Periodical cicadas: a minimal automaton model
  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. 
Giovano de O. Cardozo, Daniel de A. M. M. Silvestre, Alexandre Colato