Times birds need 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, has received little attention. Motivated by observations of rapid divergence in mating cues in birds we here compare speciation times under allopatry with those under parapatry. We assume that under allopatry the mating cues are neutral but under parapatry may be acted on by selection. The expected time needed for a neutral substitution at a mating-cue locus is approximately equal to the reciprocal of mutation rate, but the time needed under parapatry can be much shorter. The time needed is reduced by a factor of 4 x (population size) x (selection coefficient on the mating cue). In the simplest case of parapatric speciation the mating cue is an adaptive magic trait such as beak size which is acted on by selection directly, but this does not affect traits like species-specific songs or plumage colouration that are not acted on directly by selection. In an alternative model of parapatric speciation in which the locus coding for a neutral mating cue is not linked to loci producing local adaptation, local adaptation induces selection on the mating cue. We show quantitatively how, with complete phenotype matching, speciation times can be obtained from population size, migration rates between subpopulations and the ecological selective conditions within them. Our results suggest that only parapatric, not allopatric, speciation can account for the times recorded for the evolution of species-specific songs or plumage coloration.