Why Periodical Cicadas Picked 13 and 17

Seven species in the genus Magicicada spend almost their entire lives underground, sucking xylem from tree roots. Then, in a single synchronized year, an entire brood pushes up through the soil at densities that can exceed 1.5 million individuals per acre, sings, mates, lays eggs, and dies inside about six weeks. The interval between emergences for any given brood is either exactly 13 years or exactly 17 years.

Those are both prime numbers, and that is the heart of the question. A predator on a 2-, 3- or 4-year boom-bust cycle would see a 12-year cicada emergence frequently. A 13-year cicada, by contrast, only collides with a 2-year predator every 26 years, with a 3-year predator every 39, and so on. Prime intervals are mathematically the worst possible target for any predator that needs a periodic life cycle of its own.

The density does the rest of the work. Even with full predator stomachs, there are simply too many cicadas to eat in one summer. Birds, snakes, raccoons and small mammals gorge for a few weeks; the surplus mates and seeds the next generation. Ecologists call this predator satiation, and it only works if the emergence is tight.

Which is where 13 and 17 do their second job. Hybrids between a 13- and a 17-year brood would emerge off-cycle and hit the ground in tiny numbers, exposing them to predators with no satiation help. Mathematical models published in PNAS and Scientific Reports show this Allee effect — small populations dying faster than they can reproduce — selects against any non-prime cycle. The two surviving cycles share a year only once every 221 summers, which is exactly the rate at which the math says hybrids are erased.