Stochastic models for adaptive dynamics: Scaling limits and diversity

TL;DR

This paper reviews stochastic models of adaptive dynamics, explaining how various scaling limits lead to different evolutionary descriptions and discussing metastable transitions from stable states.

Contribution

It provides a comprehensive overview of how different scaling limits of stochastic models produce key adaptive dynamics equations and phenomena.

Findings

Derivation of trait substitution sequence and canonical equation

Explanation of metastable transitions from stable states

Connection between scaling limits and evolutionary models

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 conditions can occur as a metastable transition. This is a review paper that will appear in "Probabilistic Structures in Evolution", ed. by E. Baake and A. Wakolbinger.