Gradient Flow Formulations of Discrete and Continuous Evolutionary Models
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Data de Publicação: | 2021 |
Outros Autores: | , , |
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. |
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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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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