<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-00678007v2</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-10T04:18:06+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">A new proof for the convergence of an individual based model to the Trait substitution sequence</title>
            <author role="crp">
              <persName>
                <forename type="first">Ankit</forename>
                <surname>Gupta</surname>
              </persName>
              <email type="md5">f3160cd824be2fd5900a1aac0cf2f155</email>
              <email type="domain">cmap.polytechnique.fr</email>
              <idno type="idhal" notation="numeric">922125</idno>
              <idno type="halauthorid" notation="string">356817-922125</idno>
              <affiliation ref="#struct-89626"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">J.A.J.</forename>
                <surname>Metz</surname>
              </persName>
              <email type="md5">977140cd12ab96dac81db9e69bea372d</email>
              <email type="domain">biology.leidenuniv.nl</email>
              <idno type="idhal" notation="numeric">901707</idno>
              <idno type="halauthorid" notation="string">560071-901707</idno>
              <affiliation ref="#struct-73473"/>
            </author>
            <author role="crp">
              <persName>
                <forename type="first">Viet Chi</forename>
                <surname>Tran</surname>
              </persName>
              <email type="md5">bf846b500b47737539728d5f17b9796a</email>
              <email type="domain">u-pem.fr</email>
              <ptr type="url" target="https://tranvietchi59.github.io/"/>
              <idno type="idhal" notation="string">tranvietchi</idno>
              <idno type="idhal" notation="numeric">165</idno>
              <idno type="halauthorid" notation="string">185694-165</idno>
              <idno type="IDREF">https://www.idref.fr/111763665</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-3558-9420</idno>
              <idno type="ARXIV">https://arxiv.org/a/tran_v_2</idno>
              <affiliation ref="#struct-89626"/>
              <affiliation ref="#struct-32"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Viet Chi</forename>
                <surname>Tran</surname>
              </persName>
              <email type="md5">578a127d11a991223608849d39d952d9</email>
              <email type="domain">inria.fr</email>
            </editor>
            <funder ref="#projanr-38035"/>
            <funder ref="#projanr-31182"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2012-03-11 17:17:08</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2012-03-12 21:03:38</date>
              <date type="whenWritten">2012-03-11</date>
              <date type="whenModified">2025-09-02 15:27:55</date>
              <date type="whenReleased">2012-03-13 09:36:27</date>
              <date type="whenProduced">2014-06</date>
              <date type="whenEndEmbargoed">2012-03-12</date>
              <ref type="file" target="https://hal.science/hal-00678007v2/document">
                <date notBefore="2012-03-12"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00678007v2/file/Classic-v5.pdf" id="file-678445-1114667">
                <date notBefore="2012-03-12"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/1203.2361"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="115513">
                <persName>
                  <forename>Viet Chi</forename>
                  <surname>Tran</surname>
                </persName>
                <email type="md5">578a127d11a991223608849d39d952d9</email>
                <email type="domain">inria.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00678007</idno>
            <idno type="halUri">https://hal.science/hal-00678007</idno>
            <idno type="halBibtex">gupta:hal-00678007</idno>
            <idno type="halRefHtml">&lt;i&gt;Acta Applicandae Mathematicae&lt;/i&gt;, 2014, 131, pp.1-27. &lt;a target="_blank" href="https://dx.doi.org/10.1007/s10440-013-9847-y"&gt;&amp;#x27E8;10.1007/s10440-013-9847-y&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Acta Applicandae Mathematicae, 2014, 131, pp.1-27. &amp;#x27E8;10.1007/s10440-013-9847-y&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-678445-1114667"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="X">École polytechnique</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="X-CMAP" corresp="X">Centre de Mathématiques Appliquées (CMAP)</idno>
            <idno type="stamp" n="X-DEP-MATHA">Département de mathématiques appliquées de l’École polytechnique</idno>
            <idno type="stamp" n="GIP-BE">GIP Bretagne Environnement</idno>
            <idno type="stamp" n="CMAP">Centre de Mathématiques Appliquées (CMAP)</idno>
            <idno type="stamp" n="UNIV-LILLE">Université de Lille</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="LPP-MATH">Laboratoire Paul Painlevé (UMR8524)</idno>
            <idno type="stamp" n="DEPARTEMENT-DE-MATHEMATIQUES">Collection du Département de Mathématiques</idno>
