The World Population

Fugo Takasu
takasu@es.nara-wu.ac.jp
Department of Chemistry, Biology and Environmental Science
Nara Women’s Unviersity, Nara, Japan

25 July 2016

Trend in population growth

In the last lecture, we have calculated annual population growth rates for each country in the world.

Some country, like France, has nearly a constant annual growrh rate, while other country, like Australia, has annaul growth rate constantly decreasing:

Annual growth rate of French population estimated by a student:

1980- 1990: 0.979%
1990- 2000: 0.983%
2000- 2010: 0.987% 
 
Annual growrh rate of Australian population estimated by a student:

1980- 1990: 1.769%
1990- 2000: 1.441%
2000- 2010: 1.196%

data=CountryData["France",{"Population",{1970,2010}}]
DateListLogPlot[data,PlotMarkers->Automatic]

data=CountryData["Australia",{"Population",{1970,2010}}]
DateListLogPlot[data,PlotMarkers->Automatic]

data=CountryData["Japan",{"Population",{1970,2010}}]
DateListLogPlot[data,PlotMarkers->Automatic]

How to calculate averaged annual growth rates from 1970 to 2010

theCountry="Japan";

data1=CountryData[theCountry,{"Population",1970}]
data2=CountryData[theCountry,{"Population",1980}]
data3=CountryData[theCountry,{"Population",1990}]
data4=CountryData[theCountry,{"Population",2000}]
data5=CountryData[theCountry,{"Population",2010}]

Ratio of increase in 10 years (Positive means increase and negative decrease)

ratioIncrease1=(data2-data1)/data1//N
ratioIncrease2=(data3-data2)/data1//N
ratioIncrease3=(data4-data3)/data1//N
ratioIncrease4=(data5-data4)/data1//N

Averaged annual growth rate

(1+ratioIncrease1)^(1/10)
(1+ratioIncrease2)^(1/10)
(1+ratioIncrease3)^(1/10)
(1+ratioIncrease4)^(1/10)

Mathematical expression of the population change

Let (Subscript[N, t]) be the population size in year t. Then, the net increase in a year t, from t to t+1, is given as follows.

	ΔN = (Subscript[N, t+1]) - (Subscript[N, t]) = b (Subscript[N, t]) – d (Subscript[N, t])

where b is the birth rate (number of babies per individual) and d is probability of death per individual.

That is, 
	
	(Subscript[N, t+1])= (1 + b – d)(Subscript[N, t])

If b > d, the population increases. If b < d, the population decreases. If b and d are constant, the population size changes exponentially.

	(Subscript[N, t])=(Subscript[N, 0])(r^t)

where r = 1 + b – d.

Demographic transision

In primitive time, birth rate b was high but death rate d was also high. As a result, annual growth rate was low. Stage 1 in demographic transision.

As society developes and food supply becomes enough and medical care is improved, death rate d decreases. But the birth rate b may be kept high for a while. In this stage, the population grows rapidly because 1 + b – d can be larger than 1. Stage 2 in demographic transition.
   
As society matures, birth rate b may decline and the population growth rate decreases. Final stage in demographic transition.

Historically, many developed countries (not all) have experiences this demographic transision as society gets matured.

https : // en.wikipedia.org/wiki/Demographic_transition

Total Fertiliy Rate

Total Fertility Rate TFR is the average number of children a women has in her life. 

In monogamy, if a family (one husband and one wife) has two children, the population in total is expected to be stablized (two offspring suceed two parents who die earlier than the offspring). 

TFR that is needed for a population to be kept constant is called the replacement TFR. Replacement TFP is a little larger than two, 2.1, because some children die before they have baby.

TFR less than the replacement level of 2.1 does not necessary means that the population is decreasesing. Even with TFR less than 2.1, the population can increase in size IF there are more and more people who are in child-bearing age (like Japanese population after mid 70’s). 

https://en.wikipedia.org/wiki/Total_fertility_rate

Is there any difference in the trend between “developed” countries and “developping” countries?

a) Pick up a developed country and a developping country.
b) Calculate averaged annual growth rate of the two countries for four decades starting from 1970 to 2010. 
c) Compare averaged annual growrh rates of the developed and the developping country.
d) Explain why birth rate b declines as society is matured.
e) Explain a country’s population growth history in terms of the country’s TFR history.

dataJapan=CountryData["Japan",{"Population",{1960,2015}}]
DateListPlot[dataJapan,PlotMarkers->Automatic]

dataTFRJapan=CountryData["Japan",{"TotalFertilityRate",All}]
DateListPlot[dataTFRJapan,PlotMarkers->Automatic]

dataTFRFrance=CountryData["France",{"TotalFertilityRate",All}]
DateListPlot[{dataTFRJapan,dataTFRFrance},PlotMarkers->Automatic,PlotRange->{1,3}]

Country by country population size

Choose a country and examine its population size now and in the past.

CountryData[]