"Evolutionary adaptation of quantitative traits: some mathematical models and recent advances"

The NUMEV Seminars are open to a wide audience of students and researchers from all disciplines, who wish to learn more about the current research areas of the NUMEV-MIPS community (Mathematics, Computer Science, Physics and Systems) or about opportunities to develop their skills and know-how.

Sepideh Mirrahimi, Institut Montpellier Alexander Grothendieck (IMAG)

Summary:

Understanding the interaction between mutation, selection, interaction with a structured environment, and the role of these evolutionary mechanisms in the adaptation of species, is a major objective of the theory of evolutionary biology. These phenomena have been formalized mathematically from the beginning of the development of this field.

In this talk, I will present some mathematical models from quantitative genetics, a theory of evolutionary biology that studies the evolution of continuously varying traits (traits). I will present new advances in this field in a regime of low genetic variance, often referred to as "weak selection" in the biological literature, using recently developed mathematical tools. The mathematical studies of this presentation are centered on the asymptotic analysis of non-local partial differential equations. The techniques developed in this context make it possible to study different scenarios, for example by considering temporal or spatial environmental structures, or different modes of reproduction.

"Evolutionary adaptation of quantitative traits: some mathematical models and recent advances"

Sepideh Mirrahimi, Institut Montpellier Alexander Grothendieck (IMAG)

Abstract

Understanding the interplay between mutation, selection, interaction with a structured environment, and the role of such evolutionary mechanisms in the adaptation of species is a major objective of evolutionary biology theory. Such phenomena have been formalized mathematically since the early stages of the development of this field.

In this talk, I will present some mathematical models from quantitative genetics, a theory in evolutionary biology that investigates the evolution of continuously varying characters (traits). I will present some new progress in this field in a regime of small genetic variance, often called "weak selection" in the biological literature, using recently developed mathematical tools. The mathematical studies in this presentation are centered around the asymptotic analysis of non-local partial differential equations. The techniques developed within this framework allow to study various scenarios, for instance considering temporal or spatial environmental structures, or different reproduction modes.