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The Theory of Population Dynamics: Back to First Principles

  • Lev R. Ginzburg
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 71)

Abstract

Models of population dynamics are based on the population size as the complete descriptor of the dynamic state. We can write this central assumption of traditional theory as follows:
$$\frac{1}{N}\frac{{dN}}{{dt}} = f(E)$$
where N is the population size; \(\frac{1}{N}\frac{{dN}}{{dt}}\) is the relative growth rate (average number of surviving offspring per parent per unit of time); f (E) is a function of the environment with the understanding that population size itself might be one of the environmental parameters.

Keywords

Equilibrium Ratio Initial Growth Rate Malthusian Parameter Relative Equilibrium Position Balance Exponential Growth 
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.

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References

  1. Clark, G.P. 1971. The Second Derivative in Population Modelling. Ecology, 52:606–613.CrossRefGoogle Scholar
  2. Gause, G.F. 1934. The Struggle for Existence. Hafner Publishing Co., New York.CrossRefGoogle Scholar
  3. Ginzburg, L.R. 1972. The Analysis of the “Free Motion” and “Force” Concepts in Population Theory. In. Coll. “Studies in Theoretical Genetics”, V.A. Ratner, ed., Novosibirsk (in Russian).Google Scholar
  4. Ginzburg, L.R. 1980. Ecological Implications of Natural Selection. Proceedings of the Vito Volterra Symposium on Mathematical Models in Biology, 1979. Lecture Notes in Biomathematics, V. 39, Springer-Verlag.Google Scholar
  5. Ginzburg, L.R. 1982. Theory of Natural Selection and Population Growth. Benjamin/Cummings Publishing Company, Menlo Park, California.Google Scholar
  6. Hutchinson, G.E. 1975. Variation on a theme by Robert MacArthur. In. Coll. “Ecology and Evolution of Communities”, pp. 492–521, Harvard University Press. Cambridge, Massachusetts.Google Scholar
  7. Innis, G. 1972. The Second Derivative and Population Modelling: Another View. Ecology, 53:720–723.CrossRefGoogle Scholar
  8. Sugihara, G, 1984. Graph Theory, Homology and Food Webs, Proceedings of Symposia in Applied Mathematics, Vol. 30, pp. 83–101.MathSciNetGoogle Scholar
  9. Tsuchiya, H.M., J.F. Drake, J.L. Jost and A.G. Fredrickson. 1972. Predator-Prey Interactions of Dictyostelium discoideum and Escherichia coli in Continuous Culture, Journal of Bacteriology, Vol. 110, pp. 1147–1153.Google Scholar
  10. Yee, J. 1980. A. Nonlinear, Second-Order Population Model. Theoretical Population Biology, 18:175–191.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Lev R. Ginzburg
    • 1
  1. 1.Department of Ecology & EvolutionState University of New York at Stony BrookStony BrookUSA

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