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hal-00716349, version 1

Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration

Emeric Bouin () 1, Vincent Calvez () 1, Nicolas Meunier () 2, Sepideh Mirrahimi () 3, Benoit Perthame () 4, 5, Gael Raoul () 6, Raphael Voituriez () 7

(2012-07-10)

  • 1:  Unité de Mathématiques Pures et Appliquées (UMPA-ENSL)
  • http://www.umpa.ens-lyon.fr/
    CNRS : UMR5669 – École Normale Supérieure - Lyon France
  • 2:  Mathématiques appliquées Paris 5 (MAP5)
  • http://www.math-info.univ-paris5.fr/map5/
    CNRS : UMR8145 – Université Paris V - Paris Descartes UFR de Maths et informatique 45 rue des Saints Pères 75270 PARIS CEDEX 06 France
  • 3:  Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP)
  • http://www.cmap.polytechnique.fr/
    Polytechnique - X – CNRS : UMR7641 CMAP UMR 7641 École Polytechnique CNRS Route de Saclay 91128 Palaiseau Cedex France
  • 4:  BANG (INRIA Rocquencourt)
  • http://www-rocq.inria.fr/bang/
    INRIA – Laboratoire Jacques-Louis Lions Domaine de Voluceau ; BP 105 ; 78150 Rocquencourt France
  • 5:  Laboratoire Jacques-Louis Lions (LJLL)
  • http://www.ann.jussieu.fr
    CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI B.C. 187 75252 Paris Cedex 05 France
  • 6:  Centre d'écologie fonctionnelle et évolutive (CEFE)
  • http://www.cefe.cnrs.fr/
    CNRS : UMR5175 – Université Montpellier II - Sciences et techniques – Université Montpellier I – Université Paul Valéry - Montpellier III – Ecole Pratique des Hautes Etudes Campus CNRS - 1919 route de Mende - 34293 Montpellier cedex 5 France
  • 7:  Laboratoire de Physique Théorique de la Matière Condensée (LPTMC)
  • http://www.lptl.jussieu.fr
    CNRS : UMR7600 – Université Pierre et Marie Curie [UPMC] - Paris VI LPTMC, Tour 24, Boîte 121, 4, Place Jussieu, 75252 Paris Cedex 05, France France

Bibliographic reference

  • Type of document: Documents without publication reference (Preprint)
  • Subject: Mathematics/Analysis of PDEs
  • Title: Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration
  • Abstract: Invasion fronts in ecology are well studied but very few mathematical results concern the case with variable motility (possibly due to mutations). Based on an apparently simple reaction-diffusion equation, we explain the observed phenomena of front acceleration (when the motility is unbounded) as well as other quantitative results, such as the selection of the most motile individuals (when the motility is bounded). The key argument for the construction and analysis of traveling fronts is the derivation of the dispersion relation linking the speed of the wave and the spatial decay. When the motility is unbounded we show that the position of the front scales as $t^{3/2}$. When the mutation rate is low we show that the canonical equation for the dynamics of the fittest trait should be stated as a PDE in our context. It turns out to be a type of Burgers equation with source term.
  • Fulltext language: English
  • Production date: 2012-07-10
  • Keyword(s): Reaction-Diffusion Equation – WKB limit – Front invasion – Front acceleration
  • Classification: 35K57, 35Q92
  • Comment: 7 pages

Attached file list to this document: 

TEX
cane-toads-CRAS-v6.tex(39.8 KB)
bib-toads.bib(20.7 KB)
nullset.pdf(98.2 KB)
spatialsorting.pdf(42.4 KB)
elsart3-1.cls(13.1 KB)
elsart.cls(53.1 KB)
elsart-num.bst(25 KB)
PDF
cane-toads-CRAS-v6.pdf(463.7 KB)
 
  • hal-00716349, version 1
  • http://hal.archives-ouvertes.fr/hal-00716349
  • oai:hal.archives-ouvertes.fr:hal-00716349
  • From: Vincent Calvez <>
  • Submitted on: Tuesday, 10 July 2012 14:03:35
  • Updated on: Tuesday, 10 July 2012 15:59:34