Skip to main content
Log in

Analytical conditions for the conservative form of the ecological equations

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

The analytical conditions by which a Volterra's general system describingn interacting species can be put in the “conservative” form have been examined. The cases forn=2, 3, 4 have been analyzed in detail and a general condition for any value ofn is deduced. The analytical and biological constraints following by this approach are compared to the conclusions drawn by Leigh on the ground of purely biological considerations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literature

  • Deakin, M. A. B. 1971. “Restrictions on the Applicability of Volterra's Ecological Equations.”Bull. Math. Biophys.,33, 571–577.

    MATH  Google Scholar 

  • Goel, N. S., S. C. Maitra and E. W. Montroll. 1971. “On the Volterra and other Non-Linear Models of Interacting Populations.”Rev. Mod. Phys.,43, 231–276.

    Article  MathSciNet  Google Scholar 

  • Huddleston, J. V., C. G. de Wald and N. H. Jagadesh. 1974. “A Dynamic Model of an Environmental System withn Interacting Components andp Degrees of Freedom.”Bull. Math. Biol.,36, 91–96.

    Article  MATH  Google Scholar 

  • Leigh, E. G., Jr. 1969. “Ecological Role of Volterra's Equations.” InSome Mathematical Problems in Biology, (Ed. M. Gerstenhaber). Providence: American Mathematical Society.

    Google Scholar 

  • Kerner, E. H. 1971. “Statistical-Mechanical Theories in Biology.” InAdvances in Chemical Physics, Vol. 19. (Ed. E. Prigogine and S. Rice). New York, London, Sydney, Toronto: John Wiley & Sons.

    Google Scholar 

  • Kerner, E. H. 1972.Gibbs Ensemble: Biological Ensemble. New York-London-Paris: Gordon & Breach.

    Google Scholar 

  • Rescigno, A. and I. W. Richardson. 1965. “On the Competitive Exclusion Principle.”Bull. Math. Biophys.,27, 85–89.

    MathSciNet  Google Scholar 

  • Volterra, V., 1926. “Sulle variazioni e fluttuazioni di specie animali conviventi”.Memorie della R. Accademia dei Lincei S., 6,2, 31–113.

    Google Scholar 

  • Volterra, V. 1937. “Leggi delle fluttuazioni e principii di reciprocità in biologia”.Riv. Biol. XXII Fasc. III.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Granero Porati, M.I., Porati, A. & Vecli, A. Analytical conditions for the conservative form of the ecological equations. Bltn Mathcal Biology 40, 257–264 (1978). https://doi.org/10.1007/BF02461440

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02461440

Keywords

Navigation