An asymptotic expression for the fixation probability of a mutant in star graphs

Detalhes bibliográficos
Autor(a) principal: Chalub, Fabio Augusto da Costa Carvalho
Data de Publicação: 2016
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/65003
Resumo: We consider the Moran process in a graph called the ``star'' and obtain the asymptotic expression for the fixation probability of a single mutant when the size of the graph is large. The expression obtained corrects the previously known expression announced in reference [E Lieberman, C Hauert, and MA Nowak. Evolutionary dynamics on graphs. Nature, 433(7023):312–316, 2005] and further studied in [M. Broom and J. Rychtar. An analysis of the fixation probability of a mutant on special classes of non-directed graphs. Proc. R. Soc. A-Math. Phys. Eng. Sci., 464(2098):2609–2627, 2008]. We also show that the star graph is an accelerator of evolution, if the graph is large enough.
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spelling An asymptotic expression for the fixation probability of a mutant in star graphsEvolutionary graph theoryMoran processfixation probabilityasymptotic expansionsstar graphWe consider the Moran process in a graph called the ``star'' and obtain the asymptotic expression for the fixation probability of a single mutant when the size of the graph is large. The expression obtained corrects the previously known expression announced in reference [E Lieberman, C Hauert, and MA Nowak. Evolutionary dynamics on graphs. Nature, 433(7023):312–316, 2005] and further studied in [M. Broom and J. Rychtar. An analysis of the fixation probability of a mutant on special classes of non-directed graphs. Proc. R. Soc. A-Math. Phys. Eng. Sci., 464(2098):2609–2627, 2008]. We also show that the star graph is an accelerator of evolution, if the graph is large enough.DM - Departamento de MatemáticaCMA - Centro de Matemática e AplicaçõesRUNChalub, Fabio Augusto da Costa Carvalho2019-03-29T23:16:01Z20162016-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10362/65003eng2164-6066PURE: 2568304https://doi.org/10.3934/jdg.2016011info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-03-11T04:30:52Zoai:run.unl.pt:10362/65003Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:34:14.134229Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv An asymptotic expression for the fixation probability of a mutant in star graphs
title An asymptotic expression for the fixation probability of a mutant in star graphs
spellingShingle An asymptotic expression for the fixation probability of a mutant in star graphs
Chalub, Fabio Augusto da Costa Carvalho
Evolutionary graph theory
Moran process
fixation probability
asymptotic expansions
star graph
title_short An asymptotic expression for the fixation probability of a mutant in star graphs
title_full An asymptotic expression for the fixation probability of a mutant in star graphs
title_fullStr An asymptotic expression for the fixation probability of a mutant in star graphs
title_full_unstemmed An asymptotic expression for the fixation probability of a mutant in star graphs
title_sort An asymptotic expression for the fixation probability of a mutant in star graphs
author Chalub, Fabio Augusto da Costa Carvalho
author_facet Chalub, Fabio Augusto da Costa Carvalho
author_role author
dc.contributor.none.fl_str_mv DM - Departamento de Matemática
CMA - Centro de Matemática e Aplicações
RUN
dc.contributor.author.fl_str_mv Chalub, Fabio Augusto da Costa Carvalho
dc.subject.por.fl_str_mv Evolutionary graph theory
Moran process
fixation probability
asymptotic expansions
star graph
topic Evolutionary graph theory
Moran process
fixation probability
asymptotic expansions
star graph
description We consider the Moran process in a graph called the ``star'' and obtain the asymptotic expression for the fixation probability of a single mutant when the size of the graph is large. The expression obtained corrects the previously known expression announced in reference [E Lieberman, C Hauert, and MA Nowak. Evolutionary dynamics on graphs. Nature, 433(7023):312–316, 2005] and further studied in [M. Broom and J. Rychtar. An analysis of the fixation probability of a mutant on special classes of non-directed graphs. Proc. R. Soc. A-Math. Phys. Eng. Sci., 464(2098):2609–2627, 2008]. We also show that the star graph is an accelerator of evolution, if the graph is large enough.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-01-01T00:00:00Z
2019-03-29T23:16:01Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/65003
url http://hdl.handle.net/10362/65003
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2164-6066
PURE: 2568304
https://doi.org/10.3934/jdg.2016011
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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