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COMPUTING SCIENCE

Bugs That Count

Brian Hayes

Primes and Other Conundrums

One factor not addressed by the models I have described so far is feedback from prey to predator species. In an emergence year, birds that feast on cicadas should be able to raise more young than usual; the resulting increase in predator numbers will make life even harder on straggler cicadas the following year, thus sharpening the population peak. Many authors have drawn attention to this linkage, and have offered it as the key to understanding why the Magicicada species chose prime numbers for their life–cycle periods. Because a prime has no divisors other than itself and 1, the cicadas avoid falling into resonance with predators whose abundance fluctuates on some shorter cycle. For example, a hypothetical 12–year cicada would be susceptible to predators with cycle lengths of 2, 3, 4 or 6 years.

G. F. Webb of Vanderbilt University has constructed computer simulations in which such interactions of prey and predator cycles favor the 13–year and 17–year cicada periods. Eric Goles of the University of Chile and Oliver Schulz and Mario Markus of the Max–Planck Institut für molekulare Physiologie in Dortmund, Germany, have also published on this subject, referring to cicadas as "a biological generator of prime numbers." Whether the cyclic predator species exist remains an open question. And some quite different explanations have also been put forward. For example, Randel Tom Cox of Arkansas State University and C. E. Carlton of Louisiana State University argue that the heart of the matter is not predation but hybridization. Interbreeding between broods that differ in period could disrupt synchronization for both groups. Thus 13–year and 17–year broods are favored because they emerge together only once every 221 years.

Much else about the lives of cicadas remains mysterious. In the 1960s Monte Lloyd of the University of Chicago and Henry S. Dybas of the Field Museum of Natural History in Chicago offered a curious meta–theory of cicada evolution. Any theory that seems too plausible, they argued, is automatically suspect. "If there were a broad, easy evolutionary highway towards periodicity, then why would not more species have taken it?"

If one day we run out of cicada mysteries to solve, there are still harder problems waiting. Synchronized, periodic breeding is known in plants as well as animals. Daniel H. Janzen of the University of Michigan has written about the bamboo Phyllostachys bambusoides, which apparently maintains synchronized flowering even when seeds are planted continents apart. And the length of the plant's period makes the cicadas seem as ephemeral as mayflies. The bamboo knows how to count not just to 17 but to 120.

© Brian Hayes




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