Invasion fronts with variable motility: Phenotype selection, spatial sorting and wave acceleration
By Emeric Bouin, Vincent Calvez, N. Meunier, Sepideh Mirrahimi, Benoit Perthame, Gaël Raoul, Raphael Voituriez. 2012
120 citations recorded by the source corpus.
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.
Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/7f46c7760635190df4f52b45845ded7d639b3b57
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Citations in the corpus
- A Hamilton-Jacobi approach for a model of population structured by space and trait (2013, background): “Although, there have been some attempts to study models structured by trait and space (see for instance [16, 2, 10, 14, 11]), not many rigorous studies seem to have analyzed the dynamics of a population continuously structured by trait and by space, with non-local interactions.”
- Super-linear spreading in local and non-local cane toads equations (2015, methodology): “An Hamilton-Jacobi framework has been formally applied to the non-local model in [8], and rigorously justified in [38].”