Sepideh MirrahimiCNRS Research Director

Since the work of Charles Darwin, the quest to understand and predict the evolution of species has led to the development of new mathematical theories, which in turn have enriched evolutionary biology. However, in the face of today's environmental challenges, marked by rapid changes in the environment, new problems are emerging that are difficult to tackle using traditional tools. It is this need that motivates the MUSEUM project.

This project focuses on models of populations structured by phenotypic traits, and aims to develop robust methods for the asymptotic analysis of unconventional multi-scale integro-differential equations, and their links with stochastic processes. MUSEUM is particularly interested in models with nonlinear reproductive terms, characteristic of sexual reproduction. These non-linear terms generate novel behaviours, but their analysis remains highly underdeveloped, unlike models of asexual reproduction where established theories, such as those based on Hamilton-Jacobi equations, facilitate their treatment. The project also aims to integrate the random effects of population demography into deterministic models. The methods developed will enable theoretical biologists to push back the limits of current approaches and explore new avenues in the study of biological evolution.