Stochastic models for adaptive dynamics: Scaling limits and diversity

  title={Stochastic models for adaptive dynamics: Scaling limits and diversity},
  author={Anton Bovier},
  journal={Probabilistic Structures in Evolution},
  • A. Bovier
  • Published 5 September 2019
  • Biology
  • Probabilistic Structures in Evolution
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 conditions can… 
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