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- Lionel Roques, Jimmy Garnier, François Hamel, Etienne K Klein
- Proceedings of the National Academy of Sciences…
- 2012

Most mathematical studies on expanding populations have focused on the rate of range expansion of a population. However, the genetic consequences of population expansion remain an understudied body of theory. Describing an expanding population as a traveling wave solution derived from a classical reaction-diffusion model, we analyze the spatio-temporal… (More)

We investigate the inside structure of one-dimensional reaction-diffusion traveling fronts. The reaction terms are of the monostable, bistable or ignition types. Assuming that the fronts are made of several components with identical diffusion and growth rates, we analyze the spreading properties of each component. In the monos-table case, the fronts are… (More)

- Jimmy Garnier
- SIAM J. Math. Analysis
- 2011

- Jimmy Garnier, Lionel Roques, François Hamel
- Bulletin of mathematical biology
- 2012

We analyze the role of the spatial distribution of the initial condition in reaction-diffusion models of biological invasion. Our study shows that, in the presence of an Allee effect, the precise shape of the initial (or founding) population is of critical importance for successful invasion. Results are provided for one-dimensional and two-dimensional… (More)

We study a birth and death model for the adapatation of a sexual population to an environment. The population is structured by a phenotypical trait, and, possibly, an age variable. Recombination is modeled by Fisher's infinitesimal operator. We prove the existence of principal eigenelements for the corresponding eigenproblem. As the infinitesimal operator… (More)

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