  The Magicicada spp. life cycles with its prime periods and highly
synchronized emergence have defied reasonable scientific explanation since its
discovery. During the last decade several models and explanations for this
phenomenon appeared in the literature along with a great deal of discussion.
Despite this considerable effort, there is no final conclusion about this long
standing biological problem. Here, we construct a minimal automaton model
without predation/parasitism which reproduces some of these aspects. Our
results point towards competition between different strains with limited
dispersal threshold as the main factor leading to the emergence of prime
numbered life cycles.
