Lotka, Volterra and the predator–prey system (1920–1926)


In 1920 Alfred Lotka studied a predator–prey model and showed that the populations could oscillate permanently. He developed this study in his 1925 book Elements of Physical Biology. In 1926 the Italian mathematician Vito Volterra happened to become interested in the same model to answer a question raised by the biologist Umberto d’Ancona: why were there more predator fish caught by the fishermen in the Adriatic Sea during the First World War, when the fishing effort was low?


Prey Model Prey System Analytical Note Simple Pendulum Italian National Research Council 
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Further reading

  1. 1.
    Goodstein, J.R.: The Volterra Chronicles, The Life and Times of an Extraordinary Mathematician 1860–1940. American Mathematical Society (2007). books.google.com
  2. 2.
    Guerraggio, A., Nastasi, P.: Italian Mathematics between the Two World Wars. Birkhäuser, Basel (2005). books.google.com MATHGoogle Scholar
  3. 3.
    Israel, G., Gasca, A.M.: The Biology of Numbers – The Correspondence of Vito Volterra on Mathematical Biology. Birkhäuser, Basel (2002) MATHGoogle Scholar
  4. 4.
    Kingsland, S.E.: Modeling Nature, Episodes in the History of Population Ecology, 2nd edn. University of Chicago Press (1995). books.google.com
  5. 5.
    Lotka, A.J.: Analytical note on certain rhythmic relations in organic systems. Proc. Natl. Acad. Sci. 6, 410–415 (1920). www.pnas.org CrossRefGoogle Scholar
  6. 6.
    Lotka, A.J.: Undamped oscillations derived from the law of mass action. J. Amer. Chem. Soc. 42, 1595–1599 (1920). www.archive.org CrossRefGoogle Scholar
  7. 7.
    Lotka, A.J.: Elements of Physical Biology. Williams & Wilkins, Baltimore (1925). www.archive.org MATHGoogle Scholar
  8. 8.
    Volterra, V.: Variazioni e fluttuazioni del numero d’individui in specie animali conviventi. Mem. Accad. Lincei 6, 31–113 (1926) Reprinted in: Opere matematiche, vol. 5, Accademia nazionale dei Lincei, Roma (1962) Google Scholar
  9. 9.
    Volterra, V.: Fluctuations in the abundance of a species considered mathematically. Nature 118, 558–560 (1926). Reprinted in L.A. Real, J.H. Brown (eds.) Foundations of Ecology, pp. 283–285. University of Chicago Press (1991) MATHCrossRefGoogle Scholar
  10. 10.
    Volterra, V.: Leçons sur la Théorie Mathématique de la Lutte pour la Vie. Gauthier-Villars, Paris (1931) Google Scholar
  11. 11.
    Volterra, V., D’Ancona, U.: Les Associations Biologiques au Point de Vue Mathématique. Hermann, Paris (1935) Google Scholar
  12. 12.
    Whittaker, E.T.: Vito Volterra 1860–1940. Obit. Not. Fellows R. Soc. 3, 690–729 (1941) CrossRefMathSciNetGoogle 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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