Gradient Flow Formulations of Discrete and Continuous Evolutionary Models

Detalhes bibliográficos
Autor(a) principal: Chalub, Fabio A. C. C.
Data de Publicação: 2021
Outros Autores: Monsaingeon, Léonard, Ribeiro, Ana Margarida, Souza, Max O.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/158040
Resumo: 309079/2015-2, 310293/2018-9 and by CAPES - Finance Code 001.
id RCAP_50dd04c1186aef7ea2fd6689b2942cf9
oai_identifier_str oai:run.unl.pt:10362/158040
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling Gradient Flow Formulations of Discrete and Continuous Evolutionary ModelsA Unifying PerspectiveGradient flow structureKimura equationOptimal transportReducible Markov chainsReplicator dynamicsShahshahani distanceApplied Mathematics309079/2015-2, 310293/2018-9 and by CAPES - Finance Code 001.We consider three classical models of biological evolution: (i) the Moran process, an example of a reducible Markov Chain; (ii) the Kimura Equation, a particular case of a degenerated Fokker-Planck Diffusion; (iii) the Replicator Equation, a paradigm in Evolutionary Game Theory. While these approaches are not completely equivalent, they are intimately connected, since (ii) is the diffusion approximation of (i), and (iii) is obtained from (ii) in an appropriate limit. It is well known that the Replicator Dynamics for two strategies is a gradient flow with respect to the celebrated Shahshahani distance. We reformulate the Moran process and the Kimura Equation as gradient flows and in the sequel we discuss conditions such that the associated gradient structures converge: (i) to (ii), and (ii) to (iii). This provides a geometric characterisation of these evolutionary processes and provides a reformulation of the above examples as time minimisation of free energy functionals.CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNChalub, Fabio A. C. C.Monsaingeon, LéonardRibeiro, Ana MargaridaSouza, Max O.2023-09-20T22:14:39Z2021-022021-02-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10362/158040eng0167-8019PURE: 28321155https://doi.org/10.1007/s10440-021-00391-9info: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:RCAAP2024-03-11T05:40:18Zoai:run.unl.pt:10362/158040Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:56:57.504717Repositório 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 Gradient Flow Formulations of Discrete and Continuous Evolutionary Models
A Unifying Perspective
title Gradient Flow Formulations of Discrete and Continuous Evolutionary Models
spellingShingle Gradient Flow Formulations of Discrete and Continuous Evolutionary Models
Chalub, Fabio A. C. C.
Gradient flow structure
Kimura equation
Optimal transport
Reducible Markov chains
Replicator dynamics
Shahshahani distance
Applied Mathematics
title_short Gradient Flow Formulations of Discrete and Continuous Evolutionary Models
title_full Gradient Flow Formulations of Discrete and Continuous Evolutionary Models
title_fullStr Gradient Flow Formulations of Discrete and Continuous Evolutionary Models
title_full_unstemmed Gradient Flow Formulations of Discrete and Continuous Evolutionary Models
title_sort Gradient Flow Formulations of Discrete and Continuous Evolutionary Models
author Chalub, Fabio A. C. C.
author_facet Chalub, Fabio A. C. C.
Monsaingeon, Léonard
Ribeiro, Ana Margarida
Souza, Max O.
author_role author
author2 Monsaingeon, Léonard
Ribeiro, Ana Margarida
Souza, Max O.
author2_role author
author
author
dc.contributor.none.fl_str_mv CMA - Centro de Matemática e Aplicações
DM - Departamento de Matemática
RUN
dc.contributor.author.fl_str_mv Chalub, Fabio A. C. C.
Monsaingeon, Léonard
Ribeiro, Ana Margarida
Souza, Max O.
dc.subject.por.fl_str_mv Gradient flow structure
Kimura equation
Optimal transport
Reducible Markov chains
Replicator dynamics
Shahshahani distance
Applied Mathematics
topic Gradient flow structure
Kimura equation
Optimal transport
Reducible Markov chains
Replicator dynamics
Shahshahani distance
Applied Mathematics
description 309079/2015-2, 310293/2018-9 and by CAPES - Finance Code 001.
publishDate 2021
dc.date.none.fl_str_mv 2021-02
2021-02-01T00:00:00Z
2023-09-20T22:14:39Z
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 http://hdl.handle.net/10362/158040
url http://hdl.handle.net/10362/158040
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0167-8019
PURE: 28321155
https://doi.org/10.1007/s10440-021-00391-9
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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
repository.mail.fl_str_mv
_version_ 1799138153045426176

Registros relacionados