article · 01/08/2012
Invasion fronts with variable motility: Phenotype selection, spatial sorting and wave acceleration
Résumé
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 qualitative results, such as the existence of traveling waves and the selection of the most motile individuals (when the motility is bounded). The key argument for constructing and analysing the traveling waves is the derivation of a dispersion relation linking the wave speed 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 a source term. (C) 2012 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
Citer cet article
Bouin, E., Calvez, V., Meunier, N., Mirrahimi, S., Perthame, B., Raoul, G., & Voituriez, R. (2012). Invasion fronts with variable motility: Phenotype selection, spatial sorting and wave acceleration. COMPTES RENDUS MATHEMATIQUE, 350(15-16). https://doi.org/10.1016/j.crma.2012.09.010@article{Bouin2012_244,
author = {Bouin, Emeric and Calvez, Vincent and Meunier, Nicolas and Mirrahimi, Sepideh and Perthame, Benoit and Raoul, Gael and Voituriez, Raphael},
year = {2012},
month = {8},
title = {Invasion fronts with variable motility: Phenotype selection, spatial sorting and wave acceleration},
journal = {COMPTES RENDUS MATHEMATIQUE},
volume = {350},
number = {15-16},
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 qualitative results, such as the existence of traveling waves and the selection of the most motile individuals (when the motility is bounded). The key argument for constructing and analysing the traveling waves is the derivation of a dispersion relation linking the wave speed 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 a source term. (C) 2012 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.},
url = {http://www.dx.doi.org/10.1016/j.crma.2012.09.010},
doi = {10.1016/j.crma.2012.09.010},
issn = {1631-073X},
}TY - JOUR
AU - Bouin, Emeric
AU - Calvez, Vincent
AU - Meunier, Nicolas
AU - Mirrahimi, Sepideh
AU - Perthame, Benoit
AU - Raoul, Gael
AU - Voituriez, Raphael
PY - 2012
DA - 2012/08/01
TI - Invasion fronts with variable motility: Phenotype selection, spatial sorting and wave acceleration
JO - COMPTES RENDUS MATHEMATIQUE
VL - 350
IS - 15-16
SN - 1631-073X
AB - 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 qualitative results, such as the existence of traveling waves and the selection of the most motile individuals (when the motility is bounded). The key argument for constructing and analysing the traveling waves is the derivation of a dispersion relation linking the wave speed 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 a source term. (C) 2012 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
DO - 10.1016/j.crma.2012.09.010
UR - http://www.dx.doi.org/10.1016/j.crma.2012.09.010
ER -