“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 expertise.

Sepideh Mirrahimi, Alexander Grothendieck Institute of Montpellier (IMAG)

Abstract:

Understanding the interplay between mutation, selection, and interaction with a structured environment—as well as the role of these evolutionary mechanisms in species adaptation—is a central goal of evolutionary biology. These phenomena have been mathematically formalized since the field’s inception.

In this talk, I will present several mathematical models from quantitative genetics, a branch of evolutionary biology that studies the evolution of continuously varying traits. I will discuss recent advances in this field under conditions of low genetic variance—often referred to as “weak selection” in the biological literature—using newly developed mathematical tools. The mathematical studies in this presentation focus on the asymptotic analysis of nonlocal partial differential equations. The techniques developed in this context 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, Alexander Grothendieck Institute of Montpellier (IMAG)

Abstract

Understanding the interplay between mutation, selection, and interaction with a structured environment, as well as the role of these evolutionary mechanisms in species adaptation, is a major objective of evolutionary biology theory. Such phenomena have been formally modeled mathematically since the early stages of the field’s development.

In this talk, I will present some mathematical models from quantitative genetics, a branch of evolutionary biology that investigates the evolution of continuously varying traits. I will present recent advances in this field under conditions 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 non-local partial differential equations. The techniques developed within this framework enable the study of various scenarios, such as those involving temporal or spatial environmental structures, or different modes of reproduction.