Life cycle replacement by gene introduction under an allee effect in periodical cicadas

Periodical cicadas (Magicicada spp.) in the USA are divided into three species groups (-decim, -cassini, -decula) of similar but distinct morphology and behavior. Each group contains at least one species with a 17-year life cycle and one with a 13-year cycle; each species is most closely related to one with the other cycle. One explanation for the apparent polyphyly of 13- and 17-year life cycles is that populations switch between the two cycles. Using a numerical model, we test the general feasibility of life cycle switching by the introduction of alleles for one cycle into populations of the other cycle. Our results suggest that fitness reductions at low population densities of mating individuals (the Allee effect) could play a role in life cycle switching. In our model, if the 13-year cycle is genetically dominant, a 17-year cycle population will switch to a 13-year cycle given the introduction of a few 13-year cycle alleles under a moderate Allee effect. We also show that under a weak Allee effect, different year-classes ("broods") with 17-year life cycles can be generated. Remarkably, the outcomes of our models depend only on the dominance relationships of the cycle alleles, irrespective of any fitness advantages.