The History of Theoretical Population Ecology: Which Role for Mathematical Modeling?

  • Luciano Andreozzi


The use of mathematics in biology has always been controversial. At variance with economics, which became a formalized discipline quite early in its development, biologists had always been suspicious about the use of formal models in their field. During the now long history of bio-mathematics, supporters of this approach have devised quite a large number of arguments to persuade skeptics that the marriage between mathematics and biology was a good deal for both disciplines. Beside the obvious reason that formal models lead, hopefully, to quantitative predictions that are easier to falsify, mathematical’ models have been frequently defended because of their (alleged) heuristic value. According to this view, mathematical models’ most important contribution to biology consists in their ability to highlight some phenomena, or some relationships among phenomena, that could not be understood without formalization, A very clear defense of this point of view is to be found in one of the early classics of mathematical population ecology, Vito Volterra’s “Variazioni e fluttuazioni del numero d’individui in specie animali conviventi”, first published in 1926.


Competitive Exclusion Population Ecology Ordinary Language Theoretical Ecology Snowshoe Hare 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Vito Volterra, Variazioni e fluttuazioni del numero d’individui in specie animali conviventi, Memorie del Regio Comitato Talassografico Italiano, CXXXI (1927), English trans, in F. M. Scudo and J. R. Ziegler, The Golden Age of Theoretical Ecology; 1923-1940, Spring Verlag, Berlin (1978).Google Scholar
  2. 2.
    Vito Voiterra and Umberto D'Ancona, Les associations biologiques au point de vue mathématique, Hermann, Paris (1935).Google Scholar
  3. 3.
    Karl Sigmund, Games of Life: Explorations in Ecology, Evolution and Behaviour, Oxford University Press, Oxford (1993), 2nd edition Penguin Books (1996).Google Scholar
  4. 4.
    Luciano Andreozzi, Vito Volterra and Umberto D'Ancona on the effects of fishing in the Upper Adriatic Sea and their mathematical representation. Reflections on a celebrated episode in the history of population ecology, forthcoming on Sciences. et Techniques en Perspective.Google Scholar
  5. 5.
    John Maynard Smith, Evolution and the Theory of Games, Cambridge University Press, Cambridge (19S2).Google Scholar
  6. 6.
    Ernst Mayr, The Growth of Biological Thought, Harvard University Press, Cambridge (Mass.) (1982).Google Scholar
  7. 7.
    Ernst Mayr, Where are We. Genetics and Twentieth Century Darwinism, Cold Spring Harbor Symposia on Quantitative Biology, 24: 1–14 (1959).CrossRefGoogle Scholar
  8. 8.
    Ernst Mayr, Evolution and the Diverisy of Life, Belknap Press, Cambridge (Mass.) and London (1976).Google Scholar
  9. 9.
    C. H. Waddington, Epigenetics and evolution, in Symposia of the Society of Experimental Biology, 7, Academic Press, New York (1953).Google Scholar
  10. 10.
    William B. Provine, Mole of mathematical population geneticists in the evolutionary synthesis of the 1930’s and 40’s, in L. Solomon, Mathematical Models in Biological Discovery, Lecture notes in Biomathematics, Springer-Verlag, Berlin Heidelberg (1977).Google Scholar
  11. 11.
    Francesco M. Scudo and James R. Ziegler, The Golden Age of Theoretical Ecology: 1923–1940, Springer Verlag, Berlin (1978).CrossRefGoogle Scholar
  12. 12.
    Sharon E. Kingsland, Modeling Mature, Episodes in the History of Population Ecology, The University of Chicago Press, Chicago-London (1985).Google Scholar
  13. 13.
    Sharon E. Kingsland, Mathematical figments, biological facts: population ecology in the thirties, Journal of the History of Biology, 19; 235–256 (1985).CrossRefGoogle Scholar
  14. 14.
