ANR DEEV (2020-2024)

Integro-Differential Equations from EVolutionary biology

The objective of the DEEV project is to analyze multi-scale integro-differntial equations, with possible stochastic components, modeling the evolutionary dynamics of structured populations. The mathematical modeling of dynamics of phenotypically structured populations lead to nonlocal parabolic Lotka-Volterra type equations or systems, Hamilton-Jacobi equations with constraint and nonstandard kinetic equations. Some characteristics of such equations are that they typically lead to concentration phenomena (occurrence of dominant traits) or propagation phenomena (spatial invasions). Among the mathematical challenges we can mention complex underlying dynamics, lack of comparison principle and non-standard regularity estimates.

We will focus on three biological motivations that we believe to be of major importance in this field:

Adaptation of populations to spatially heterogeneous environments
Co-evolutionary dynamics of interacting populations with different evolutionary time scales
The impact of the mixing of the gene pool (for instance as a consequence of sexual reproduction) on the adaptation of populations

The DEEV project is funded by the french funding agency « Agence Nationale de la Recherche ».

Members of the project

Permanent researchers

S. Mirrahimi (coordinator), Institut Montpelliérain Alexander Grothendieck
M. Alfaro, Laboratoire de mathématiques Raphaël Salem, Rouen
M. Costa, Institut de mathématiques de Toulouse
F. Débarre, Institute of ecology and environmental sciences, Sorbonne Université
G. Raoul, Centre de mathématiques appliquées, Ecole Polytechnique

PhD students

L. Dekens, Institut Camille Jordan, Lyon
G. Peltier, Institut Montpelliérain Alexander Grothendieck

Postdoc

A. Gárriz, Institut de mathématiques de Toulouse and Institut Montpelliérain Alexander Grothendieck.

Scientific events

18 November 2020, project virtual meeting, themes of the talks: adaptation to spatially heterogeneous environments considering sexual or asexual reproduction.
8 March 2021, project virtual meeting, themes of the talks: models of spatial propagation.
7 June 2021, project virtual meeting, themes of the talks: gene drive and adaptation to fragmented environments.