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Demography

The demographic model �. Analysis of population pyramids. �Critical analysis of the data. �World population, history and present.

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The demographic model

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Important. Population dynamics

Demographic models can distinguish the population by age groups to obtain more accurate forecasts. As a first approximation, only women are considered.

  • The number of newborns in the following year will be the sum of the number of women in the current year in each age group multiplied by their corresponding reproduction rate .
  • The population of an age group in the following year will be the population of the previous age group in the current year multiplied by the survival rate of that age.

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Important. Population dynamics

  • The following data is currently available:
    • The number of women in each age group,
    • Survival rates,
    • Reproduction rates.
  • For the next moment:
    • The number of women in the first age group (newborns) at the next instant is the sum of the number of women in each age group at present times their reproduction rate,
      • In other words, the number of newborns at the next instant will be equal to: the number of women in the first group times the reproduction rate of the first group, plus the number of women in the second group times the reproduction rate of the second group, plus the number of women in the third group times the reproduction rate of the third group, plus those in the fourth group times their reproduction rate, plus those in the fifth group times their reproduction rate, etc.
    • The number of women in the second age group at the next instant is the number of women in the first age group at the present times the survival rate of the first age group.
    • The number of women in the third age group at the next instant is the number of women in the second age group at the present times the survival rate of the second age group.
    • The number of women in the fourth age group at the next instant is the number of women in the third age group at the present times the survival rate of the third age group.
    • The number of women in the fifth age group at the next instant is the number of women in the fourth age group at the present times the survival rate of the fourth age group.
    • Etc.
  • Once we have calculated all the age groups at the next instant, we can do the same to calculate the following instant; and, once this has been calculated, for the instant that follows that one; and so on.

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Survival and reproduction rates (women only), Spain 1963.

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Population dynamics

The evolution of a population on a hypothetical island is studied, where one million women aged 30 to 34 are introduced at the initial time. Reproduction and survival rates are those of the Spanish population in 1963. After 250 years, at the end of the graph, the initial one million women would have more than nine million descendants.

We used a variant of the Lexis diagram . Horizontally, we represent time (in five-year increments), vertically, the age group, and the color encodes the population size according to the sidebar. The graph is pixelated because time, in our case, is a discrete quantity.

Double-clicking on the spreadsheet allows you to modify survival and reproduction rates, as well as the incorporated population.

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Important. Long-term population dynamics; stationary population

The stationary population is the population pyramid structure that corresponds to long-term evolution, if survival and reproduction rates remain constant.

  • The pyramid shown in red represents the survival and reproduction rates of the Spanish population (women only) in 1963. This population has a growth factor of 1.047 per five-year period, which is equivalent to an annual growth rate of 0.92%. This population would double every 75 years.
  • The population pyramid shown in green would show the population if reproduction rates were divided by 1,346. The population would remain in a steady state.
  • The pyramid in blue shows what it would look like if reproduction rates were halved, resulting in a five-year factor of 0.941, which corresponds to an annual growth rate of -1.2%, meaning the population would be halved every 34 years.

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Optional. Long-term population dynamics; reproductive value

Reproductive value is proportional to the number of offspring a woman will have in the long term, based on the daughters she will have, not the daughters she has already had. That's why women aged 50 and over have a reproductive value of 0.

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Optional. Leslie Matrices

in Leslie matrices . The reproduction rate corresponding to age i is r i . The survival rate corresponding to age i is s i . For a population with 6 ages we have

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PH Leslie, On the Use of Matrices in Certain Population Mathematics, Biometrika , Vol. 33, No. 3 (Nov., 1945), pp. 183-212 http://www.jstor.org/stable/2332297

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Analysis of population pyramids

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Real population pyramid. Spain 1963

https://datosmacro.expansion.com/demografia/estructura-poblacion/espana

Civil War, 1936-1939

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Real population pyramid. Spain 2022

To see the evolution in recent years, consult https://www.ine.es/covid/piramides.htm

At https://www.populationpyramid.net/spain/ you can consult the pyramids from 1950 onwards, with forecasts up to 2100

The pyramids from 1900 to 2010 can be found at https://www.youtube.com/watch?v=LAHQLoCdjgo .

