Background: Periodical cicadas (Magicicada spp.) have a life cycle that ends with the entire underground nymph population exhibiting a synchronized mass emergence to mate above ground. Previous studies have hypothesized that the periodical cicadas evolved from non-periodical cicadas by switching from a life-cycle length determined by body size to one determined by age. Questions: When can a mutation coding for fixed life-cycle length invade a resident population in which life-cycle length is variable? What determines the length of the fixed cycle? Methods: Numerical analysis of a mathematical model and simulations of an individual-based model. Results: If there is a sufficiently strong predation intensity affecting the pool of individuals emerging to reproduce, a non-periodical population may become proto-periodical such that reproductive success varies yearly. Then, an emergence strategy with a fixed life-cycle length targeting years of high emergence density can invade. © 2018 Jaakko Toivonen