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On models for the dynamics of predator-prey interaction

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Predation in Organisms
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9.1 Abstract

A brief account of attempts at modelling the dynamics of predator-prey systems is presented. The original deterministic Lotka-Volterra model is not biologically realistic. Later workers have attempted to modify the basic features of that model to include biologically relevant parameters and to introduce the stochastic aspect into the computations. Mathematical models cannot solve a problem; only point to factors needing biologically oriented attention. The problem of formulating multi-tiered predation models is discussed in relation to myticulture.

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References

  • Bartlett MS (1957) On theoretical models for competitive and predatory biological systems. Biometrika 44: 27–42

    Google Scholar 

  • Drossel B, Higgs PG, McKane AJ (2000) The influence of predator-prey population dynamics on the long-term evolution of food web structure. Arxiv:nlen, AO/0002032, 2000: 1–40

    Google Scholar 

  • Emlen JM (1973) Ecology: an evolutionary approach. Addison-Wesley publishing Company 493 p

    Google Scholar 

  • Gause GF (1934) The struggle for existence. Williams and Wilkens, Baltimore (Translated from the Russian)

    Google Scholar 

  • Fischer-Piette E (1935) Histoire d’une moulière. Bull Biol France et Belgique 69: 153–177

    Google Scholar 

  • Hernandez-Bermejo B, Fairen V (2001). Volterra-Lapunov stability of n-dimensional conservative systems with non-linearities of arbitrary degree. Journal of Mathematical Analysis and Applications 256: 242–256

    Article  Google Scholar 

  • LeBreton J, Lubet T (1992) Résultats d’une intervention sur une parasitose à Protoeces maculatus (Trematode, Diogenea) affectant la myticulture de l’Ouest Cotentin. Société Française de Malacologie “Les Mollusques marins, biologie et aquaculture”, Ifremo, Actes de Colloques 14: 107–118

    Google Scholar 

  • Leslie PH (1958) A stochastic model for studying the properties of certain biological systems by numerical methods. Biometrika 45: 16–31

    Google Scholar 

  • Leslie PH, Gower JC (1958). The properties of a stochastic model for two competing species. Biometrika 45: 316–330

    Google Scholar 

  • Lotka AJ (1925). Elements of Mathematical Biology. Dover Publications, New York 465 p

    Google Scholar 

  • Moore HB (1958). Marine Ecology, Wiley and Sons 493 p

    Google Scholar 

  • Moran PAP (1953). The statistical analysis of the Canadian lynx cycle. I. Structure and prediction. Australian Journal of Zoology 1: 163–173

    Article  Google Scholar 

  • Pielou EC (1976) Mathematical Ecology. Wiley and Sons, New York 385 p

    Google Scholar 

  • Reyment RA (1988) A foraging model for shelled cephalopods. In Wiedmann J, Kullman J (eds) Cephalopods Present and Past (1988). Schweizerbart’sche Verlagsbuchhandlung, Stuttgart 687–203

    Google Scholar 

  • Roughgarden J (1979). Theory of Population Genetics and Evolutionary Ecology: an Introduction. MacMillan, New York 634 p

    Google Scholar 

  • Stephens DW, Krebs JR (1986) Foraging Theory. Princeton University Press, New Jersey 248 p

    Google Scholar 

  • Swift RJ (2002) A stochastic predator-prey model. Irish Mathematical Society Bulletin 48: 57–63

    Google Scholar 

  • Volterra V (1926) Variazioni e fluttuazioni del numero d’individui in specie animali conviventi. Mem R Accad Naz dei Lincei ser VI, vol. 2

    Google Scholar 

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© 2007 Springer-Verlag Berlin Heidelberg

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Reyment, R.A. (2007). On models for the dynamics of predator-prey interaction. In: Elewa, A.M.T. (eds) Predation in Organisms. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46046-6_9

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