Explore a comprehensive analysis of adaptation dynamics in heterogeneous environments through this 46-minute lecture by Lionel Roques from INRAE. Delve into a system of nonlocal reaction-diffusion equations that model the adaptation of multiple phenotypically structured populations across diverse environmental patches. Examine the long-term behavior of solutions, focusing on persistence and extinction, based on principal eigenvalue analysis. Investigate the impact of migration on population persistence and compare scenarios with two versus three hosts. Discover how the addition of a third host can create a springboard effect or hinder adaptation, depending on its position in the phenotypic space. Gain insights into the complex interplay between mutation, selection, and migration in shaping evolutionary outcomes, with potential applications to understanding zoonotic disease patterns.