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Part of the book series: Mathematical Modelling ((MMO,volume 6))

Abstract

In a constant environment, evolutionary process should result in evolutionarily stable strategies for the creatures which ultimately survive to inhabit that environment. It is shown here that by adding a strategy dynamic to a previously developed theory, one not only obtains a convenient way of determining evolutionarily stable strategies, but interesting features about the process itself can be observed. Of particular interest, as demonstrated here, progression to evolution arily stable strategies can take place even when the population densities are experiencing chaotic motion.

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References

  1. Brown, J.S. and T.L. Vincent. 1987a. A theory for the evolutionary game. Theoretical Population Biology 31, pp. 140–166.

    Article  MathSciNet  MATH  Google Scholar 

  2. Brown J.S. and T.L. Vincent. 1987b. Predator-prey coevolution as an evolutionary game. Lecture Notes in Biomathematics Vol 73, pp. 83–101.

    MathSciNet  Google Scholar 

  3. Case, T.J. 1982. Coevolution in resource-limited competition communities, Theoretical Population Biology 21, pp. 69–91.

    Article  MathSciNet  MATH  Google Scholar 

  4. Hines, W.G.S. 1987. Evolutionary stable strategies: A review of basic theory, Theoretical Population Biology 31, pp. 195–272.

    Article  MathSciNet  MATH  Google Scholar 

  5. Maynard Smith, J. 1982. Evolution and the theory of games. Cambridge, Cambridge University Press.

    MATH  Google Scholar 

  6. Riechert, S.E. and P. Hammerstein. 1983. Game theory in the ecological context. Annual Review Ecological System 14, pp. 377–409.

    Article  Google Scholar 

  7. Roughgarden, J. 1983. The theory of coevolution, in D.J. Futuyma and M. Slatkin (eds.), Coevolution, Sinauer, Sunderland, MA. pp. 383–403.

    Google Scholar 

  8. Rummel, J.D. and J. Roughgarden. 1983. Some differences between invasion-structured and coevolution-structured competitive communities: A preliminary theoretical analysis, Oikos 41, pp. 477–486.

    Article  Google Scholar 

  9. Rummel, J.D. and J. Roughgarden. 1985. A theory of faunal buildup for competition communities. Evolution 39, pp. 1009–1033.

    Article  Google Scholar 

  10. Vincent, T.L. and J.S. Brown. 1984. Stability in an evolutionary game. Theoretical Population Biology 26, pp. 408–42.

    Article  MathSciNet  MATH  Google Scholar 

  11. Vincent, T.L. and J.S. Brown. 1987. Evolution under nonequilibrium dynamics, Mathematical Modelling 8, pp. 766–771.

    Article  MathSciNet  MATH  Google Scholar 

  12. Vincent, T.L. and J.S. Brown. 1988. The evolution of ESS theory. Annual Review of Ecology and Systematics 19, pp. 423–443.

    Article  Google Scholar 

  13. Vincent, T.L. and M.E. Fisher. 1988. Evolutionaly stable strategies in differential and difference equation models. Evolutionary Ecology 2, pp. 321–337.

    Article  Google Scholar 

  14. Vincent, T.L. and J.S. Brown. 1989. The Evolutionary response to a changing environment, Applied Mathematics and Computation, In Press.

    Google Scholar 

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© 1990 Birkhäuser Boston

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Vincent, T.L. (1990). Strategy Dynamics and the ESS. In: Vincent, T.L., Mees, A.I., Jennings, L.S. (eds) Dynamics of Complex Interconnected Biological Systems. Mathematical Modelling, vol 6. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6784-0_13

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  • DOI: https://doi.org/10.1007/978-1-4684-6784-0_13

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4684-6786-4

  • Online ISBN: 978-1-4684-6784-0

  • eBook Packages: Springer Book Archive

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