Illustration of the individual-based model (IBM).
(a) Image of the accumulated temperature. The area in green above Tthre represents growth based on accumulated temperature. When the sum of accumulated temperature (Taccume) reaches the threshold amount for maturation (Tmature), the non-periodical cicadas emerge. (b) Simulation flow. The variable Tthre is defined as the temperature threshold of individual cicada i, such that if Tt ≤ Tthre,i (for some t), then Tmature,i is fixed, resulting in a longer time of emergence. An individual cicada nymph i(t) emerges at time t if Taccume,i(t−1) ≥ Tmature. If Taccume,i(t−1) < Tmature, a nymph cannot emerge the next year. Illustration by Yoshihiko Ishimori.