![]() This provides a way to understand the role of geographic separation between patches in promoting convergent adaptation and the genomic signals it leaves behind. We address the following questions: How long does it take for a novel, locally adapted allele to appear in a patch of habitat where it is favored through mutation? Or, through migration from another, already adapted patch? Which is more likely to occur, as a function of distance between the patches? How can we tell which has occurred, i.e., what population genetic signal is left by the spread of migrant alleles? To answer these questions we examine the family structure underlying migration–selection equilibrium surrounding an already adapted patch, in particular treating those rare families that reach new patches as spatial branching processes. This paper studies a model of the balance between these two routes to adaptation in continuous environments with patchy selection pressures. The tension between the two reflects the degree of constraint imposed on evolution by the underlying genetic architecture versus how effectively selection and geographic isolation act to inhibit the geographic spread of locally adapted alleles. ![]() Such adaptation can occur through convergent evolution if different alleles arise and spread in different patches, or through the spread of shared alleles by migration acting to synchronize adaptation across the species. Species often encounter, and adapt to, many patches of locally similar environmental conditions across their range.
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