Generalized Moran process
| Thesis title in Czech: | Zobecněný Moranův proces |
|---|---|
| Thesis title in English: | Generalized Moran process |
| Key words: | stochastické procesy, Moranův proces, evoluční dynamika, graf |
| English key words: | stochastic process, Moran process, evolutionary dynamics, graph |
| Academic year of topic announcement: | 2018/2019 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| Department: | Computer Science Institute of Charles University (32-IUUK) |
| Supervisor: | doc. Mgr. Robert Šámal, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 07.05.2019 |
| Date of assignment: | 07.05.2019 |
| Confirmed by Study dept. on: | 15.05.2019 |
| Date and time of defence: | 10.06.2019 09:00 |
| Date of electronic submission: | 08.05.2019 |
| Date of submission of printed version: | 10.05.2019 |
| Date of proceeded defence: | 10.06.2019 |
| Opponents: | doc. RNDr. Martin Balko, Ph.D. |
| Guidelines |
| The Moran process [2] is a general model -- stochastic process, used in biology to simulate evolution.
It describes probabilistic dynamics of a toy model: two genetic variants of a species competing for dominance; their habitat is described by a finite graph. Two basic questions are: what is the probability that one or the other variant will prevail (so-called fixation probability)? And what is the expected time when this happens (fixation time)? How does this depend on the structure of the graph? The literature about Moran processes is vast, we refer in particular to [2] and [3]. The student's goal is to explore the setting where every individual has a different fitness based not only on his type but also on the vertex it is inhabiting. |
| References |
| [1] C. Hauert, M. A. Nowak, E. Lierberman. Evolutionary dynamics on graphs. Nature, 433, 2005.
[2] P. A. P. Moran. Random processes in genetics. Mathematical Proceedings of the Cambridge Philosophical Society, 54(1), 1958. doi: 10.1017/ S0305004100033193. [3] M. A. Nowak. Evolutionary Dynamics: Exploring the Equations of Life. Harvard University Press, 2006. ISBN 975-0-674-02338-3. |