Cicadas

The periodical cicada is one of the world’s longest-living insects, but nobody knows why it times its death with bizarre precision: It either lives for 13 years or 17 years, on the dot. Now, Japanese researchers have developed a model that may explain the animals’ mysteriously accurate biological clocks.

The noisy winged critters spend more than 99 percent of their 13 or 17 years as juveniles, sucking on roots in underground lairs. In the summertime, they crawl out en masse — up to 40,000 can emerge from under a single tree within days. Their subterranean tenures are intriguing not only because 13 and 17 years are long periods over which to remain synchronized, but also because both numbers are prime — divisible only by themselves and the number 1.

“Their life cycles have been suspicious since the beginning,” said John Cooley, who collaborated on the research with researchers in Japan. “It’s a surprising and unique combination of a long life cycle and mass emergence. And on top of that, why do they have to be prime? [This study] ties that all together.”

A leading theory is that long, prime-numbered life cycles minimize the likelihood that the 13-year broods and 17-year broods will ever mate. If the animals lived smaller prime-numbered lives, like 5 and 7, they’d synch up every 35 years; if their lifespans were large, non-prime numbers, like 12 and 16 years, they might inadvertently mate every 48 years. But the large prime numbers 13 and 17 only match up every 221 years.

Though this theory is mathematically sound, no one could say why the animals would need to minimize hybridization, so Jin Yoshimura at Shizuoka University developed a mathematical model to explore the rationale. He thought if 13-year and 17-year broods interbred, they might produce offspring with intermediate lifecycles — for example 15 years. This would result in their emergence two years before or after the vast majority of their fellow cicadas.

This is a problem, Cooley said, because periodical cicadas find strength in numbers. They’re easy to catch and don’t bite or sting, so they easily become snacks for hungry predators. But by buzzing around with hundreds of thousands of other cicadas, the probability of any one being eaten is close to zero.

Yoshimura’s model shows that this negative consequence of hybridization could explain the prime life cycles. In his model, which starts with all possible life cycles, the only way to arrive at enduring 13- and 17- year life cycles is to include this density-dependent effect. The findings were published May 18 in the Proceedings of the National Academy of Sciences.

Mathemetician Glenn Webb of Vanderbilt University says the explanation is reasonable, but that there are other alternatives. “Our hypothesis is that cicada emergences minimize overlap with the periodic cycles of their predators, like birds and small animals, which are 2 to 5 years,” he said. “By choosing prime number, through evolution, cicadas avoid meshing with these shorter cycles.”

Webb also mentioned another hypothesis: that the prime numbers are coincidental, and not significant at all.

Cooley acknowledges the model made a number of assumptions, as the difficulty of studying cicadas leaves many mysteries around their biology and evolution. For example, it isn’t known whether hybridization actually produces offspring with intermediate lifecycles. And currently, the 13-year and 17-year broods’ habitats do not overlap, so they don’t have a chance to interbreed in present day — though their distribution has likely changed since they first diverged.

“This explores the plausibility of this idea, to help understand the problem cicadas have when they get to a low population density,” said Cooley. “This is the first explicit mathematical treatment of this problem.”

Citation: “Allee effect in the selection for prime-numbered cycles in periodical cicadas” by Yumi Tanaka, Jin Yoshimura, Chris Simon, John R. Cooley, and Kei-ichi Tainaka. PNAS, May 18 2009.