Cicadas emerge after a prime time. Credit: © SPL

Bob Dylan immortalized the rare appearance of periodic cicadas in his 1970 song Day of the Locusts. But he may not have realized that he was honouring a mathematical event as well as a biological one.

Periodic cicadas emerge from their underground homes to mate every 13 or 17 years. Both of these numbers are prime - they can only be divided by one. Evolution could have selected for appearance in prime cycles, a new model suggests1.

The notion is simple: cicadas with prime cycles coincide with their predators and parasites less often. "The philosophy is that if cicadas have 12-year cycles, all the predators with two, three, four, and six-year cycles will eat them," says Mario Markus, a physicist at the Max-Planck Institute for Molecular Physiology, who led the study. "If the cicadas mutate to 13-year cycles, they will survive."

Now a mathematical model created by Markus' team shows that cicadas naturally evolve such cycles. Cicadas were assigned a random fitness score on the basis of cycle length and the frequency with which they encountered competitors. Over time, cycle length evolved until the cicadas hit a prime number, they found.

The model assumes that in the past there were cicada predators and parasites that became extinct though a lack of the insects. "It's a bold assumption," says Markus. Evidence of such a creature would give the model a boost.

An ancient wasp is one hypothetical parasite. The wasp couldn't lengthen its life cycle to keep up, explains Christine Simon, who studies cicadas at the University of Connecticut in Storrs, "so the periodical cicada outran it in time". But the idea is highly speculative, as fossil records of the wasp have never been found.

Why cicadas evolved such long cycles is also unexplained, says Simon. A long cycle seems to be a disadvantage, as the population would grow more slowly than that of competitors who reproduce more often.

The idea that prime cycles exist to evade predators has been around for a while, says Sir Robert May, a zoologist at the University of Oxford, but no one could understand how they evolved. "This new work is an interesting contribution," he says.

Markus' model has an unexpected spin-off: it is a machine for generating prime numbers. Large primes are rare and difficult to find, but starting with any cycle length, the evolutionary model drives it towards one. Although the model is not as efficient as some prime-locating methods, its biological source makes it unique, says Markus. "This bridges the gap between biology and number theory," he says.