Difference in flowering time as an isolating barrier

Although many theoretical studies have reported strong effects of different flowering times on reproductive isolation, such studies have all focused on the different flowering time within a season, and the subsequently developed models are difficult to apply to the cases of diurnal- and nocturnal-flowering species pairs. The different flowering times within a day differ from those within a season because of the simultaneous opening and closing of the flowers for each species and the carry-over of the pollen from early to later times. In this study, we consider pollinator-mediated, diurnal- and nocturnal-flowering plants and build a new model to study the effects of the different flowering times within a day on reproductive isolation. We assume two loci, each with two alleles, which determine the opening and closing times of flowers, respectively. We numerically calculate the changes in the frequencies of the gametes in a model incorporating the reductions in hybrid viability, flowering costs, recombination rate and degree of dominance at each locus. We found that the early-opening flowers had a much higher fitness than the late-opening flowers and that the maintenance of the two species was difficult even if their flowering times were not overlapping. Therefore, some other mechanisms, such as pollinator preference, may be required to explain the coexistence of closely related diurnal and nocturnal flowers.