            <idno type="stamp" n="IP-PARIS-MATHEMATIQUES">IP Paris Département de Mathématiques</idno>
          </seriesStmt>
          <notesStmt>
            <note type="commentary">23 pages</note>
            <note type="audience" n="1">Not set</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">A new proof for the convergence of an individual based model to the Trait substitution sequence</title>
                <author role="crp">
                  <persName>
                    <forename type="first">Ankit</forename>
                    <surname>Gupta</surname>
                  </persName>
                  <email type="md5">f3160cd824be2fd5900a1aac0cf2f155</email>
                  <email type="domain">cmap.polytechnique.fr</email>
                  <idno type="idhal" notation="numeric">922125</idno>
                  <idno type="halauthorid" notation="string">356817-922125</idno>
                  <affiliation ref="#struct-89626"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">J.A.J.</forename>
                    <surname>Metz</surname>
                  </persName>
                  <email type="md5">977140cd12ab96dac81db9e69bea372d</email>
                  <email type="domain">biology.leidenuniv.nl</email>
                  <idno type="idhal" notation="numeric">901707</idno>
                  <idno type="halauthorid" notation="string">560071-901707</idno>
                  <affiliation ref="#struct-73473"/>
                </author>
                <author role="crp">
                  <persName>
                    <forename type="first">Viet Chi</forename>
                    <surname>Tran</surname>
                  </persName>
                  <email type="md5">bf846b500b47737539728d5f17b9796a</email>
                  <email type="domain">u-pem.fr</email>
                  <ptr type="url" target="https://tranvietchi59.github.io/"/>
                  <idno type="idhal" notation="string">tranvietchi</idno>
                  <idno type="idhal" notation="numeric">165</idno>
                  <idno type="halauthorid" notation="string">185694-165</idno>
                  <idno type="IDREF">https://www.idref.fr/111763665</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-3558-9420</idno>
                  <idno type="ARXIV">https://arxiv.org/a/tran_v_2</idno>
                  <affiliation ref="#struct-89626"/>
                  <affiliation ref="#struct-32"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">9546</idno>
                <idno type="issn">0167-8019</idno>
                <idno type="eissn">1572-9036</idno>
                <title level="j">Acta Applicandae Mathematicae</title>
                <imprint>
                  <publisher>Springer Verlag</publisher>
                  <biblScope unit="volume">131</biblScope>
                  <biblScope unit="pp">1-27</biblScope>
                  <date type="datePub">2014-06</date>
                  <date type="dateEpub">2013-09-28</date>
                </imprint>
              </monogr>
              <idno type="arxiv">1203.2361</idno>
              <idno type="doi">10.1007/s10440-013-9847-y</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">birth and death process</term>
                <term xml:lang="en">structured population</term>
                <term xml:lang="en">adaptive dynamics</term>
                <term xml:lang="en">individual based model</term>
                <term xml:lang="en">averaging technique</term>
                <term xml:lang="en">trait substitution sequence</term>
              </keywords>
              <classCode scheme="classification">92D15; 60J80; 60K35; 60F99</classCode>
              <classCode scheme="halDomain" n="math.math-pr">Mathematics [math]/Probability [math.PR]</classCode>
              <classCode scheme="halDomain" n="sdv.bid.evo">Life Sciences [q-bio]/Biodiversity/Populations and Evolution [q-bio.PE]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We consider a continuous time stochastic individual based model for a population structured only by an inherited vector trait and with logistic interactions. We consider its limit in a context from adaptive dynamics: the population is large, the mutations are rare and we view the process in the timescale of mutations. Using averaging techniques due to Kurtz (1992), we give a new proof of the convergence of the individual based model to the trait substitution sequence of Metz et al. (1992) first worked out by Dieckman and Law (1996) and rigorously proved by Champagnat (2006): rigging the model such that ''invasion implies substitution'', we obtain in the limit a process that jumps from one population equilibrium to another when mutations occur and invade the population.</p>
            </abstract>
            <particDesc>
              <org type="consortium">Chaire MMB</org>
            </particDesc>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-89626" status="VALID">
          <idno type="IdRef">197373461</idno>
          <idno type="ISNI">000000010944436X</idno>
