Synchronization of periodical cicada emergences.

Synchronized insect emergences are shown to be a possible consequence of predation in the presence of a limited environmental carrying capacity through a mathematical model for cicada populations that includes these two features. Synchronized emergences, like those observed in 13- and 17-year cicades, are predicted for insects with sufficiently long life-spans. Balanced solutions, in which comparable emergences occur each year, are found for insects having sufficiently short life-spans, such as 3-, 4-, and 7-year cicadas. For the values used here, synchronized emergences occur for insects with life-spans of 10 years or more, and balanced emergences occur for life-spans of fewer than 10 years.