Additional Laboratory Notes for BIO 2020

© 20 April 2004, Mary Jean Holland

Population Dynamics

Use the data provided in the table below to calculate the annual rate of population increase and the doubling time for the populations listed (assuming no migration in or out). These data are for 1998 (published by the United Nations Development Program)

Country Per Capita GDP ($ US) Total Fertility Rate Crude Birth Rate Crude Death Rate Annual Rate of Pop. Change (%) Doubling Time (years)
Argentina 8,030 2.6 19.9 7.9    
Bolivia 800 4.4 33.2 9.1    
Japan 39,640 1.5 10.3 8.2    
Thailand 2740 1.7 16.7 6.6    
Korea 9,700 1.7 15.0 6.4    
India 340 3.1 25.2 9.0    
Switzerland 40,630 1.5 10.9 9.1    
The Netherlands 24,000 1.6 11.9 8.8    
Italy 19,020 1.2 9.1 9.9    
Uganda 240 7.1 51.1 21.0    
Egypt 790 3.4 26.1 7.1    
Mexico 3,320 2.8 24.6 5.1    
Canada 19,380 1.6 11.9 7.4    
United States 26,980 2.0 13.8 8.7    

Remember that:

Annual Rate of Population Change (%) = 100 (Change in Pop/Total Pop)
Crude Birth Rate (CBR) = Annual number. of live births per 1000 population
Crude Death Rate (CDR) = Annual number. of deaths per 1000 population
Ignoring Migration (Immigration and Emigration) then
     Annual Rate of Population Change (%) = (CBR - CDR)/10

Doubling Time (Years) = 70/ Percent Annual Rate of Population Change (Why?)

N(t) = number in pop at time t
N0 = number in pop at starting time
r = annual rate of pop growth (as a decimal fraction, not as a percent)
then: N(t) = N0 ert
and N(t)/N0 = e-rt
When population has doubled, N(t)/ N0 = 2 = ert
and ln (2) = rt
t = ln(2)/r
t = 0.693/r

Answer the following questions using the table on the preceding page and the definitions on the next page.

1. Is there a relationship between the total fertility rate (TFR) and the per capita GDP?

2. Which countries have a TFR below replacement?

3. In general, which demographic statistic show the greatest variation, CBR or CDR? Explain your answer.

4. From looking at the crude birth and death rates can you estimate which countries are just beginning the demographic transition? Name at least one.

5. From looking at the crude birth and death rates can you estimate which countries have completed the demographic transition? Name at least one.

6. Which country is experiencing negative population growth?


  • Crude Birth Rate (CBR) - annual number of live births per 1000 people in a given area.
  • Crude Death Rate (CDR) - annual number of deaths per 1000 people in a given area.
  • Annual Population Change* = (# of Births ) - (# of Deaths)
  • Annual Population Growth Rate (%) = (Annual Pop Change / total population) x 100
  • Zero Population Growth (ZPG)—the birth rate (plus immigration) equals the death rate (plus emigration) so that the population in a given area is neither increasing or decreasing
  • Total Fertility Rate (TFR)—estimate of the average number of children (live births) that a woman will have if she conforms to prevailing age-specific fertility rates in her geographical area.
  • Replacement Level Fertility—number of children (live births) a woman must have to replace herself and her partner in her geographic area. In an area with goo public health, replacement level fertility is about 2.1. In an area where many people die before reproductive age, replacement fertility is higher, perhaps as high as 2.6
  • Infant Mortality Rate—number of babies who die before 1 year of age per 1000 live births
  • Child Mortality Rate—number of children who die before 5 years of age per 1000 live births
  • Life Expectancy (at birth)—the average number of years that a newborn baby is expected to live if the age-specific mortality rates effective at the time of birth apply throughout his or her lifetime.

* If changes in population due to migration are included then: Annual Population Change = (Births + Immigration) - (Deaths + Emigration)

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Last updated 20 April 2004 (MJCH/JHW)