Sympatric speciation illustrates how natural and sexual selection may create new species in isolation without geographic barriers. However, recent genomic reanalyses of classic examples of sympatric speciation reveal complex histories of secondary gene flow from outgroups into the radiation. In contrast, the rich theoretical literature on this process distinguishes among a diverse range of models based on simple genetic histories and different types of reproductive isolating barriers. Thus, there is a need to revisit how to connect theoretical models of sympatric speciation and their predictions to empirical case studies in the face of widespread gene flow. Here, theoretical differences among different types of sympatric speciation and speciation-with-gene-flow models are reviewed and summarized, and genomic analyses are proposed for distinguishing which models apply to case studies based on the timing and function of adaptive introgression. Investigating whether secondary gene flow contributed to reproductive isolation is necessary to test whether predictions of theory are ultimately borne out in nature.
