Thematic Session 3: Reaction-diffusion equations, new theoretical and applied trends

Structural Models, Eigenvalues, and Biological Evolution

Yuan Lou
Shanghai Jiao Tong University
Peoples Rep of China
Co-Author(s):    
Abstract:
In biological evolution, certain specific traits (such as particular dispersal rates or resource utilization patterns) are often observed to dominate in populations, forming what are known as "evolutionarily stable strategies" (ESS). This talk aims to explore how structural models based on partial differential equations, together with related principale eigenvalue theory, can be used to mathematically characterize the formation mechanisms of these advantageous traits. The core idea is to relate population fitness to the principal eigenvalue of differential operator, and then to locate ESS by examining the extremal behavior of the eigenvalue as a function of the advantageous trait.