Lotka and stable population theory (1907–1911)


In 1907 the American chemist Alfred Lotka started to study the relation between birth rate, age-specific death rates and the rate of population growth using a continuous-time model. In 1911 he published another article on the same subject with F.R. Sharpe, which also included age-specific fertility rates. The implicit equation giving the population growth rate is often called “Lotka’s equation”.


Implicit Equation Life Insurance Company Male Birth Male Birth Rate Metropolitan Life Insurance 
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Further reading

  1. 1.
    Crump, K.S., Mode, C.J.: A general age-dependent branching process. J. Math. Anal. Appl. 24, 494–508 (1968) MATHCrossRefGoogle Scholar
  2. 2.
    Dublin, L.I., Lotka, A.J.: On the true rate of natural increase. J. Amer. Stat. Assoc. 20, 305–339 (1925) CrossRefGoogle Scholar
  3. 3.
    Feller, W.: On the integral equation of renewal theory. Ann. Math. Stat. 12, 243–267 (1941). projecteuclid.org MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Fisher, R.A.: The actuarial treatment of official birth records. Eugen. Rev. 19, 103–108 (1927). digital.library.adelaide.edu.au Google Scholar
  5. 5.
    Gridgeman, N.T.: Lotka, Afred James. In: Gillespie, C.C. (ed.) Dictionary of Scientific Biography, vol. 8, p. 512. Scribner, New York (1981) Google Scholar
  6. 6.
    Kingsland, S.E.: Modeling Nature, Episodes in the History of Population Ecology, 2nd edn. University of Chicago Press (1995). books.google.com
  7. 7.
    Lotka, A.J.: Relation between birth rates and death rates. Science 26, 21–22 (1907) Reprinted in Smith & Keyfitz (1977) CrossRefGoogle Scholar
  8. 8.
    Lotka, A.J.: Théorie analytique des associations biologiques, 2ième partie. Hermann, Paris (1939) English translation: Analytical Theory of Biological Populations. Plenum Press, New York (1998). books.google.com
  9. 9.
    Sharpe, F.R., Lotka, A.J.: A problem in age-distribution. Philos. Mag. Ser. 6, 21, 435–438 (1911) Reprinted in Smith & Keyfitz (1977) CrossRefGoogle Scholar
  10. 10.
    Smith, D.P., Keyfitz, N.: Mathematical Demography, Selected Papers. Springer, Berlin (1977) MATHGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.IRD (Institut de Recherche pour le Développement)BondyFrance

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