A tipping point in parapatric speciation

More than two loci are involved in reproductive isolation in most cases of putative recent speciation. We study the speciation between two geographically isolated populations connected by infrequent migration, in which incompatibility is controlled by quantitative loci. Incompatibility genetic distance is defined as the fraction of compatibility controlling loci that are different between individuals. Speciation is established when genetic distance reaches a threshold level in spite of occasional migration and subsequent hybridization that reduce genetic distance. With stochastic analysis, we investigate how the time to speciation depends on the manner in which the magnitude of incompatibility increases with genetic distance. Results are: (1) The time to speciation is short if the migration rate is smaller than the mutation rate, or if intermediate levels of genetic distance cause mild incompatibility, making migrants less effective in reducing genetic distance. (2) Genetic distance may fluctuate around a positive quasi-equilibrium level for a long time, and suddenly show a quick passage to speciation when it goes beyond a "tipping point." Notably a gradual increase in incompatibility can result in a sudden and rapid formation of a new species. (3) Speciation becomes very slow if incompatibility is effective for individuals differing at only one locus. These findings provide testable predictions on reproductive traits controlled by specific incompatibility accumulation forms that facilitate the speciation process. (C) 2017 Elsevier Ltd. All rights reserved.