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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.
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https://hal.archives-ouvertes.fr/hal-00716349
Contributor : Vincent Calvez Connect in order to contact the contributor
Submitted on : Tuesday, July 10, 2012 - 2:03:35 PM
Last modification on : Friday, November 26, 2021 - 6:20:32 PM
Long-term archiving on: : Thursday, December 15, 2016 - 10:03:04 PM

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Emeric Bouin, Vincent Calvez, Nicolas Meunier, Sepideh Mirrahimi, Benoît Perthame, et al.. Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration. Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2012, 350 (15-16), pp.761-766. ⟨10.1016/j.crma.2012.09.010⟩. ⟨hal-00716349⟩

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