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The transition from ‘well-marked varieties’ of a single species into ‘well-defined species’—especially in the absence of geographic barriers to gene flow (sympatric speciation)—has puzzled evolutionary biologists ever since Darwin^,. Gene flow counteracts the buildup of genome-wide differentiation, which is a hallmark of speciation and increases the likelihood of the evolution of irreversible reproductive barriers (incompatibilities) that complete the speciation process. Theory predicts that the genetic architecture of divergently selected traits can influence whether sympatric speciation occurs, but empirical tests of this theory are scant because comprehensive data are difficult to collect and synthesize across species, owing to their unique biologies and evolutionary histories. Here, within a young species complex of neotropical cichlid fishes (Amphilophus spp.), we analysed genomic divergence among populations and …