Stochastics models in evolution
Advanced topics in applied probability
Time and place: Tuesdays and Wednesdays, 10-12, Room 1.008
In this lecture we will introduce and discuss what has become known as "stochastic individual based models of adaptive dynamics". Mathematically, these are measure valued continuous time Markov processes that describe the dynamics of populations of individuals that are subject to the evolutionary mechanisms of birth, death, mutation and competition/interaction. They have been introduced to furnish simple mathematical models that allow to derive basic ferature of the biological theory of adaptive dynamics. This will mainly involve the derivation of scaling limits with respect to population size, mutation rates, and mutations step size.
I will write lecture notes as we go
1) Ethier, Stewart N.; Kurtz, Thomas G. Markov processes. Characterization and convergence. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons, Inc., New York,
2) Bansaye, Vincent; Méléard, Sylvie Stochastic models for structured populations. Scaling limits and long time behavior. Mathematical Biosciences Institute Lecture Series. Stochastics in Biological Systems, 1.4. Springer, Cham; MBI Mathematical Biosciences Institute, Ohio State University, Columbus, OH, 2015
Requirements: Good knowledge of probability theory on the level of Stochastic Processes or better Markov processes