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

Comptes Rendus Mathematique

Volumn 350, Issue 15-16, 2012, Pages 761-766

  Bouin, Emeric ^a   Calvez, Vincent ^a   Meunier, Nicolas ^b   Mirrahimi, Sepideh ^c   Perthame, Benoît ^d   Raoul, Gaël ^e   Voituriez, Raphaël ^d  

^a UNITÉ DE MATHÉMATIQUES PURES ET APPLIQUÉES   (France)

^b UNIVERSITÉ PARIS DESCARTES   (France)

^c CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^d SORBONNE UNIVERSITÉ   (France)

^e CENTRE D ECOLOGIE FONCTIONNELLE ET EVOLUTIVE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84867333475     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2012.09.010     Document Type: Article

References (17)

1. Arnold A., Desvillettes L., Prévost C. Existence of nontrivial steady states for populations structured with respect to space and a continuous trait. Commun. Pure Appl. Anal. 2012, 11(1):83-96.
2. Barles G., Perthame B. Concentrations and constrained Hamilton-Jacobi equations arising in adaptive dynamics. Contemp. Math. 2007, vol. 439:57-68. Amer. Math. Soc., Providence, RI.
3. O. Bénichou, V. Calvez, N. Meunier, R. Voituriez, Front acceleration by dynamic selection in Fisher population waves, preprint.
4. Bouin E., Calvez V. A kinetic eikonal equation. C. R. Acad. Sci. Paris, Ser. I 2012, 350(5-6):243-248.
5. Champagnat N., Méléard S. Invasion and adaptive evolution for individual-based spatially structured populations. J. Math. Biol. 2007, 55(2):147-188.
6. Champagnat N., Ferrière R., Méléard S. From individual stochastic processes to macroscopic models in adaptive evolution. Stoch. Models 2008, 24(Suppl. 1):2-44.
7. Dieckmann U., Law R. The dynamical theory of coevolution: a derivation from stochastic ecological processes. J. Math. Biol. 1996, 34(5-6):579-612.
8. Diekmann O., Jabin P.-E., Mischler S., Perthame B. The dynamics of adaptation: an illuminating example and a Hamilton-Jacobi approach. Theor. Popul. Biol. 2005, 67(4):257-271.
9. Dockery J., Hutson V., Mischaikow K., Pernarowski M. The evolution of slow dispersal rates: a reaction diffusion model. J. Math. Biol. 1998, 37(1):61-83.
10. Evans L.C., Souganidis P.E. A PDE approach to geometric optics for certain semilinear parabolic equations. Indiana Univ. Math. J. 1989, 38(1):141-172.
11. Freidlin M.I. Geometric optics approach to reaction-diffusion equations. SIAM J. Appl. Math. 1986, 46(2):222-232.
12. Kokko H., López-Sepulcre A. From individual dispersal to species ranges: perspectives for a changing world. Science 2006, 313(5788):789-791.
13. Lorz A., Mirrahimi S., Perthame B. Dirac mass dynamics in multidimensional nonlocal parabolic equations. Comm. Partial Differential Equations 2011, 36(6):1071-1098.
14. Phillips B.L., Brown G.P., Webb J.K., Shine R. Invasion and the evolution of speed in toads. Nature 2006, 439(7078):803.
15. Ronce O. How does it feel to be like a rolling stone? Ten questions about dispersal evolution. Annu. Rev. Ecol. Syst. 2007, 38:231-253.
16. Shine R., Brown G.P., Phillips B.L. An evolutionary process that assembles phenotypes through space rather than through time. Proc. Natl. Acad. Sci. USA 2011, 108(14):5708-5711.
17. Simmons A.D., Thomas C.D. Changes in dispersal during species' range expansions. Amer. Nat. 2004, 164:378-395.