Periodical cicadas are enigmatic organisms: broods spanning large spatial ranges consist of developmentally synchronized populations of 3-4 sympatric species that emerge as adults every 13 or 17 years. Only one brood typically occupies any single location, with well-defined boundaries separating distinct broods. The cause of such synchronous development remains uncertain, but it is known that synchronous emergence of large numbers of adults in a single year satiates predators, allowing a substantial fraction of emerging adults to survive long enough to reproduce. Competition among nymphs feeding on tree roots almost certainly plays a role in limiting populations. However, due to the difficulty of working with such long-lived subterranean life stages, the mechanisms governing competition in periodical cicadas have not been identified. A second process that may affect synchrony among periodical cicadas is their ability to delay or accelerate their emergence as adults by 1 year and accelerate it by 4 years (stragglers). We develop a nonlinear Leslie matrix-type model that describes cicada dynamics accounting for predation, competition, and stragglers. Using numerical simulations, we identify conditions that generate dynamics in which a single brood occupies a given geographical location. Our results show that while stragglers have the potential for introducing multiple sympatric broods, the interaction of interbrood competition with predation-driven Allee effects creates a system resistant to such invasions, and populations maintain developmental synchrony.
Keywords: Allee effect; Leslie matrix; competitive exclusion; synchrony.