In 1838 the Belgian mathematician Verhulst introduced the logistic equation, which is a kind of generalization of the equation for exponential growth but with a maximum value for the population. He used data from several countries, in particular Belgium, to estimate the unknown parameters. The work of Verhulst was rediscovered only in the 1920s.


Logistic Equation Geometric Progression Royal Academy Maximum Population Imate Equation 
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Further reading

  1. 1.
    Lloyd, P.J.: American, German and British antecedents to Pearl and Reed’s logistic curve. Pop. Stud. 21, 99–108 (1967) CrossRefGoogle Scholar
  2. 2.
    McKendrick, A.G., Kesava Pai, M.: The rate of multiplication of micro-organisms: A mathematical study. Proc. R. Soc. Edinb. 31, 649–655 (1911) Google Scholar
  3. 3.
    Pearl, R.: The Biology of Death. Lippincott, Philadelphia (1922). Google Scholar
  4. 4.
    Pearl, R., Reed, L.J.: On the rate of growth of the population of the United States since 1790 and its mathematical representation. Proc. Natl. Acad. Sci. 6, 275–288 (1920). CrossRefGoogle Scholar
  5. 5.
    Quetelet, A.: Sur l’homme et le développement de ses facultés. Bachelier, Paris (1835). Google Scholar
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    Quetelet, A.: Pierre-François Verhulst. Annu. Acad. R. Sci. Lett. B.-Arts Belg. 16, 97–124 (1850). Google Scholar
  7. 7.
    Quetelet, A.: Sciences mathématiques et physiques au commencement du xix ième siècle. Mucquardt, Bruxelles (1867). Google Scholar
  8. 8.
    Robertson, T.B.: On the normal rate of growth of an individual and its biochemical significance. Arch. Entwicklungsmechanik Org. 25, 581–614 (1908) CrossRefGoogle Scholar
  9. 9.
    Verhulst, P.-F.: Notice sur la loi que la population poursuit dans son accroissement. Corresp. Math. Phys. 10, 113–121 (1838). Google Scholar
  10. 10.
    Verhulst, P.-F.: Recherches mathématiques sur la loi d’accroissement de la population. Nouv. Mém. Acad. R. Sci. B.-lett. Brux. 18, 1–45 (1845). Google Scholar
  11. 11.
    Verhulst, P.-F.: Deuxième mémoire sur la loi d’accroissement de la population. Mém. Acad. R. Sci. Lett. B.-Arts Belg. 20, 142–173 (1847). Google Scholar

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© Springer-Verlag London Limited 2011

Authors and Affiliations

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

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