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

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 expertise.

Sepideh Mirrahimi, Montpellier Alexander Grothendieck Institute (IMAG)

Summary:

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

In this presentation, I will introduce some mathematical models from quantitative genetics, a theory of evolutionary biology that studies the evolution of continuously varying traits. I will present recent 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 in this presentation focus on the asymptotic analysis of nonlocal partial differential equations. The techniques developed in this framework allow us 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, Montpellier Alexander Grothendieck Institute (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 us to study various scenarios, for instance considering temporal or spatial environmental structures, or different reproduction modes.