#### Filter Results:

- Full text PDF available (13)

#### Publication Year

2009

2017

- This year (2)
- Last 5 years (9)
- Last 10 years (15)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

- Pierre-Emmanuel Jabin, Gaël Raoul
- Journal of mathematical biology
- 2011

In this paper, we are interested in an integro-differential model that describe the evolution of a population structured with respect to a continuous trait. Under some assumption, we are able to find an entropy for the system, and show that some steady solutions are globally stable. The stability conditions we find are coherent with those of Adaptive… (More)

- Klemens Fellner, Gaël Raoul
- Mathematical and Computer Modelling
- 2011

We study the large-time behaviour of a non-local evolution equation for the density of particles or individuals subject to an external and an interaction potential. In particular, we consider interaction potentials which are singular in the sense that their first derivative is discontinuous at the origin. For locally attractive singular interaction… (More)

We study a generalized system of ODE’s modeling a finite number of biological populations in a competitive interaction. We adapt the techniques in [8] and [2] to prove the convergence to a unique stable equilibrium. Résumé. Nous étudions un système généralisé d’équations différentielles modélisant un nombre fini de populations biologiques en interaction… (More)

We consider a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypic trait. To sustain the possibility of invasion in the case where an underlying principal eigenvalue is negative, we investigate the existence of travelling wave solutions. We identify a minimal speed c∗ > 0, and prove the existence… (More)

- Quentin Griette, Gaël Raoul, Sylvain Gandon
- Evolution; international journal of organic…
- 2015

Understanding and predicting the spatial spread of emerging pathogens is a major challenge for the public health management of infectious diseases. Theoretical epidemiology shows that the speed of an epidemic is governed by the life-history characteristics of the pathogen and its ability to disperse. Rapid evolution of these traits during the invasion may… (More)

We consider a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypical trait. To sustain the possibility of invasion in the case where an underlying principal eigenvalue is negative, we investigate the existence of travelling wave solutions. We identify a minimal speed c∗ > 0, and prove the existence… (More)

- Gaël Raoul
- 2009

Adaptive dynamics (see [10], [11], [7], [8]) is a branch of evolutionary ecology, that aims at describing the Darwinian evolution of populations along a phenotypic trait, which characterises each individual. This trait as well as the state of the resident population define the survival rate and reproduction rate of the individual. In the asexual case that… (More)

- Gaël Raoul
- 2015

In this paper, we consider a long time and vanishing mutations limit of an integro-differential model describing the evolution of a population structured with respect to a continuous phenotypic trait. We show that the asymptotic population is a steadystate of the evolution equation without mutations, and satisfies an evolutionary stability condition.… (More)

- Sepideh Mirrahimi, Gaël Raoul
- Theoretical population biology
- 2013

We study sexual populations structured by a phenotypic trait and a space variable, in a non-homogeneous environment. Departing from an infinitesimal model, we perform an asymptotic limit to derive the system introduced in Kirkpatrick and Barton (1997). We then perform a further simplification to obtain a simple model. Thanks to this simpler equation, we can… (More)

- Gaël Raoul
- 2015

This equation can be seen as a many particles limit of discret processes where particles (or individuals) can interact at a large distance, through an interaction potential W (see [27, 20]), and may be subjected to an external potential V . Such equations appear in various biological phenomenons like swarming (see [7, 15]), distribution of actin-filament… (More)