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The Dynamical Theory of Coevolution: A Derivation from Stochastic Ecological Processes

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  • U. Dieckmann
  • R. Law
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    Abstract

    In this paper we develop a dynamical theory of coevolution in ecological communities. The derivation explicitly accounts for the stochastic components of evolutionary change and is based on ecological processes at the level of the individual. We show that the coevolutionary dynamics can be envisaged as a random walk in the community's trait space. A quantitative description of this stochastic process in terms of a master equation is derived. By determining the first jump moment of this process we abstract the dynamic of the mean evolutionary path. To first order the resulting equation coincides with a dynamic that has been frequently assumed in evolutionary game theory. Apart from recovering this canonical equation we systematically establish the underlying assumptions. We provide higher order corrections and show that these can give rise to new, unexpected evolutionary effects including shifting evolutionary isoclines and evolutionary slowing down of mean paths as they approach evolutionary equilibria. Extensions of the derivation to more ecological settings are discussed. In particular we allow for multi-trait coevolution and analyze coevolution under nonequilibrium population dynamics.

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    File URL: http://www.iiasa.ac.at/Publications/Documents/WP-96-001.pdf
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    Bibliographic Info

    Paper provided by International Institute for Applied Systems Analysis in its series Working Papers with number wp96001.

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    Date of creation: Mar 1996
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    Handle: RePEc:wop:iasawp:wp96001

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    Cited by:
    1. Rodrick Wallace, 2013. "A new formal approach to evolutionary processes in socioeconomic systems," Journal of Evolutionary Economics, Springer, vol. 23(1), pages 1-15, January.
    2. William Brock & Anastasios Xepapadeas, 2004. "Ecosystem Management in Models of Antagonistic Species Coevolution," Working Papers 0503, University of Crete, Department of Economics.
    3. Åke Brännström & Jacob Johansson & Niels von Festenberg, 2013. "The Hitchhiker’s Guide to Adaptive Dynamics," Games, MDPI, Open Access Journal, vol. 4(3), pages 304-328, June.
    4. Richard Horan & Erwin Bulte & Jason Shogren, 2008. "Coevolution of human speech and trade," Journal of Economic Growth, Springer, vol. 13(4), pages 293-313, December.
    5. M. Doebeli & U. Dieckmann, 2000. "Evolutionary Branching and Sympatric Speciation Caused by Different Types of Ecological Interactions," Working Papers ir00040, International Institute for Applied Systems Analysis.
    6. Horan, Richard D. & Shogren, Jason F. & Bulte, Erwin H., 2011. "Joint determination of biological encephalization, economic specialization," Resource and Energy Economics, Elsevier, vol. 33(2), pages 426-439, May.
    7. U. Dieckmann & M. Doebeli, 1999. "On the Origin of Species by Sympatric Speciation," Working Papers ir99013, International Institute for Applied Systems Analysis.
    8. S.A.H. Geritz & E. Kisdi & G. Meszena & J.A.J. Metz, 1996. "Evolutionary Singular Strategies and the Adaptive Growth and Branching of the Evolutionary Tree," Working Papers wp96114, International Institute for Applied Systems Analysis.
    9. Durrett, Rick & Mayberry, John, 2010. "Evolution in predator-prey systems," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1364-1392, July.
    10. E. Kisdi & S.A.H. Geritz, 1998. "Adaptive Dynamics in Allele Space: Evolution of Genetic Polymorphism by Small Mutations in a Heterogeneous Environment," Working Papers ir98038, International Institute for Applied Systems Analysis.
    11. Ross Cressman, 2009. "Continuously stable strategies, neighborhood superiority and two-player games with continuous strategy space," International Journal of Game Theory, Springer, vol. 38(2), pages 221-247, June.
    12. E. Kisdi & F.J.A. Jacobs & S.A.H. Geritz, 2000. "Red Queen Evolution by Cycles of Evolutionary Branching and Extinction," Working Papers ir00030, International Institute for Applied Systems Analysis.
    13. Laurent Lehmann & Georg Nöldeke & Jorge Peña, 2013. "Gains from switching and evolutionary stability in multi-player matrix games," Working papers 2013/13, Faculty of Business and Economics - University of Basel.
    14. Joëlle Noailly, 2008. "Coevolution of economic and ecological systems," Journal of Evolutionary Economics, Springer, vol. 18(1), pages 1-29, February.
    15. G. Meszena & J.A.J. Metz, 1999. "Species Diversity and Population Regulation: The Importance of Environmental Feedback Dimensionality," Working Papers ir99045, International Institute for Applied Systems Analysis.
    16. T.J.M. van Dooren, 1998. "The Evolutionary Ecology of Dominance-Recessivity," Working Papers ir98096, International Institute for Applied Systems Analysis.
    17. Champagnat, Nicolas, 2006. "A microscopic interpretation for adaptive dynamics trait substitution sequence models," Stochastic Processes and their Applications, Elsevier, vol. 116(8), pages 1127-1160, August.

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