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  Speed of evolution on graphs

Sui, X., Wu, B., & Wang, L. (2015). Speed of evolution on graphs. Physical Review E, 92(6): 062124. doi:10.1103/PhysRevE.92.062124.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-4D66-D Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-4D67-B
Genre: Journal Article

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Sui_et_al_2015.pdf (Publisher version), 411KB
 
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 Creators:
Sui, Xiukai, Author
Wu, Bin1, Author              
Wang, Long, Author
Affiliations:
1Department Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society, ou_1445641              

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Free keywords: Stochastic systems Benefit to cost ratios; Birth-death process; Diffusion approximations; Evolutionary game theory; Frequency dependent; Population structures; Prisoner's dilemma game; Structured population
 Abstract: The likelihood that a mutant fixates in the wild population, i.e., fixation probability, has been intensively studied in evolutionary game theory, where individuals' fitness is frequency dependent. However, it is of limited interest when it takes long to take over. Thus the speed of evolution becomes an important issue. In general, it is still unclear how fixation times are affected by the population structure, although the fixation times have already been addressed in the well-mixed populations. Here we theoretically address this issue by pair approximation and diffusion approximation on regular graphs. It is shown (i) that under neutral selection, both unconditional and conditional fixation time are shortened by increasing the number of neighbors; (ii) that under weak selection, for the simplified prisoner's dilemma game, if benefit-to-cost ratio exceeds the degree of the graph, then the unconditional fixation time of a single cooperator is slower than that in the neutral case; and (iii) that under weak selection, for the conditional fixation time, limited neighbor size dilutes the counterintuitive stochastic slowdown which was found in well-mixed populations. Interestingly, we find that all of our results can be interpreted as that in the well-mixed population with a transformed payoff matrix. This interpretation is also valid for both death-birth and birth-death processes on graphs. This interpretation bridges the fixation time in the structured population and that in the well-mixed population. Thus it opens the avenue to investigate the challenging fixation time in structured populations by the known results in well-mixed populations.

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Language(s): eng - English
 Dates: 2015-09-172015-12-14
 Publication Status: Published online
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: DOI: 10.1103/PhysRevE.92.062124
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Title: Physical Review E
  Other : Phys. Rev. E
Source Genre: Journal
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Publ. Info: Melville, NY : American Physical Society
Pages: 10 S. Volume / Issue: 92 (6) Sequence Number: 062124 Start / End Page: - Identifier: ISSN: 1539-3755
CoNE: /journals/resource/954925225012