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Measure Dynamics on a One-Dimensional Continuous Trait Space: Theoretical Foundations for Adaptive Dynamics

By R. Cressman and J. Hofbauer


The measure dynamic approach to modeling single-species coevolution with a one-dimensional trait space is developed and compared to traditional method of adaptive dynamics and the Maximum Principle. It is shown that among monomorphisms (i.e. measures supported on single trait value), the CSS (Continuously Stable Strategy) characterize those that are Lyapunov stable and attract all initial measures supported in an interval containing this trait value. In the cases where adaptive dynamics predicts evolutionary branching, convergence to dimorphism is established

Publisher: IR-04-016
Year: 2004
OAI identifier: oai:pure.iiasa.ac.at:7430
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