    Ana Milan Gasca, Volterra’s biomathematics and biologists’ biological facts, Hist. St. in the Phys. and Biolog. Sc., 26:347–403 (1996).MathSciNetGoogle Scholar
  15. 15.
    Francesco M. Scudo, The 'golden age of theoretical ecology': a conceptual appraisal, Rev. Euro, des Sc. Soc, 22, 67 (1986).Google Scholar
  16. 16.
    Herbert Andrewartha, The use of conceptual models in population ecology, Cold Spr. Harbor Symp. on Quant. Biol, 22: 219–236 (1957).CrossRefGoogle Scholar
  17. 17.
    Luciano Andreozzi, Vito Volterra organizzatore scientifico e la nascita della biologia matematica in Italia, forthcoming on Nuncius.Google Scholar
  18. 18.
    Alfred Lotka, Analytical note on certain rhythmic relations in organic systems, Proc. of the Nat. Acad. of Sc. , 6 (1920).Google Scholar
  19. 19.
    Alfred Lotka, Elements of physical biology, Williams and Wilkins, Baltimore (1925)MATHGoogle Scholar
  20. A.Lotka, republished as Elements of Mathematical Biology, Dover, New York (1956).MATHGoogle Scholar
  21. 20.
    Umberto D'Ancona, La lotta per I’esistenza, Einaudi, Torino (1942).Google Scholar
  22. 21.
    Umberto D'Ancona, The Struggle for Existence, Engl. transl. by A. Charles and R.F. Withers, Bibliotheca Biotheoretica, Leiden (1954).Google Scholar
  23. 22.
    George Evelyn Hutchinson, An Introduction to Population Ecology, Yale University Press, New Haven and London (1978).MATHGoogle Scholar
  24. 23.
    Charles S. Elton, Periodic fluctuations in the number of animals, their causes and effects, Brit. J. of Exper. Biol., II (1924).Google Scholar
  25. 24.
    Charles S. Elton, Animal Eecology, Sidgwik and Jacson, London (1927), 2nd enlarged edition New York, MacMillan (1935).Google Scholar
  26. 25.
    Charles S. Elton and Mary Nicholson, The ten-year cycle in numbers of the lynx in Canada, J. of Anim. Ecol, XI (1942), pp. 215–244.CrossRefGoogle Scholar
  27. 26.
    Volterra Archive, letters from Elton to Volterra, letter number 1.Google Scholar
  28. 27.
    Umberto D'Ancona, Dell’influenza della stasi peschereccia del periodo 1914-18 sul patrimonio ittico dell’Alto Adriatico, Memorie del Regio Comitato Talassografico Italiano, CXXVI (1926).Google Scholar
  29. 28.
    Antonio Berlese, Considerazioni sui rapporti tra piante, loro insetti nemici e cause nemiche di questi, Redia, IV (1906).Google Scholar
  30. 29.
    Lorenzo Camerano, Dell’equilibrio dei viventi mercé la reciproca distruzione, Atti della Regia Accademia delle Scienze di Torino, XV (1880).Google Scholar
  31. 30.
    Joel E. Cohen, Lorenzo Camerano's contribution to early food web theory, in Frontiers of Theoretical Biology. Lecture Notes in Biomathematics, 100, Simon A. Levin (ed.), Springer-Verlag, New York (1994): 351–359.Google Scholar
  32. 31.
    Pascal Acot and Jean-Marc Drouin, L'introduction en France des idées de I’écologie scientifique américaine dans I’entre-deux-guerres, Rev. d'Histoire des Sci., 50,4: 461–479 (1997).CrossRefGoogle Scholar
  33. 32.
    William R. Thompson, Biological control and the theories of the interactions of populations, Parasitology, XXXI: 301–388 (1939).Google Scholar
  34. 33.
    Leland O. Howard, A study of insect parasitism, U.S. Department of Agricolture, Division of Entomology, Techincal Series no. 5 (1897): pp. 5–57.Google Scholar
  35. 34.
