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Fluctuation domains in adaptive evolution

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  • Boettiger, Carl
  • Dushoff, Jonathan
  • Weitz, Joshua S.

Abstract

We derive an expression for the variation between parallel trajectories in phenotypic evolution, extending the well known result that predicts the mean evolutionary path in adaptive dynamics or quantitative genetics. We show how this expression gives rise to the notion of fluctuation domains–parts of the fitness landscape where the rate of evolution is very predictable (due to fluctuation dissipation) and parts where it is highly variable (due to fluctuation enhancement). These fluctuation domains are determined by the curvature of the fitness landscape. Regions of the fitness landscape with positive curvature, such as adaptive valleys or branching points, experience enhancement. Regions with negative curvature, such as adaptive peaks, experience dissipation. We explore these dynamics in the ecological scenarios of implicit and explicit competition for a limiting resource.

Suggested Citation

  • Boettiger, Carl & Dushoff, Jonathan & Weitz, Joshua S., 2010. "Fluctuation domains in adaptive evolution," Theoretical Population Biology, Elsevier, vol. 77(1), pages 6-13.
    • Handle: RePEc:eee:thpobi:v:77:y:2010:i:1:p:6-13
    DOI: 10.1016/j.tpb.2009.10.003
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    References listed on IDEAS

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    1. Ulf Dieckmann & Michael Doebeli, 1999. "On the origin of species by sympatric speciation," Nature, Nature, vol. 400(6742), pages 354-357, July.
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    3. U. Dieckmann & R. Law, 1996. "The Dynamical Theory of Coevolution: A Derivation from Stochastic Ecological Processes," Working Papers wp96001, International Institute for Applied Systems Analysis.
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