2.2 ( r1.022)
• 6 billion reached in 1993

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(No Transcript)
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1.36 Growth Rate

• r 1.0136
• Population does not reach 6 billion until 2011

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Graph of 2.2 1.36 Growth Rates

• Same starting point 3.2 billion in 1965
• 0.84 difference in growth rate (lt 1!)
• In 35 years, 1.72 billion difference in people

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Exponential Growth Projecting toward the future

• Assuming Exponential Growth, what will be the
  human population of the planet in the when you
  are my age.
• Assume youre 20. Im 52, so 32 years 2004
  32 2036
• The current population, N0 6.2 billion
• Assume a stable growth rate of 1.36/year

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Brut Force Method

• Takes a long time
• Theres a better way to make projections

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Exponential Growth

• When introducing the exponential growth
  equations, we can imagine a case of tiny
  creatures with a 25 increases in the population
  (r1.25). One population began with a population
  (N0) of 100, and after a year, there were 125.
  The other population had an initial population
  (N0) of 5000, and one year later, it grew to
  6250. Note the ratios of final to initial
  populations, 'N/ N0 ', were both the same
• N/ N0 125/100 6250/5000
• As you can see, for a one year interval, this
  ratio was 1.25.
• Now we need to introduce the concept of a growth
  constant (k)
• This is used in the formula
• N No e kt

Modified from http//www.physics.uoguelph.ca/tuto
rials/exp/intro.html
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Exponential Growth

• This is used in the formula
• N No e kt
• You can solve for 'k', the growth constant,
• For this example, r 1.25 (Since N/ N0 1.25),
  and t 1.0 (year),
• The ln (r ) kt
• So we have
• ln (1.25) k t k (1.0)
• Since ln (1.25) 0.223, then k 0. 223/year.
• Recall that an exponent must be dimensionless. So
  'k' will always have dimensions of reciprocal
  time. In the case of the wee beasties, k has
  units of year .
• (ln natural log, e 2.7182818 ln (2.7182818 )
  1)

Modified from http//www.physics.uoguelph.ca/tuto
rials/exp/intro.html
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Exponential Growth

• Now that we know the value of the growth constant
  for our wee beasties, k 0.223, we can
  substitute this into our first equation.
• N No e kt
• Suppose the initial population were 2000 and we
  wish to calculate what it will be in 5.5 years.
  We know 'k' ( 0.223 year ), 't' ( 5.5 year),
  and ' No ' ( 2000). Then we can calculate 'N'
• N 2000 e 0.223 5.5
• N 6819
• Note that if the growth constant 'k' were larger,
  then 'kt' would be larger at any given time, and
  so the population increase would be greater.

Modified from http//www.physics.uoguelph.ca/tuto
rials/exp/intro.html
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Exponential Growth Projecting toward the future

• Assuming Exponential Growth, what will be the
  human population of the planet in the when you
  are my age.
• Assume youre 20. Im 52, so 32 years 2004
  32 2036
• The current population, N0 6.2 billion
• Assume a stable growth rate of 1.36/year
• ln ( 1.0136) 0.0135 (Remember you need the 1
  to continue to add the original population.
• So, k0.0135, t32,
• World population in 2036 9.55 billion

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Ball Park Estimating Doubling Time

• What is the doubling time (Td)?
• This is the time for a population to double in
  size?
• Note Notice that Td is independent of the size
  of the population!
• Rule of Thumb
• In exponentially growing populations
• 70 / annual growth Doubling Time

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70 / annual growth Doubling Time

• Rule of Thumb
• 25gt 70/25 3
• 2.2 70/2.2 32
• 1.36 70/1.36 51

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Another Chance to Show off Excel

• Calculate exponential population growth
• Think of population growth as occurring in steps.
• Example is for 1.25 growth
• Time increments can any units, days, 100s of
  years

22
Lets Look at Some Real Numbers

• World population in 1965 was 3.2 billion
• Annual growth rate (r) was 2.2
• 6 billion reached in 1993

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Population Dynamics

• Rate of increase, decreased
• But population still grew by billions
• Why?
• Population is still increasing
• Age structure
• ZPG 2.06 birth rate we are not there yet.

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Predicting the Worlds Population

• Even if fertility is at the replacement rate
  (2.06 births per female), the human population
  would still increase exponentially.
• This is because the world has too high a fraction
  of young people!
• Growth rate is also a function of the age
  structure, independent of the birth rate

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Predicting the Worlds Population

• Growth rate is also a function of the age
  structure, independent of the birth rate.
• Consider the number of women in 2003 who are 25
  years old
• There are more babies born today than there were
  25 years ago
• Hence, in 25 years, there will be more 25 year
  old women then there are today

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Predicting the Worlds Population

• Zero Population Growth (ZPG) has two components
• Births Deaths
• Stationary or Stable Age Distribution (def
  constant fractions of ages over time) This is not
  the case for the majority of the world.

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Predicting the Worlds Population

• Momentum of Population Growth the changes
  required to bring a growing population to ZPG
  like stopping a ship at sea. (i.e. not easy and
  takes a long time.)
• A population with many young people cannot stop
  growing quickly unless fertility rate falls below
  replacement rate

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Predicting the Worlds PopulationAge
Distributions
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Figure from Botkins and Keller, 2003,
Environmental Science.
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Figure from Botkins and Keller, 2003,
Environmental Science.
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• 1991 monsoon in Bangledesh caused flooding that
  killed 131,000 people
• At current rate of population growth, the dead
  were replaced within 3 weeks!

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Factors Affecting Dynamics of Human Population

• Dispersal
• Reproductive Rate
• Age Structure
• Available resources
• Income Level
• Culture Society
• Health
• Human Nature
• Can you think of others?

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From http//www.unitedglobalcitizens.jp/data/
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Earths Future