On the momentum of population growth

Abstract

If age-specific birth rates drop immediately to the level of bare replacement the ultimate stationary number of a population will be given by (9):

$$\left( {{\textstyle{{b\mathop e\limits^ \bullet {}_0} \over {r\mu }}}} \right)\left( {\frac{{R_0 - 1}}{{R_0 }}} \right)$$

multiplied by the present number, where b is the birth rate, r the rate of increase, \(\mathop e\limits^ \bullet _0 \) the expectation of life, and R 0 the Net Reproduction Rate, all before the drop in fertility, and μ the mean age of childbearing afterwards. This expression is derived in the first place for females on the stable assumption; extension to both sexes is provided, and comparison with real populations shows the numerical error to be small where fertility has not yet started to drop. The result (9) tells how the lower limit of the ultimate population depends on parameters of the existing population, and for values typical of underdeveloped countries works out to about 1. 6. If a delay of 15 years occurs before the drop of the birth rate to replacement the population will multiply by over 2. 5 before attaining stationarity. The ultimate population actually reached will be higher insofar as death rates continue to improve. If stability cannot be assumed the ultimate stationary population is provided by the more general expression (7), which is still easier to calculate than a detailed projection.

This is a preview of subscription content, access via your institution.

References

  1. Bourgeois-Pichat, J. 1968. The Concept of a Stable Population: Application to the Study of Populations of Countries with Incomplete Demographic Statistics. Population Studies, No. 39, ST/SOA/Series A/39. New York: United Nations. Original version in French dated 1966.

    Google Scholar 

  2. —. 1970. Un taux d’accroissement nul pour les pays en voie de développement en l’an 2000—rêve ou réalité? Population 25: 957–974.

    Article  Google Scholar 

  3. Frejka, Tomas. 1968. Reflections on the demographic conditions needed to establish a U. S. stationary population growth. Population Studies 22: 379–397.

    Article  Google Scholar 

  4. Keyfitz, N. 1968. Introduction to the Mathematics of Population. Reading, Mass.: Addison-Wesley.

    Google Scholar 

  5. —. 1969. Age distribution and the stable equivalent. Demography 6:261–269.

    Article  Google Scholar 

  6. Leslie, P. H. 1945. On the use of matrices in certain population mathematics. Biometrika 33:183–212.

    Article  Google Scholar 

  7. Lotka, A. J. 1939. Théorie analytique des associations biologiques. Part II. Analyse démographique avec application particulière à I’espèce humaine (Actualités Scientifiques et Industrielles, No. 780). Paris: Hermann & Cie.

    Google Scholar 

  8. Ryder, N. B. 1970. Letter of August 12.

  9. Vincent, P. 1945. Potentiel d’accroissement d’une population stable. Journal de la Société de Statistique de Paris 86:16–29.

    Google Scholar 

  10. Whelpton, P. K. 1936. An empirical method of calculating future population. Journal of the American Statistical Association 31:457–473.

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Keyfitz, N. On the momentum of population growth. Demography 8, 71–80 (1971). https://doi.org/10.2307/2060339

Download citation

Keywords

  • Underdeveloped Country
  • Matical Curve
  • Girl Child
  • Stable Assumption
  • Fixed Regime