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Real population pyramid. Spain, 1950 to 2015

https://es.wikipedia.org/wiki/Demograf%C3%ADa_de_Espa%C3%B1a

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Real population pyramid. Spain, 2002 to 2021

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

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Demographics of the USSR

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

World War II (1939-1945)

Stalin's collectivization (1929-)

Civil War (1918-1920), War Communism (1918-1921)

World War I (1914-1918)

World War II (1939-1945)

Stalin's collectivization (1929-)

Civil War (1918-1920), War Communism (1918-1921)

World War I (1914-1918)

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Demographics of Germany

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

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China

Liu Suinian , Wu Qungan and others,

A Brief History of China's Socialist Economy (1949-1984 ), page 484.

Beijing Informa, 1987, People's Republic of China

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Censuses in China

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

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Critical analysis of the data

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Data?

El País: The Carlos III Health Institute underestimates deaths in the second wave https://elpais.com/sociedad/2020-10-20/el-instituto-de-salud-carlos-iii-subestima-las-muertes-de-la-segunda-ola.html

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Data?

“ The Soviet census of January 6, 1937, was a particularly controversial census of the Union of Soviet Socialist Republics. Although it showed population growth compared to the 1926 census, from 147 million to 162 million, its detailed results were not published and its organizers were sent to Gulag forced labor camps, accused of being “saboteurs,” because the count yielded significantly lower population figures than previously anticipated, leading some historians and demographers to later attempt to estimate the number of victims of Stalin’s Great Purge.”

https://es.wikipedia.org/wiki/Censo_sovi%C3%A9tico_de_1937

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Data?

  • Official Chinese data on the web today: http://www.stats.gov.cn/sj/ndsj/2020/indexeh.htm . Five-year data from 1952 to 1970, annual data for the rest (Why?).

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  • The official data for the 1987 publications are annual from 1949 to 1984.

Liu Suinian , Wu Qungan and others, A Short History of China's Socialist Economy (1949-1984) , page 484.

Beijing Informa, 1987, People's Republic of China

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World population, history and present

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Population

https://ourworldindata.org/world-population-growth

(Billions in English and Russian = billions, rest = 1,000,000,000 https://es.wikipedia.org/wiki/Millardo )

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Growth for some countries

https://ourworldindata.org/population-growth

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World population

https://ourworldindata.org/population-growth

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Estimation of population evolution

https://ourworldindata.org/region-population-2100

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Life expectancy throughout history

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Wikipedia (various sources), https://es.wikipedia.org/wiki/Esperanza_de_vida

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Eras

Average life expectancy at birth �(years)

Comment

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Life expectancy at age 15 was estimated to be 54 years. 5 ​6 ​7

26

 

25-28

According to data from the Agora of Athens and Corinth , the total life expectancy at age 15 would be between 37 and 41 years.

22-28

 

25-35

It is estimated that the average life expectancy was probably between 25 and 35 years.

35+

It is said that the average lifespan of the elites was between 55–80 years in the Middle East 12 ​13​ and between 65–75 in Al-Andalus . 14

Great Britain in the 13th century ( Middle Ages ) 15

31

The average life expectancy of a child born in the United Kingdom was 31; however, if they reached 20, they could expect to live to 45, and if they reached 30, they had a good chance of reaching 50.

India from 1871 to 1925 16

23-27

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19th Century

28-32

 

50-65

Life expectancy is increasing thanks to reforms and the widespread adoption of healthcare and hygiene in society as a whole.

Part of the 20th century and the beginning of the 21st century 17

52-69

World life expectancy from 1960 to 2008.

Current world average 17 ​18

70-73

Global life expectancy from 2009 to the 2020s.

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Life expectancy, UN 2019

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

Years a newborn can expect to live if the age-specific mortality patterns prevailing at the time of their birth were to remain the same throughout their life.

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Birth rate, 2023

CIA World Factbook – Wikipedia, https://en.wikipedia.org/wiki/Birth_rate

Number of live births in a population per thousand inhabitants in a year

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Population density (2020)

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Center for International Earth – Wikipedia, https://es.wikipedia.org/wiki/Poblaci%C3%B3n_mundial

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The demographic transition

https://ourworldindata.org/demographic-transition

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Population pyramid

https://ourworldindata.org/population-growth

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Optional. References

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