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We are motivated by a question arising in population genetics, and try to describe the effect of migratory fluxes and spatial structure on the genealogy of a population. This leads to the study of systems of particles performing simple random walk on a given graph, and where particles coalesce according to a certain mechanism (typically, Kingman's coalescent) when they are on the same site. We obtain various asymptotic results for this process, at both small and large time scales, which are of interest to population genetics. We will also discuss some related conjectures. Joint work with Omer Angel, Alan Hammond and Vlada Limic.