- Thesis:
- Master in Mathematics
- Author:
- Nico Bruder
- Title:
- Dormancy in stochastic population models
- Supervisors:
- Martin Slowik (Universität Mannheim)
- Jan JOHANNES
- Abstract:
- In this thesis, we first give a short overview of Markov process theory and describe the connection between infinitesimal generators and stochastic differential equations. Markov processes play a crucial role in the population genetic models that are subsequently presented. Specifically, the Wright–Fisher model and the Moran model, as well as the derivation of the Wright–Fisher diffusion, are shown. The concepts of stochastic duality and coalescence are introduced. We also present the extension of the Wright–Fisher diffusion via a seed-bank component to model the biological concept of dormancy. Finally, we show that infinitely many seed-bank components can be used to obtain heavy-tailed dormancy times, and we demonstrate that this infinite-dimensional diffusion is well-defined.
- Reference:
- J. Blath, A. G. Casanova, N. Kurt, and M. Wilke-Berenguer. A new coalescent for seed-bank models, The Annals of Applied Probability 26(2):857–891, 2016.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |