lation and eventually goes to fixation, it is known that the time to fixation

is approximately 2 log(α)/α for a large selection coefficient α. For a popula-

tion that is distributed over finitely many colonies, with migration between

these colonies, we detect various regimes of the migration rate μ for which

the fixation times have different asymptotics as α → ∞.

If μ is of order α, the allele fixes (as in the spatially unstructured case)

in time ∼ 2 log(α)/α. If μ is of order α γ , 0 ≤ γ ≤ 1, the fixation time

is ∼ (2 + (1 − γ)∆) log(α)/α, where ∆ is the number of migration steps

that are needed to reach all other colonies starting from the colony where

the beneficial allele appeared. If μ = 1/ log(α), the fixation time is ∼ (2 +

S) log(α)/α, where S is a random time in a simple epidemic model.

The main idea for our analysis is to combine a new moment dual for

the process conditioned to fixation with the time reversal in equilibrium of

a spatial version of Neuhauser and Krone’s ancestral selection graph.