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Allee effect in the selection for prime-numbered cycles in periodical cicadas

Tanaka, Yumi, Yoshimura, Jin, Simon, Chris, Cooley, John R., Tainaka, Kei-ichi
Proceedings of the National Academy of Sciences of the United States of America 2009 v.106 no.22 pp. 8975-8979
life cycle (organisms), Magicicada, population dynamics, natural selection, phenology, mathematics and statistics, mathematical models
Periodical cicadas are well known for their prime-numbered life cycles (17 and 13 years) and their mass periodical emergences. The origination and persistence of prime-numbered cycles are explained by the hybridization hypothesis on the basis of their lower likelihood of hybridization with other cycles. Recently, we showed by using an integer-based numerical model that prime-numbered cycles are indeed selected for among 10- to 20-year cycles. Here, we develop a real-number-based model to investigate the factors affecting the selection of prime-numbered cycles. We include an Allee effect in our model, such that a critical population size is set as an extinction threshold. We compare the real-number models with and without the Allee effect. The results show that in the presence of an Allee effect, prime-numbered life cycles are most likely to persist and to be selected under a wide range of extinction thresholds.