Murderous Maths

The Cicadas 17-year Life Cycle

In May 1987 billions and billions of Cicadas bugs swarmed all over North America. During a 5-6 week period they chirped, fed and most importantly bred, then they disappeared underground again.

A Cicadas is 50mm long
In May 2004 they're at it again!

The amazing thing is that the 17-year gap is no accident. The cicadas are using a prime number to avoid predators.

17 is a prime number. This means it doesn't divide by any numbers apart from 17 or 1.

Suppose you have a predator desperate to catch cicadas when they're out of the ground. Suppose the predator had a life cycle of e.g. 3 years, and the first year depended on eating cicadas. If the cicadas appeared e.g. every 6 years, then every 2nd generation of predators would be able to rely on eating them. Good news for the predators, but bad news for the cicadas.


At the peak of the 2004 swarming season...

  • There were about 10 trillion cicadas - that's 1,500 for every human on earth.
  • Their combined weight is almost double the weight of the entire population of the US.
  • They produce enough poo to fill 300 Olympic sized swimming pools every day.
  • At the height of the 2004 swarm there were about 100,000 cicidas per acre - which is about 25 for every square metre!
  • When they went they left behind about 500 trillion eggs. "In a single square mile of forest there could be as many eggs as there are stars in the Milky Way"
We read these facts in The Week May 2004
If the cicadas cycle was another number such as 14 years, then a predator with either a 2 year or 7 year life cycle could come to rely upon them within a reasonable number of generations. Therefore the cicadas rather cleverly decided to pick quite a large prime number of years between appearances.

Unless a predator adopted a life cycle of 17 years (or a multiple of 17 such as 34 or 51), then it will always be 17 generations before it can expect cicadas arriving.

Not surprisingly predators can't be bothered to wait.

Incidentally, there are also some 13-year cycle cicadas.

Cicadas swarming
How do they know when 17 years are up when they are underground in the dark?
Apparently they nibble on plant roots, and they can tell by the health of the roots what time of year it is and how many years have passed.

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