    Paul Marchal, L’équilibre numérique des espéces et ses relations avec les parasites chez les insects, Comp. Rend. Soc. Biol., XLIX, 49: p. 129 (1897).Google Scholar
  36. 35.
    Paul Marchal, The utilization of auxiliary entomophagous insects in the struggle against insects injurious to agricolture, Pop. Sc. Montly, 72: 352–70,406-419 (1908).Google Scholar
  37. 36.
    Richard M. Goodwin, Essays in Economic Dynamics, The Macmillan Press, London (1982).Google Scholar
  38. 37.
    Thomas R. Malthus, An Essay on the Principle of Population, edited by Patricia James, Cambridge University Press, Cambridge (1989), first published in 1803.Google Scholar
  39. 38.
    Paul De Bach and Harry S. Smith, Are Population Oscillations Inherent in the Host-Parasite Relation?, Ecology, XXII (1941): 363–369.CrossRefGoogle Scholar
  40. 39.
    Georgii Frantsevich Gause, The Struggle for Existence, Williams and Wilkins, Baltimore (1934), reprint New York, Dover (1971).CrossRefGoogle Scholar
  41. 40.
    Georgii Frantsevich Gause, Verifications Expérimentales de la Théorie Mathématique de la Lutte Pour la Vie, Hermann, Paris (1935).Google Scholar
  42. 41.
    Michael E. Gilpin, Do hares eat lynx?, Amer. Naturist, 107 (1973).Google Scholar
  43. 42.
    E. Leigh, The ecological role of Volterra's equations, in M. Gerstenhaber, (ed.) Some Mathematical Problems in Biology, The American Mathematical Society, Providence (1968).Google Scholar
  44. 43.
    Jordi Bascompte, Ricard V. Solé, Norbert Martinez, Population cycles and spatial patterns in snowshoe hares: an individual-oriented simulation, J. of Theor. Biol, 187: 213–222 (1987).CrossRefGoogle Scholar
  45. 44.
    E.C. Pielou, The usefulness of ecological models: a sotck-taking, The Quart. Rev. of Biol, 56 (1981).Google Scholar
  46. 45.
    A.R. Sinclair, J.M. Gosline, J.M. Krebs, C.J. Boutin, S. Smith, R. Boonstra, Can the solar cycle and climate syncronize the snowshoe hare cycle in Canada?, Amer. Naturalist, 141: 173–198 (1993).CrossRefGoogle Scholar
  47. 46.
    Charles Darwin, On the Origin of the Species, in The Works of Charles Darwin, edited by Paul H. Barrett and R. B. Freeman, William Pichering, London (1988), vol. 15 (first published in 1859).Google Scholar
  48. 47.
    Giorgio Israel, La Mathématization du Réel Essai sur la Modélisation Mathématique, Editions du Seuil, Paris (1996).Google Scholar
  49. 48.
    Garrett Hardin, The competitive exclusion principle, Science, 131 (1960).Google Scholar
  50. 49.
    P. A. Riley, The origin of the principle of competitive exclusion: was Darwin influenced by Sismondi?, Linnean, 2 (3): 20–22(1986).Google Scholar
  51. 50.
    Andrei N. Kolmogoroff, Sulla teoria di Volterra della lotta per I’esistenza, Giornale Istit. Ital Attuari, 1 (1936).Google Scholar
  52. 51.
    Vladimir A. Kostitzin, Sur les solutions asymptotiques d'équations différentielles biologiques, Compt. Rendus de I'Académ. des Sc, 203: 1124–1126 (1936).Google Scholar
  53. 52.
    Robert May, On relationships among various types of population models, Amer. Natur., 107: 46–57 (1973).CrossRefGoogle Scholar
  54. 53.
    Alfred Lotka, The growth of mixed populations: two species competing for a common food supply, J. of the Wash. Ac. of Sc, 22 (1932).Google Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Luciano Andreozzi
    • 1
  1. 1.Università degli Studi di BariBariItalia

Personalised recommendations