Explore a 47-minute conference talk by Sylvie Méléard on multiscale eco-evolutionary models, focusing on the effects of small and random populations on long-term dynamics. Delve into the quantification of these effects on macroscopic approximations, with individual behaviors described using stochastic measure-valued processes. Examine various long-term asymptotic behaviors based on mutation size, frequency, and horizontal transmission rates. Discover surprising cyclic behaviors in simulations and investigate a simple model with log-scale population and time sizes. Learn about explicit criteria for characterizing asymptotic behaviors and the impact of time and size scales on macroscopic approximations, leading to Hamilton-Jacobi equations. The talk covers topics such as adaptation and evolution for asexual populations, individual-based models, large population dynamics, rare mutations, evolutionary time scales, and the emergence of cyclic behaviors in evolutionary processes.