English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
  Fixation probability and time for the Moran process on graphs

Möller, M. (2018). Fixation probability and time for the Moran process on graphs. Master Thesis, Universität zu Lübeck, Lübeck.

Item is

Basic

show hide
Item Permalink: http://hdl.handle.net/21.11116/0000-0003-C6C7-D Version Permalink: http://hdl.handle.net/21.11116/0000-0003-C77A-4
Genre: Thesis

Files

show Files
hide Files
:
Masterarbeit.pdf (Any fulltext), 5MB
 
File Permalink:
-
Name:
Masterarbeit.pdf
Description:
-
Visibility:
Restricted (Max Planck Institute for Evolutionary Biology, Plön; )
MIME-Type / Checksum:
application/pdf
Technical Metadata:
Copyright Date:
-
Copyright Info:
-
License:
-

Locators

show

Creators

show
hide
 Creators:
Möller, Marius1, Author              
Traulsen, Arne1, Referee              
Hindersin, Laura1, Contributor              
Affiliations:
1Department Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society, ou_1445641              

Content

show
hide
Free keywords: -
 Abstract: For a long time, model populations were generally assumed to be well-mixed. Recently however there has been heightened interest in the infuence of spatial structures on evolutionary processes. In this thesis we look especially at the Moran process on graphs, which is one way of introducing these spatial structures. There have been some hints that fixation probability and time of an advantageous mutant are correlated. This thesis aims to find graphs that break out of this pattern and with other unusual properties, as well as finding out what structural properties lead to these unusual values in terms of fixation probability and time. We find various graphs maximizing or minimizing either the fixation probability or the time for different fitness values and prove some properties by analytical means. The most interesting graph that has been found here is the 'kite' graph, which is an amplifier of selection for a high or low fitness and a suppressor of selection for a fitness close to 1, which is an entirely new category of graphs.

Details

show
hide
Language(s): eng - English
 Dates: 2018-01-312018-01-31
 Publication Status: Published in print
 Pages: 61
 Publishing info: Lübeck : Universität zu Lübeck
 Table of Contents: Contents
1 Introduction 1
2 Basics 4
2.1 Markov Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Graph Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Evolutionary Processes on Graphs . . . . . . . . . . . . . . . . . 9
2.4 Algorithm for the Exact Calculation of Graph Properties . . . . 14
2.5 Ampliers and Suppressors of Selection . . . . . . . . . . . . . . 16
2.6 Fixation Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 All Graphs up to Size 10 18
3.1 Percentage of Ampliers and Suppressors . . . . . . . . . . . . . 18
3.2 Comparison of ER Versus all Graphs . . . . . . . . . . . . . . . . 19
3.3 Distribution of Fixation Time and Fixation Probability . . . . . 22
3.4 Strongest Suppressors . . . . . . . . . . . . . . . . . . . . . . . . 24
3.5 Suppressors with high Fixation Time . . . . . . . . . . . . . . . . 25
3.6 Pseudo-Suppressors . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.7 High Fixation Probability and Time . . . . . . . . . . . . . . . . 28
3.8 High Fixation Probability and low Fixation Time . . . . . . . . . 29
3.9 Overview and Comparison . . . . . . . . . . . . . . . . . . . . . . 30
4 Graphs Greater Than Size 10 32
4.1 Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.2 Extreme Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5 Graph Properties 40
5.1 Properties of Strong Ampliers and Suppressors . . . . . . . . . . 40
5.2 Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.3 Continuity Correlation up to Size 10 . . . . . . . . . . . . . . . . 42
5.4 Continuity Correlation From Size 11 to 16 . . . . . . . . . . . . . 43
6 Analytical Calculations 46
6.1 Overview of Dierent Approaches . . . . . . . . . . . . . . . . . . 46
6.2 Double Star . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
6.3 Coupled Star . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
6.4 Detour Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
7 Discussion 54
7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
7.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
 Rev. Method: -
 Identifiers: Other: Dipl/13175
 Degree: Master

Event

show

Legal Case

show

Project information

show

Source

show