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Evolutionary Dynamics
Last Updated: 2026-02-05 15:24:52
Abstract
The goal of this course is to understand and to appreciate mathematical models and computational methods that provide insight into the evolutionary process.
Content
Evolutionary dynamics is concerned with the mathematical principles according to which life has evolved. The goal of this course is to understand and to appreciate mathematical models and computational methods that provide insight into the evolutionary process. Emphasis is on asexual populations under selective pressure. Viruses and cancer cells provide the most prominent examples of such systems and they are at the same time of great biomedical interest. The course will cover some classical mathematical population genetics and also introduce several new approaches. This is reflected in a diverse set of mathematical concepts which make their appearance throughout the course, all of which are introduced from scratch. Topics covered include the quasispecies equation, evolution of HIV, evolutionary game theory, birth-death processes, evolutionary stability, evolutionary graph theory, somatic evolution of cancer, stochastic tunneling, cell differentiation, hematopoietic tumor stem cells, genetic progression of colon cancer, traveling mutation waves, diffusion theory, fitness landscapes, genotype-phenotype maps, neutral networks, branching processes, evolutionary escape, partially ordered sets and order ideals, epistasis, triangulations of polytopes, and discrete Fourier transform. Syllabus: 1. What is evolution? Basic concepts and examples 2. The quasispecies equation 3. Evolutionary game theory 4. Stochastic models of finite populations 5. Evolutionary games in finite populations 6. Evolutionary Graph Theory 7. Evolutionary dynamics of cancer 8. Stochastic dynamics of hematopoietic tumor stem cells 9. The speed of adaptive evolution 10. Diffusion approximation 11. Combinatorial landscapes 12. Evolution on distributive lattices 13. Epistasis and the geometry of fitness landscapes 14. Exam
General Information
- Language
- English
- Levels
- MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- oral 15 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Evolutionary Dynamics |
|
2 h weekly |
| exercise | Evolutionary Dynamics |
|
1 h weekly |