Evolutionary graph theory: breaking the symmetry between interaction and replacement.

Evolutionary graph theory: breaking the symmetry between interaction and replacement. Research Abstract Details 

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Evolutionary graph theory: breaking the symmetry between interaction and replacement. Abstract Text:

Hisashi Ohtsuki,Jorge M Pacheco,Martin A Nowak,

We study evolutionary dynamics in a population whose structure is given by two graphs: the interaction graph determines who plays with whom in an evolutionary game; the replacement graph specifies the geometry of evolutionary competition and updating. First, we calculate the fixation probabilities of frequency dependent selection between two strategies or phenotypes. We consider three different update mechanisms: birth-death, death-birth and imitation. Then, as a particular example, we explore the evolution of cooperation. Suppose the interaction graph is a regular graph of degree h, the replacement graph is a regular graph of degree g and the overlap between the two graphs is a regular graph of degree l. We show that cooperation is favored by natural selection if b/c>hg/l. Here, b and c denote the benefit and cost of the altruistic act. This result holds for death-birth updating, weak-selection and large population size. Note that the optimum population structure for cooperators is given by maximum overlap between the interaction and the replacement graph (g=h=l), which means that the two graphs are identical. We also prove that a modified replicator equation can describe how the expected values of the frequencies of an arbitrary number of strategies change on replacement and interaction graphs: the two graphs induce a transformation of the payoff matrix.

Evolutionary graph theory: breaking the symmetry between interaction and replacement. Publishing Authors By Initials

H Ohtsuki,JM Pacheco,MA Nowak,

For similar investigative techniques: epidemiologic methods: statistics as topic: probability research abstracts see: investigative techniques: epidemiologic methods: statistics as topic: probability research

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Evolutionary graph theory: breaking the symmetry between interaction and replacement. Journal Published:

PUBLICATION TYPE: Research Support, U.S. Gov't,

Journal: Journal of theoretical biology

VOLUME: 246

Page Numbers: 681-94

Journal Abbreviation: J. Theor. Biol.

ISSN: 0022-5193

DAY: 8

MONTH: 02

YEAR: 2007

Evolutionary graph theory: breaking the symmetry between interaction and replacement. Information

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LANGUAGE: eng

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Evolutionary graph theory: breaking the symmetry between interaction and replacement. Keywords Mesh Terms:

KEYWORDS: Probability

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Grant and Affiliation Information for Evolutionary graph theory: breaking the symmetry between interaction and replacement.

AFFILIATION: Program for Evolutionary Dynamics, Harvard University, Cambridge MA 02138, USA. ohtsuki@bio-math10.biology.kyushu-u.ac.jp

Country: Netherlands

AGENCY: United States NIGMS

GRANT: 1 R01 GM078986-01

ACRONYM: GM

MEDLINETA: J Theor Biol

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