In the spring of 2024, two enormous populations of periodical cicadas emerged simultaneously from the soil across the eastern and midwestern United States for the first time since 1803. Brood XIX, a 13-year cicada population concentrated across the Southeast, surfaced in 13 states from Oklahoma to North Carolina. Brood XIII, a 17-year population centred on the Midwest, surfaced in Illinois, Iowa, Wisconsin, and Indiana. Together, the two broods comprised trillions of individual insects emerging within a span of weeks, mating, laying eggs in tree branches, and dying — with the next generation of nymphs falling to the ground, burrowing underground, and beginning the 13- or 17-year wait until the next emergence. The two broods will not co-emerge again until 2245.
The most striking feature of the periodical cicada’s life cycle is not its length, which is exceptional in itself for any insect, but the specific numbers involved. Periodical cicadas of the genus Magicicada come in two flavours: those with 13-year cycles and those with 17-year cycles. Both 13 and 17 are prime numbers — integers divisible only by themselves and one. According to a 2024 analysis in The Conversation of the mathematical structure underlying the cicada emergence pattern, this is widely considered to be one of the few examples in nature where the mathematical property of primality itself appears to have direct evolutionary consequences.
Why prime numbers matter
The leading explanation for the prime-numbered cicada cycles is predator avoidance, an idea first formally proposed by entomologists Monte Lloyd and Henry Dybas in a 1966 paper and popularised by the evolutionary biologist Stephen Jay Gould in a 1977 essay. The reasoning is straightforward. Suppose that cicada predators — birds, small mammals, wasps, parasitic fungi — have life cycles of 2, 3, 4, 5, 6, or 7 years. A cicada population emerging on a 12-year cycle would coincide with the peak abundance of predators with 2-, 3-, 4-, and 6-year cycles, because 12 is divisible by all of those numbers. A cicada population emerging on a 14-year cycle would coincide with 2-year and 7-year predator cycles. A 15-year cicada population would coincide with 3-year and 5-year predator cycles. A 16-year population would coincide with 2-, 4-, and 8-year cycles.
A 13-year or 17-year cycle, by contrast, is divisible only by 1 and itself. The lowest common multiple of a 13-year cicada cycle and a 2-year predator cycle is 26 years. The lowest common multiple of a 17-year cicada cycle and a 5-year predator cycle is 85 years. Each emergence of a periodical cicada population is therefore extremely unlikely to coincide with the peak abundance of any short-cycled predator. Over the millions of years across which cicadas have been evolving, populations whose cycle lengths happened to be prime numbers would have suffered systematically lower predation than populations whose cycles were divisible by small numbers, and over enough generations the prime-numbered populations would have dominated.
The mathematical elegance of the argument is what makes the cicada example unusually compelling. There are few cases in evolutionary biology where the trait under selection corresponds to such a clean mathematical concept. The cicadas are not selecting for “long life cycle” in general; they are selecting specifically for life cycle lengths that are coprime with the cycle lengths of every nearby predator species. Primality, in this account, is essentially a mathematical proxy for “maximally coprime.”
The hybridization hypothesis
The predator-avoidance hypothesis is not the only explanation that has been proposed. According to an Anthropocene Magazine review of alternative models of cicada evolution, a competing explanation developed by the Japanese mathematical biologist Jin Yoshimura in the 1990s holds that prime-numbered cycles emerge from selection against hybridization, rather than from selection against predators. The hybridization model focuses on what happens when two cicada populations with different cycle lengths emerge in the same year and interbreed. The hybrid offspring inherit intermediate cycle lengths that are unlikely to be synchronised with either parent population, breaking the synchronised mass emergence that is itself essential to the cicada’s survival strategy.
If cicada populations of different cycle lengths interbreed frequently, the resulting hybridization erodes the synchronisation that mass emergence depends on. Prime-numbered cycles are the cycles that, mathematically, have the lowest probability of simultaneous emergence with cycles of other lengths. A 17-year and a 13-year population only co-emerge once every 221 years (the product of the two primes). A 14-year and a 16-year population, by contrast, would co-emerge every 112 years (their lowest common multiple), substantially more often. The hybridization model and the predator-avoidance model are not mutually exclusive, and many cicada researchers now consider both forces to have contributed to the evolution of prime-numbered cycles, with the relative importance of each being a subject of continued research.
The other half of the strategy
The prime-numbered cycle is only one part of how periodical cicadas survive being eaten. The other part is mass emergence at densities so extreme that predators cannot consume more than a small fraction of the cicada population. According to the University of Wisconsin Insect Research Collection’s reference page on periodical cicadas, peak emergence densities can exceed 1.5 million cicadas per acre, with billions or trillions of individuals appearing in a brood’s range over a span of a few weeks. The local birds, mammals, and predatory insects in any given habitat can consume only so much. Most of the cicada population survives long enough to mate and lay eggs precisely because the predators are saturated within the first few days of emergence and the remaining cicadas, however slow-moving and conspicuous, are essentially ignored.
The mass-emergence strategy is called “predator satiation,” and it is a common defensive pattern in nature. What makes the cicada case unusual is the combination: predator satiation plus prime-numbered cycles. The mass emergence ensures that any given emergence overwhelms whatever predators happen to be present. The prime-numbered cycle ensures that predator populations cannot grow specifically to exploit cicada emergences, because the predator generations cannot reliably synchronise with the cicada generations. Each defence reinforces the other. A cicada population emerging in massive numbers every 12 years would still face heavy predation from predators whose populations had built up over the intervening years specifically to exploit the cicada emergence. A cicada population emerging in massive numbers every 17 years cannot be tracked by any predator with a shorter cycle.
What the cicadas tell us
The periodical cicada is a comparatively recent topic in evolutionary biology, having been formally described as a distinct biological phenomenon only in the 19th century. The brood numbering system used today was created by the entomologist Charles Lester Marlatt in 1907, who assigned Roman numerals to each known year-class of periodical cicadas. There are now 15 named broods of Magicicada — 12 with 17-year cycles and 3 with 13-year cycles — distributed across the eastern half of the United States, with each brood emerging in a different year. According to Atlas Obscura’s coverage of the 2024 emergence, the seven recognised species of Magicicada distribute themselves across these broods in various combinations, with multiple species often co-emerging within a single brood’s range.
What the cicadas offer, beyond their immediate biological interest, is one of the cleanest cases in nature where a mathematical concept — primality — appears to have a direct evolutionary cause. Most of the patterns of life on Earth do not map neatly onto mathematical concepts. The branching patterns of trees, the curves of seashells, the spacings of stripes on animals all involve mathematics, but the math involved is typically continuous geometry rather than the discrete, integer-based mathematics of primes. The cicadas, by contrast, are doing arithmetic. Their life cycle lengths are integer numbers of years, the predator life cycles they need to avoid are integer numbers of years, and the relationship between the two reduces to the question of common divisors. The cicadas have evolved a strategy whose effectiveness depends on a mathematical property — primality — that humans recognised and named only a few thousand years ago, but that has been guiding the evolution of cicada life cycles for millions of years longer than that. The mathematics in this case is not a description of biology imposed by human observers. It is, in the most concrete sense available, the thing biology has been selecting for.
