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Speciation in peripheral populations has long been considered one of the most plausible scenarios for speciation with gene flow. In this study, however we identify two additional problems of peripatric speciation, as compared to the parapatric case, that may impede the completion of the speciation process for most parameter regions. First, with (predominantly) unidirectional gene flow, there is no selection pressure to evolve assortative mating on the continent. We discuss the implications of this for different mating schemes. Second, genetic load can build up in small populations. This can lead to extinction of the peripheral species, or generate selection pressure for lower assortative mating to avoid inbreeding. In this case, either a stable equilibrium with intermediate assortment evolves or there is cycling between phases of hybridization and phases of complete isolation.

International audience; Adaptive speciation with gene flow via the evolution of assortative mating has classically been studied in one of two different scenarios. First, speciation can occur if frequency-dependent competition in sympatry induces disruptive selection, leading to indirect selection for mating with similar phenotypes. Second, if a subpopulation is locally adapted to a specific environment, then there is indirect selection against hybridizing with maladapted immigrants. While both of these mechanisms have been modeled many times, the literature lacks models that allow direct comparisons between them. Here we incorporate both frequency-dependent competition and local adaptation into a single model and investigate whether and how they interact in driving speciation. We report two main results. First, we show that individually, the two mechanisms operate under separate conditions, hardly influencing each other when one of them alone is sufficient to drive speciation. Second, we also find that the two mechanisms can operate together, leading to a third speciation mode in which speciation is initiated by selection against maladapted migrants but completed by within-deme competition in a distinct second phase. While this third mode bears some similarity to classical reinforcement, it is considerably faster, and both newly formed species go on to coexist in sympatry.