Given a spatially structured population (of constant size) and a novel, highly beneficial allele, we are dealing with asymptotics of the fixation time of this mutant. We use the selection strength (called $\alpha$) as a scaling parameter and find various regimes dependent on the scaling of the migration strength (called $\mu$) with $\alpha$. We treat the cases $\mu \sim \alpha^p$ for $0\leq p\leq 1$ and $\mu \sim 1/\log(\alpha)$. The main tool for our proofs is an equilibrium version of a dual process, which stems from the ancestral selection graph of Krone and Neuhauser.

Joint work with Andreas Greven (Erlangen), Cornelia Pokalyuk (Lausanne) and Anton Wakolbinger (Frankfurt).