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. Here we show that the expected time needed for a neutral substitution at a mating-cue locus under allopatry 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 trait which is acted on by selection directly, but this does not in general result in species-specific songs or plumage coloration. Alternatively, (Sibly and Curnow, 2022) showed that, with phenotype matching, local adaptation induces selection on a mating cue even if the locus coding for the mating cue is not linked to those producing local adaptation. Detailed analysis of two cases shows how mating cue selection then depends on the migration rates between the locally-adapted populations and the selective conditions within them. Comparison with data from molecular phylogenies suggests if mating cues are selectively neutral, only parapatric, not allopatric, speciation can account for the times recorded for the evolution of species-specific songs or plumage coloration.