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Evolutionary Dynamics
Last Updated: 2026-02-05 16:01:32
Abstract
Evolutionary dynamics is concerned with the mathematical principles according to which life has evolved. This course offers an introduction to mathematical modeling of evolution, including deterministic and stochastic models, with an emphasis on tumor evolution.
Objective
The goal of this course is to understand and to appreciate mathematical models and computational methods that provide insight into the evolutionary process in general and tumor evolution in particular. Students should analyze and evaluate models and their application critically and be able to design new models.
Content
Evolution is the one theory that encompasses all of biology. It provides a single, unifying concept to understand the living systems that we observe today. We will introduce several types of mathematical models of evolution to describe gene frequency changes over time in the context of different biological systems, focusing on asexual populations. 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 population dynamics, 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, evolutionary stability, evolutionary graph theory, tumor evolution, stochastic tunneling, genetic progression of cancer, diffusion theory, fitness landscapes, branching processes, and evolutionary escape.
Resources
Lecture Notes
No.
Literature
- Evolutionary Dynamics. Martin A. Nowak. The Belknap Press of Harvard University Press, 2006. - Evolutionary Theory: Mathematical and Conceptual Foundations. Sean H. Rice. Sinauer Associates, Inc., 2004.
General Information
- Language
- English
- Levels
- DR , MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 90 minutes
- Aids
- None
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture |
Evolutionary Dynamics
Attention: lecture starts on Thursday, September 29
Lecture and tutorial will take place via Zoom (flipped classroom) - rooms on campus remain blocked for students.
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2 h weekly |
| exercise |
Evolutionary Dynamics
Lecture and tutorial will take place via Zoom (flipped classroom) - rooms on campus remain blocked for students.
|
|
1 h weekly |
| independent project |
Evolutionary Dynamics
Project Work (compulsory continuous performance assessment), no fixed presence required.
|
No time listed | 2 h weekly |
Offered In
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Application Area (Only necessary and eligible for the Master degree in Applied Mathematics. One of the application areas specified must be selected for the category Application Area for the Master degree in Applied Mathematics. At least 8 credits are required in the chosen application area. Credits from other application areas cannot be recognised for further application areas.)
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Computational Biology and Bioinformatics Master (More information at: )
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Core Courses (Please note that the list of core courses is a closed list. Other courses cannot be added to the core course category in the study plan. Also the assignments of courses to core subcategories cannot be changed. Students need to pass at least one course in each core subcategory. A total of 40 ECTS needs to be acquired in the core course category.)
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Bioinformatics (Please note that all Bioinformatics core courses are offered in the autumn semester)
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Doctorate Biosystems Science and Engineering (More Information at: )