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Gradient Flow Formulations of Discrete and Continuous Evolutionary Models

2021-02Artigo científico Acesso aberto
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dc.contributor.authorChalub, Fabio A. C. C.
dc.contributor.authorMonsaingeon, Léonard
dc.contributor.authorRibeiro, Ana Margarida
dc.contributor.authorSouza, Max O.
dc.contributor.institutionCMA - Centro de Matemática e Aplicações
dc.contributor.institutionDM - Departamento de Matemática
dc.contributor.pblSpringer Science Business Media
dc.date.accessioned2023-09-20T22:14:39Z
dc.date.available2023-09-20T22:14:39Z
dc.date.issued2021-02
dc.description309079/2015-2, 310293/2018-9 and by CAPES - Finance Code 001.
dc.description.abstractWe 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.en
dc.description.versionpublishersversion
dc.description.versionpublished
dc.format.extent1344756
dc.identifier.doi10.1007/s10440-021-00391-9
dc.identifier.issn0167-8019
dc.identifier.otherPURE: 28321155
dc.identifier.otherPURE UUID: 70f07f3b-61e3-46dd-9b8a-0543cf4dedb6
dc.identifier.otherScopus: 85100563213
dc.identifier.otherWOS: 000617786100002
dc.identifier.urihttp://hdl.handle.net/10362/158040
dc.identifier.urlhttps://www.scopus.com/pages/publications/85100563213
dc.language.isoeng
dc.peerreviewedyes
dc.relationinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID%2FMAT%2F00297%2F2019/PT
dc.relationCenter for Mathematics and Applications
dc.relationFrom Stochastic Geometric Mechanics to Mass Transportation Problems
dc.relationinfo:eu-repo/grantAgreement/FCT/3599-PPCDT/PTDC%2FMAT-STA%2F28812%2F2017/PT
dc.relationFACCC also benefited from an "Investigador FCT" grant. LM was supported by MOS was partially supported by CNPq under grants
dc.subjectGradient flow structure
dc.subjectKimura equation
dc.subjectOptimal transport
dc.subjectReducible Markov chains
dc.subjectReplicator dynamics
dc.subjectShahshahani distance
dc.subjectApplied Mathematics
dc.titleGradient Flow Formulations of Discrete and Continuous Evolutionary Modelsen
dc.title.subtitleA Unifying Perspectiveen
dc.typejournal article
degois.publication.issue1
degois.publication.titleActa Applicandae Mathematicae
degois.publication.volume171
dspace.entity.typePublication
oaire.awardNumberUID/MAT/00297/2019
oaire.awardNumberPTDC/MAT-STA/0975/2014
oaire.awardNumberPTDC/MAT-STA/28812/2017
oaire.awardTitleCenter for Mathematics and Applications
oaire.awardTitleFrom Stochastic Geometric Mechanics to Mass Transportation Problems
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID%2FMAT%2F00297%2F2019/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/3599-PPCDT/PTDC%2FMAT-STA%2F0975%2F2014/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/3599-PPCDT/PTDC%2FMAT-STA%2F28812%2F2017/PT
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream3599-PPCDT
oaire.fundingStream3599-PPCDT
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccess
relation.isProjectOfPublication64f434a5-5508-48c9-9c51-7c5c1c285f68
relation.isProjectOfPublicatione9d56614-afac-4152-864b-d1522d5fd8f4
relation.isProjectOfPublication651e30da-afdf-457a-89aa-daebd9f7725b
relation.isProjectOfPublication.latestForDiscovery651e30da-afdf-457a-89aa-daebd9f7725b

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