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Natural microbial populations often have complex spatial structures. This canimpact their evolution, in particular the ability of mutants to take over.While mutant fixation probabilities are known to be unaffected by sufficientlysymmetric structures, evolutionary graph theory has shown that some graphs canamplify or suppress natural selection, in a way that depends on microscopicupdate rules. We propose a model of spatially structured populations on graphsdirectly inspired by batch culture experiments, alternating within-deme growthon nodes and migration-dilution steps, and yielding successive bottlenecks.This setting bridges models from evolutionary graph theory with Wright-Fishermodels. Using a branching process approach, we show that spatial structure withfrequent migrations can only yield suppression of natural selection. Moreprecisely, in this regime, circulation graphs, where the total incomingmigration flow equals the total outgoing one in each deme, do not impactfixation probability, while all other graphs strictly suppress selection.Suppression becomes stronger as the asymmetry between incoming and outgoingmigrations grows. Amplification of natural selection can nevertheless exist ina restricted regime of rare migrations and very small fitness advantages, wherewe recover the predictions of evolutionary graph theory for the star graph.

Frequent asymmetric migrations suppress natural selection in spatially structured populations