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  Evolutionary game dynamics driven by mutations under frequency dependent selection

Huang, W. (2012). Evolutionary game dynamics driven by mutations under frequency dependent selection. PhD Thesis, Christian-Albrechts-Universität, Kiel.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0010-21C1-B Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0010-21C4-5
Genre: Thesis

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 Creators:
Huang, Weini1, Author              
Traulsen, Arne1, Referee              
Schulenburg, Hinrich, Referee
Affiliations:
1Research Group Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society, ou_1445641              

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 Abstract: Evolutionary game theory and theoretical population genetics are two different fields sharing many common properties. In both fields, theoretical models are built to explore evolutionary dynamics; various evolutionary forces, such as selection, mutation, and random genetic drift, are involved in the modeling. However, in terms of concrete models, evolutionary game theory is often considered to deal with phenotypes, while theoretical population genetics describes genotypes. Is it possible and worth to combine approaches from both fields? We address this question by analyzing the evolutionary dynamics driven by random mutations in the framework of evolutionary game theory. Mutations provide a continuous input of new variability into a population, which is exposed to natural selection. In evolutionary game theory, mutations are often assumed to occur among predefined types. This assumption initially made in the study of behavioral phenotypes (i.e. human behaviors), might be less reasonable in studies at the level of genes or genotypes. An alternative assumption is made in the infinite allele model in theoretical population genetics, where every mutation brings a new allele to the population. However, the resulting evolutionary dynamics based on the infinite allele model has only been studied in the context of neutral and constant selection. In this thesis, we propose an evolutionary game theoretic model, which combines the assumption of infinite alleles and frequency dependent fitness. We investigate the evolutionary dynamics in finite and infinite populations based on this model. The fixation probability of a single mutant, the diversity of a population, and the changes of the average population fitness are strikingly different under constant selection and frequency dependent selection scenarios. These results imply that connecting evolutionary game theory and theoretical population genetics approaches can bring a different and insightful view in understanding evolutionary dynamics.

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Language(s): eng - English
 Dates: 2012-08-132012-09-262012-08
 Publication Status: Published in print
 Pages: IV, 106 S.
 Publishing info: Kiel : Christian-Albrechts-Universität
 Table of Contents: 1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Infinite and finite populations . . . . . . . . . . . . . . . . . . 6
1.2.1 Replicator dynamics . . . . . . . . . . . . . . . . . . . 6
1.2.2 Moran process and fixation probabilities . . . . . . . . 7
1.2.3 Wright-Fisher process . . . . . . . . . . . . . . . . . . . 13
1.3 Constant and frequency dependent selection . . . . . . . . . . 16
1.3.1 Constant selection . . . . . . . . . . . . . . . . . . . . 16
1.3.2 Frequency dependent selection and diploidy . . . . . . 17
1.3.3 Frequency dependent selection in evolutionary game
theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.4 Frequency dependent mutant model . . . . . . . . . . . . . . . 24
1.4.1 Random mutant model with two types . . . . . . . . . 24
1.4.2 Payoff distribution and fitness distribution . . . . . . . 25
1.4.3 Random mutant games with n types . . . . . . . . . . 27
2 Fixation probability in the frequency dependent mutation
model with two types 30
2.1 Fixation probability of random mutants under frequency dependent
selection . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2 Generalizing the definition of the payoff distribution . . . . . . 40
3 Diversity in the frequency dependent mutation model with
many types 41
3.1 Diversity under neutrality . . . . . . . . . . . . . . . . . . . . 42
3.2 Diversity under frequency dependent selection for various selection
intensities . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3 Rescaling the average fitness . . . . . . . . . . . . . . . . . . . 57
4 Average fitness in the frequency dependent mutation model
in infinite populations 59
4.1 The average population fitness . . . . . . . . . . . . . . . . . . 59
4.2 Random frequency dependent mutations can decease the average
fitness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5 Summary and outlook 87
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Bibliography 92
Acknowledgements cvii
Curriculum vitae cviii
Declaration cix
 Rev. Method: -
 Identifiers: Other: Diss/12411
 Degree: PhD

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