Evolutionary Hysteresis and Ratchets in the Evolution of Periodical Cicadas

It has been previously hypothesized that the perfectly synchronized mass emergence of periodical cicadas (Magicicada spp.) evolved as a result of a switch from size-based to age-based emergence. In the former case, cicada nymphs emerge immediately (at the first opportunity) on reaching maturity, whereas in the latter case, nymphs wait in order to emerge at a specific age. Here we use an individual-based model to simulate the cicada life cycle and to study the evolution of periodicity. We find that if age-based emergence evolves in a constant abiotic environment, it typically results in a population that is protoperiodic, and synchronous emergence of the whole population is not achieved. However, perfect periodicity and synchronous emergence can be attained, if the abiotic environment changes back and forth between favorable and unfavorable conditions (hysteresis). Furthermore, once age-based emergence evolves, generally it can only be invaded by other age-based emergence strategies with longer cycle lengths (evolutionary ratchet). Together, these mechanisms promote the evolution of long periodic life cycles and synchronous emergence in the Magicicada. We discuss how our results connect to previous theories and recent phylogenetic studies on Magicicada evolution.