Times needed to evolve mating cues under allopatry and parapatry

The time needed for the evolution of mating cues that distinguish species, such as species-specific songs or plumage coloration in birds, has received little attention. Aiming to gain some understanding of the timing of the evolutionary process we here present models of how mating cues evolve in populations split into subpopulations between which there may (parapatry) or may not (allopatry) be migration. Mating cues can be either neutral or directly selected. In models in which evolution commences with a substitution at a neutral mating-cue locus, under allopatry there is no selection on the mating cue, but under parapatry, selection may be induced on the mating cue by the selective conditions in the subpopulations, and the migration rates between them. We use simulation to calculate how selection pressures on mating cues then depend on selective conditions in subpopulations and migration rates between them. In the second part of the paper, we demonstrate quantitatively how the resulting selection pressures on new mating cues together with mutation rate affect speciation time. Our results suggest that species-specific songs or plumage colorations that are selectively neutral evolve faster under parapatry than under allopatry, and this may explain the short speciation times that are sometimes reported. Although our modelling assumptions are restrictive so that caution is needed in comparing the results to empirical data, we hope that our main results, showing quantitatively how parapatry can reduce speciation times, will encourage further work relaxing model assumptions or studying different models of mate choice.