Fixation in large populations: a continuous view of a discrete problem

Detalhes bibliográficos
Autor(a) principal: Chalub, Fabio Augusto da Costa Carvalho
Data de Publicação: 2016
Outros Autores: Souza, Max
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://doi.org/10.1007/s00285-015-0889-9
Resumo: 308113/2012-8. The authors thank two anonymous reviewers and the associate editor for several remarks that greatly improved the paper.
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spelling Fixation in large populations: a continuous view of a discrete problemAsymptotic approximationsBirth-death processesEvolutionary dynamicsFixation probability308113/2012-8. The authors thank two anonymous reviewers and the associate editor for several remarks that greatly improved the paper.We study fixation in large, but finite, populations with two types, and dynamics governed by birth-death processes. By considering a restricted class of such processes, which includes many of the evolutionary processes usually discussed in the literature, we derive a continuous approximation for the probability of fixation that is valid beyond the weak-selection (WS) limit. Indeed, in the derivation three regimes naturally appear: selection-driven, balanced, and quasi-neutral-the latter two require WS, while the former can appear with or without WS. From the continuous approximations, we then obtain asymptotic approximations for evolutionary dynamics with at most one equilibrium, in the selection-driven regime, that does not preclude a weak-selection regime. As an application, we study the fixation pattern when the infinite population limit has an interior evolutionary stable strategy (ESS): (1) we show that the fixation pattern for the Hawk and Dove game satisfies what we term the one-half law: if the ESS is outside a small interval around , the fixation is of dominance type; (2) we also show that, outside of the weak-selection regime, the long-term dynamics of large populations can have very little resemblance to the infinite population case; in addition, we also present results for the case of two equilibria, and show that even when there is weak-selection the long-term dynamics can be dramatically different from the one predicted by the replicator dynamics. Finally, we present continuous restatements valid for large populations of two classical concepts naturally defined in the discrete case: (1) the definition of an strategy; (2) the definition of a risk-dominant strategy. We then present three applications of these restatements: (1) we obtain an asymptotic definition valid in the quasi-neutral regime that recovers both the one-third law under linear fitness and the generalised one-third law for -player games; (2) we extend the ideas behind the (generalised) one-third law outside the quasi-neutral regime and, as a generalisation, we introduce the concept of critical-frequency; (3) we recover the classification of risk-dominant strategies for -player games.DM - Departamento de MatemáticaCMA - Centro de Matemática e AplicaçõesRUNChalub, Fabio Augusto da Costa CarvalhoSouza, Max2017-10-30T23:01:23Z2016-012016-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://doi.org/10.1007/s00285-015-0889-9eng0303-6812PURE: 1168900https://arxiv.org/abs/1408.6501https://doi.org/10.1007/s00285-015-0889-9info: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:RCAAP2024-03-11T04:12:55Zoai:run.unl.pt:10362/24768Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:28:07.481887Repositório 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 Fixation in large populations: a continuous view of a discrete problem
title Fixation in large populations: a continuous view of a discrete problem
spellingShingle Fixation in large populations: a continuous view of a discrete problem
Chalub, Fabio Augusto da Costa Carvalho
Asymptotic approximations
Birth-death processes
Evolutionary dynamics
Fixation probability
title_short Fixation in large populations: a continuous view of a discrete problem
title_full Fixation in large populations: a continuous view of a discrete problem
title_fullStr Fixation in large populations: a continuous view of a discrete problem
title_full_unstemmed Fixation in large populations: a continuous view of a discrete problem
title_sort Fixation in large populations: a continuous view of a discrete problem
author Chalub, Fabio Augusto da Costa Carvalho
author_facet Chalub, Fabio Augusto da Costa Carvalho
Souza, Max
author_role author
author2 Souza, Max
author2_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
Souza, Max
dc.subject.por.fl_str_mv Asymptotic approximations
Birth-death processes
Evolutionary dynamics
Fixation probability
topic Asymptotic approximations
Birth-death processes
Evolutionary dynamics
Fixation probability
description 308113/2012-8. The authors thank two anonymous reviewers and the associate editor for several remarks that greatly improved the paper.
publishDate 2016
dc.date.none.fl_str_mv 2016-01
2016-01-01T00:00:00Z
2017-10-30T23:01:23Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://doi.org/10.1007/s00285-015-0889-9
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dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0303-6812
PURE: 1168900
https://arxiv.org/abs/1408.6501
https://doi.org/10.1007/s00285-015-0889-9
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