          <idno type="RNSR">199719340P</idno>
          <idno type="ROR">https://ror.org/012e1xn46</idno>
          <idno type="Wikidata">Q16008922</idno>
          <orgName>Centre de Mathématiques Appliquées de l'Ecole polytechnique</orgName>
          <orgName type="acronym">CMAP</orgName>
          <date type="start">2005-01-01</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://cmap.ip-paris.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
            <relation active="#struct-300340" type="direct"/>
            <relation active="#struct-563936" type="indirect"/>
            <relation name="UMR7641" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-73473" status="VALID">
          <orgName>Mathematical institute</orgName>
          <desc>
            <address>
              <addrLine>Niels Bohrweg 1 2333 CA Leiden Fax: +31-71-527-7101 Phone: +31-71-527-7111</addrLine>
              <country key="NL"/>
            </address>
            <ref type="url">http://www.math.leidenuniv.nl/en/home/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-121723" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-32" status="VALID">
          <idno type="IdRef">161603971</idno>
          <idno type="ISNI">0000000403684081</idno>
          <idno type="RNSR">199812852H</idno>
          <idno type="ROR">https://ror.org/043n4fm24</idno>
          <idno type="Wikidata">Q3214464</idno>
          <orgName>Laboratoire Paul Painlevé - UMR 8524</orgName>
          <orgName type="acronym">LPP</orgName>
          <date type="start">2004-01-01</date>
          <desc>
            <address>
              <addrLine>Université de Lille - Sciences et technologies - U.F.R. de Mathématiques - 59655 Villeneuve d'Ascq Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://math.univ-lille.fr/</ref>
          </desc>
          <listRelation>
            <relation name="UMR8524" active="#struct-374570" type="direct"/>
            <relation name="UMR8524" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
          <orgName type="acronym">Inria</orgName>
          <desc>
            <address>
              <addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/en/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300340" status="VALID">
          <idno type="IdRef">027309320</idno>
          <idno type="ISNI">0000000121581279</idno>
          <idno type="ROR">https://ror.org/05hy3tk52</idno>
          <idno type="Wikidata">Q273626</idno>
          <orgName>École polytechnique</orgName>
          <orgName type="acronym">X</orgName>
          <date type="start">1794-03-11</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.polytechnique.edu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-563936" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-563936" status="VALID">
          <idno type="IdRef">238327159</idno>
          <idno type="ISNI">0000000502717600</idno>
          <idno type="ROR">https://ror.org/042tfbd02</idno>
          <idno type="Wikidata">Q48759778</idno>
          <orgName>Institut Polytechnique de Paris</orgName>
          <orgName type="acronym">IP Paris</orgName>
          <date type="start">2019-06-02</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91120 Palaiseau Cedex, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ip-paris.fr</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-121723" status="VALID">
          <idno type="ROR">https://ror.org/027bh9e22</idno>
          <orgName>Universiteit Leiden = Leiden University</orgName>
          <desc>
            <address>
              <addrLine>Leiden University | 2300 RA Leiden The Netherlands</addrLine>
              <country key="NL"/>
            </address>
            <ref type="url">https://www.universiteitleiden.nl/en/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-374570" status="VALID">
          <idno type="IdRef">223446556</idno>
          <idno type="ISNI">0000 0001 2242 6780</idno>
          <idno type="ROR">https://ror.org/02kzqn938</idno>
          <idno type="Wikidata">Q3551621</idno>
          <orgName>Université de Lille</orgName>
          <desc>
            <address>
              <addrLine>EPE Université de Lille. -- 42 rue Paul Duez, 59000 Lille</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-lille.fr/</ref>
          </desc>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-38035" status="VALID">
          <idno type="anr">ANR-11-LABX-0007</idno>
          <idno type="program">Laboratoires d'excellence</idno>
          <orgName>CEMPI</orgName>
          <desc>Centre Européen pour les Mathématiques, la Physique et leurs Interactions</desc>
          <date type="start">2011</date>
        </org>
        <org type="anrProject" xml:id="projanr-31182" status="VALID">
          <idno type="anr">ANR-09-BLAN-0215</idno>
          <idno type="program">Blanc</idno>
          <orgName>MANEGE</orgName>
          <desc>Modèles Aléatoires eN Ecologie, Génétique et Evolution</desc>
          <date type="start">2009</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>