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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.

We consider a model of sympatric speciation due to frequency-dependent competition, in which it was previously assumed that the evolving traits have a very simple genetic architecture. In the present study, we use numerical simulations to test the consequences of relaxing this assumption. First, previous models assumed that assortative mating evolves in infinitesimal steps. Here, we show that the range of parameters for which speciation is possible increases when mutational steps are large. Second, it was assumed that the trait under frequency-dependent selection is determined by a single locus with to alleles and additive effects. As a consequence, the resultant intermediate phenotype is always heterozygous and can never breed true. To relax this assumption, we now add a second locus influencing the trait. We find three new possible evolutionary outcomes: evolution of three reproductive isolated species, a monomorphic equilibrium with only the intermediate phenotype, and a randomly mating population with a steep unimodal distribution of phenotypes. Both extensions of the original model thus increase the likelihood of competitive speciation.