A review of evolutionary graph theory with applications to game theory

Paulo Shakarian; Patrick Roos; Anthony Johnson

doi:10.1016/j.biosystems.2011.09.006

A review of evolutionary graph theory with applications to game theory

Paulo Shakarian, Patrick Roos, Anthony Johnson

Research output: Contribution to journal › Review article › peer-review

119 Scopus citations

Abstract

Evolutionary graph theory (EGT), studies the ability of a mutant gene to overtake a finite structured population. In this review, we describe the original framework for EGT and the major work that has followed it. This review looks at the calculation of the " fixation probability" - the probability of a mutant taking over a population and focuses on game-theoretic applications. We look at varying topics such as alternate evolutionary dynamics, time to fixation, special topological cases, and game theoretic results. Throughout the review, we examine several interesting open problems that warrant further research.

Original language	English (US)
Pages (from-to)	66-80
Number of pages	15
Journal	BioSystems
Volume	107
Issue number	2
DOIs	https://doi.org/10.1016/j.biosystems.2011.09.006
State	Published - Feb 2012
Externally published	Yes

Keywords

Evolutionary dynamics
Fixation probability
Game theory
Structured populations
Time to fixation

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
General Biochemistry, Genetics and Molecular Biology
Applied Mathematics

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10.1016/j.biosystems.2011.09.006

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title = "A review of evolutionary graph theory with applications to game theory",

abstract = "Evolutionary graph theory (EGT), studies the ability of a mutant gene to overtake a finite structured population. In this review, we describe the original framework for EGT and the major work that has followed it. This review looks at the calculation of the {"} fixation probability{"} - the probability of a mutant taking over a population and focuses on game-theoretic applications. We look at varying topics such as alternate evolutionary dynamics, time to fixation, special topological cases, and game theoretic results. Throughout the review, we examine several interesting open problems that warrant further research.",

keywords = "Evolutionary dynamics, Fixation probability, Game theory, Structured populations, Time to fixation",

author = "Paulo Shakarian and Patrick Roos and Anthony Johnson",

note = "Funding Information: We would all like to thank the anonymous reviewers for their comments that helped improve the paper. P.S. and A.J. are supported by ARO grant 611102B74F as well as the Office of the Secretary of Defense (OSD). P.R. is supported by AFOSR grant FA95500610405 and NAVAIR contract N6133906C0149 . The opinions in this paper are those of the authors and do not necessarily reflect the opinions of the funders. P.S. would like to thank Prof. Jan Rycht{\'a}{\v r} from the University of North Carolina at Greensboro for his personal correspondence in response to questions about his work. ",

year = "2012",

month = feb,

doi = "10.1016/j.biosystems.2011.09.006",

language = "English (US)",

volume = "107",

pages = "66--80",

journal = "BioSystems",

issn = "0303-2647",

publisher = "Elsevier Ireland Ltd",

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T1 - A review of evolutionary graph theory with applications to game theory

AU - Shakarian, Paulo

AU - Roos, Patrick

AU - Johnson, Anthony

N1 - Funding Information: We would all like to thank the anonymous reviewers for their comments that helped improve the paper. P.S. and A.J. are supported by ARO grant 611102B74F as well as the Office of the Secretary of Defense (OSD). P.R. is supported by AFOSR grant FA95500610405 and NAVAIR contract N6133906C0149 . The opinions in this paper are those of the authors and do not necessarily reflect the opinions of the funders. P.S. would like to thank Prof. Jan Rychtář from the University of North Carolina at Greensboro for his personal correspondence in response to questions about his work.

PY - 2012/2

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N2 - Evolutionary graph theory (EGT), studies the ability of a mutant gene to overtake a finite structured population. In this review, we describe the original framework for EGT and the major work that has followed it. This review looks at the calculation of the " fixation probability" - the probability of a mutant taking over a population and focuses on game-theoretic applications. We look at varying topics such as alternate evolutionary dynamics, time to fixation, special topological cases, and game theoretic results. Throughout the review, we examine several interesting open problems that warrant further research.

AB - Evolutionary graph theory (EGT), studies the ability of a mutant gene to overtake a finite structured population. In this review, we describe the original framework for EGT and the major work that has followed it. This review looks at the calculation of the " fixation probability" - the probability of a mutant taking over a population and focuses on game-theoretic applications. We look at varying topics such as alternate evolutionary dynamics, time to fixation, special topological cases, and game theoretic results. Throughout the review, we examine several interesting open problems that warrant further research.

KW - Evolutionary dynamics

KW - Fixation probability

KW - Game theory

KW - Structured populations

KW - Time to fixation

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DO - 10.1016/j.biosystems.2011.09.006

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JF - BioSystems

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ER -

A review of evolutionary graph theory with applications to game theory

Abstract

Keywords

ASJC Scopus subject areas

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