Accueil Population Evolution and Interaction Particle Systems

Population Evolution and Interaction Particle Systems

Sylvie Méléard

Team leader

Research themes

We develop relevant random and deterministic models to capture phenomena related to biodiversity, ecology and evolution. More specifically, we consider complex systems built essentially on individual behaviours (cells, bacteria, species, populations, metapopulations) and which take the biology of the problem into account as much as possible.

Research areas

Mathematical modeling and statistical analysis of biological or medical data.

Random modelling can be used to quantify fluctuations, the sources of which can be diverse: randomness in the size of a small population linked to the births and deaths of individuals (genetic drift), randomness of mutations that appear at the time of reproduction (in DNA replication), randomness of environmental changes (climate change), randomness in the movement of individuals (impact of habitat fragmentation).
Deterministic modelling offers a more macroscopic viewpoint in which individual behaviours are integrated into an evolution describing the overall behaviour of the system. Our approach is to work with biologists to build ‘good’ models, in the sense that they are as close as possible to the phenomenon under study but also simple enough to provide quantitative answers to the problem posed.

These are multi-scale models, dependent on numerous parameters that will quantify the links between these different scales of time, space, genetic, ecological and phenotypic parameters. Biological questions mainly concern evolution – invasion and mutation fixation, spatially structured genealogies, evolutionary branching, speciation, and population dynamics, extinction, competition, scaling limits, quasi-stationary states, behavior in a random environment. The tools we use mainly involve stochastic calculus, partial differential equations, measure-valued processes, coalescent and processes in a random environment.

Featured research projects

Regulation of haematopoietic stem cells in mice: a combined biological and mathematical approach

Modelling the regulation of stem cells and early progenitors under stress for healthy cells and cells with JAK2 mutation.

C. Bonnet, P. Gou, S. Girel, V. Bansaye, E. Lauret, S. Méléard, S. Giraudier

Effect of secondary mutations on the evolution of MPS under treatment

To gain a better understanding of the effect of additional mutations on the development of SMP.

N. Belmabrouk, A. Fernandez-Baranda, S. Giraudier, N. Maslah, S. Méléard

Mathematical models to predict clonal evolution and relapse after chemotherapy in acute myeloid leukaemia

A. Auger, V. Bansaye, C. Bonnet, F. Chesson, M. Duchmann, R. Itzykson, C. Legrand, L. Freiman, N. Lecornec, S. Méléard

Team members

Bansaye Vincent	Professor at École Polytechnique
Bonnet Céline	Research Scientist at Inria (Lyon)
Doumic Marie	Senior Research Director at Inria (École Polytechnique)
Girel Simon	Associate Professor (Nice)
Méléard Sylvie	Professor at École Polytechnique
Belmabrouk Nadia	Postdoc
Fernandez-Baranda Ana	PhD Student