Filling the Gap Between Individual-Based Evolutionary Models and Hamilton-Jacobi Equations
Explore a 50-minute lecture on the derivation of Hamilton-Jacobi equations directly from stochastic individual-based models in evolutionary biology. Delve into the work of Sepideh Mirrahimi and colleagues, who bridge the gap between individual-based evolutionary models and Hamilton-Jacobi equations. Examine how this approach provides a better understanding of results obtained through the Hamilton-Jacobi method and its potential for improving the analysis of sub-population extinctions. Learn about the evolution of quantitative genetics models and the analytical description of phenotypic density through Hamilton-Jacobi equations. Gain insights into the asymptotic derivations involved in transitioning from stochastic individual-based models to integro-differential models, and finally to Hamilton-Jacobi equations in the regime of small mutational variance.