Seth Nickell

Apparently, according to an article in the Economist, cicadas have prime-numbered life cycles of 17 or 13 years. Simplistically, when the number of prey increase after some time lag the number of predators increases, driving the number of prey down, resulting in equalibrium. Call this smoothly varying population. Prey that have a cycle where you spike every n years rather than smoothly varying have a leg up on a smoothly varying predator. When cicadas bloom there is a number of predators appropriate to no cicada. They reproduce before predator numbers rise, and then disappear. Effectively non-smoothly varying popultions can avail of the time lag before predator numbers rise to match prey.

This results in selection pressure for predators that have the same length of cycle as the prey. While same length is perfect, a predator cycle that is a factor of the prey length will also work. E.g. if prey has a cycle of 6 years, a predator with a cycle of 3 years can still arise in numbers to consume the prey. So the problem, from the predator phenotype’s non-existantperspective is to guess (through random mutations, etc) the cycle length that overlaps most frequently with the prey. Factors of the prey’s cycle length will, of course, overlap more frequently. The best length the largest factor of the prey’s cycle length, namely the prey’s cycle length itself. (As an aside, interesting abstract algebra connections with cyclic groups, etc.)

From the prey phenotype’s non-existant perspective: It now becomes an information hiding game. Given a cyclic group of order t (constant time between cycles), how do we minimize the overlap with groups of all other orders? The answer is choose a large t with the fewest factors, i.e. to choose a long cycle that is also a prime number. Cicada’s long prime cycles are a very rudimentary form of encryption to keep random mutations in predators from “guessing” a compatible cycle length. Cool!

Now of course, using a non constant function for time_between_cycles(cycle_number) would work even better. And in some sense Cicadas have that too by having two different cycle lengths. According to the economist article populations have even been observed shifting from a 17 year to a 13 year cycle in response to selection pressures caused by a fungus that developed a 17 yeard cycle.