Sylvie Méléard- Multiscale Eco-Evolutionary Models- From Individuals to Populations

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.

Intro
Adaptation and Evolution for asexual populations
Some motivating questions
The individual based model
Transitions
Large population, time scale (1)
Large population, Rare mutations, Evolution time scale
Intermediary horizontal transfer rates
To capture the emergence of evolutionary cyclic behavior Discretized soy model
Exponents for binary branching processes (BP)
Case of three traits
Main result
Derivation of a Hamiton Jacobi equation from the individual base model