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Antagonistic coevolution between hosts and parasites in spatially structured populations can result in local adaptation of parasites; that is, the greater infectivity of local parasites than foreign parasites on local hosts. Such parasite specialization on local hosts has implications for human health and agriculture. By contrast with classic single-species population-genetic models, theory indicates that parasite migration between subpopulations might increase parasite local adaptation, as long as migration does not completely homogenize populations. To test this hypothesis we developed a system-specific mathematical model and then coevolved replicate populations of the bacterium Pseudomonas fluorescens and a parasitic bacteriophage with parasite only, with host only or with no migration. Here we show that patterns of local adaptation have considerable temporal and spatial variation and that, in the absence of migration, parasites tend to be locally maladapted. However, in accord with our model, parasite migration results in parasite local adaptation, but host migration alone has no significant effect. [ABSTRACT FROM AUTHOR]