BooksecrCollected Volumepp. 127–150

Stochastic models for adaptive dynamics: Scaling limits and diversity

  • Anton Bovier

    Rheinische-Friedrich-Wilhelms-Universität Bonn, Germany
Stochastic models for adaptive dynamics: Scaling limits and diversity cover
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Abstract

I discuss the so-called stochastic individual based model of adaptive dynamics and in particular how different scaling limits can be obtained by taking limits of large populations, small mutation rate, and small effect of single mutations together with appropriate time rescaling. In particular, one derives the trait substitution sequence, polymorphic evolution sequence, and the canonical equation of adaptive dynamics. In addition, I show how the escape from an evolutionary stable condition can occur as a metastable transition.