Research activities

Short presentation:

I work on mathematical models from evolutionary biology and ecology. I am interested in the description of joint demographic and evolutionary dynamics of populations structured by quantitative traits in heterogeneous environments. Such phenomena can be modeled by nonlocal parabolic Lotka-Volterra type equations or by nonstandard kinetic equations depending on whether or not mixing of the gene pool is taken into account. My previous works mainly concern models with asexual reproduction and with no mixing of the gene pool (hence parabolic Lotka-Volterra type equations). However, more recently I have also become interested in the study of the mixing of the gene pool (due for instance to the exchange of genetic information between bacteria or to sexual reproduction).

Such models have typically various temporal regimes. Some characteristics of such multi-scale equations are that they lead to some concentration phenomena (occurrence of dominant traits) or propagation phenomena (spatial invasions). An important part of my work has been devoted to the development of an asymptotic approach based on Hamilton-Jacobi equations with constraint to study such models. Furthermore, I have been interested in the study of the impact of temporal and spatial heterogeneity on species' range and phenotypic distribution. Another axis of my research is the study of models with heavy-tailed non-local diffusion terms (due for instance to a non-local dispersion or a heavy-tailed mutation distribution).

Articles:

Hamilton-Jacobi approach (homogeneous environments):

Models with heavy-tailed diffusion:

Temporally heterogeneous environments:

Spatially heterogeneous environments:

Evolution of dispersal:

Interaction with resources:

Other contributions:

Dissertations and book chapter