Ah OK, the full explanation is in the linked paper: The present work is based on the hypothesis that the cycle length is a prime number in order to optimally e

Ah OK, the full explanation is in the linked paper: The present work is based on the hypothesis that the cycle length is a prime number in order to optimally escape predators. For example, a prey with a 12-year cycle will meet—every time it appears—properly synchronized preda- tors appearing every 1, 2, 3, 4, 6 or 12 years, whereas a mutant with a 13-year period has the advantage of being subject to fewer predators. So it has to do with the number of available (different) predators, because their populations also go through cycles. Link: http://www.cims.nyu.edu/~eve2/predprey.pdf http://www.cims.nyu.edu/~eve2/predprey.pdf