Waiting time to (and duration of) parapatric speciation

Using a weak migration and weak mutation approximation, I study the average waiting time to and the average duration of parapatric speciation. The description of reproductive isolation used is based on the classical Dobzhansky model and its recently proposed multilocus generalizations. The dynamics of parapatric speciation is modeled as a biased random walk with absorption performed by the average genetic distance between the residents and immigrants. If a small number of genetic changes is sufficient for complete reproductive isolation, mutation and random genetic drift alone can cause speciation on the time scale of 10-1000 times the inverse of the mutation rate. Even relatively weak selection for local adaptation can dramatically decrease the waiting time to speciation. The duration of parapatric speciation is shorter by orders of magnitude than the waiting time to speciation. For a wide range of parameter values, the duration of speciation is order one over the mutation rate. In general, parapatric speciation is expected to be triggered by changes in the environment.