Demystifying Prime Number Cicadas
In the eastern region of North America lives a truly remarkable species of insect. What really strikes this species as unique has got little to do with the insect’s morphology, but rather its exceptional life cycle. The Magicicada is a genus of periodical cicada which spends the majority of its life underground for durations of either 13 or 17 years, called their 𝘦𝘮𝘦𝘳𝘨𝘦𝘯𝘤𝘦 𝘱𝘦𝘳𝘪𝘰𝘥, where they will then emerge to reproduce and die after only about two weeks spent on the surface. You might be wondering why the magicicada would wait for so long, and more curiously, why do these emergence periods happen to be prime numbers?
For the uninitiated, a prime number is any integer larger than 1, and is only divisible by 1 and itself. For example 7 is a prime number, since 7 can’t be divided by anything other than 1 and 7, so we’ll use 7 in a later example. As a result, the list of prime numbers below 20 are : 2,3,5,7,11,13,17, and 19.
This begs the question: why do magicicadas spend their lives underground for only prime number of years? (13 and 17). Do these insects have the ability to count? No, the real explanation is actually a clever result of Evolution by Natural Selection. Here’s why :
The cicada’s natural predators (i.e birds and wasps) have shorter life cycles than the cicada (roughly 3 or 4 years respectively), and for every 3 or 4 years the predators will come out to hunt. If the cicada has a life cycle of say 12 years (not prime), then a predator with a 3-year life cycle will hunt the cicadas in every fourth generation (3 x 4 = 12). The predators with 4-year life cycles will hunt the cicadas in every third generation (4 x 3 = 12). The same applies to predators with 2-year life spans, feasting on cicadas every sixth generation (2 x 6 = 12).
So how could the cicadas avoid being eating each time they emerge? The solution : wait underground for any prime number of years.
Why prime numbers? Because only prime numbers won’t ‘overlap’ with the life cycle of any potential predators. For example, if a cicada has a 13-year life cycle, then any predators with life cycles between 2 to 12 years will miss the window for hunting cicadas, since 13 is not divisible by anything other than 1 and 13. So if a predator has say, a 6 year cycle, it will miss the cicadas with 13 year life cycles, since 6 x 2 = 12 and 6 x 3 = 18. The second generation of the predators will be too early by a year, and the third generation will be too late by five years. Only the cicadas with 13 and 17-year life cycles will avoid being ‘overlapped’ by potential predators.
You might also be wondering, why are only the relatively large primes chosen (13 and 17) instead of smaller primes like 3, 5 or 7? The answer is that different cicada species are not allowed to meet, or else there would be excessive competition for food resources as well as confusion that would arise during mating season. As it turns out, the 13 and 17-year cicadas are actually different species. If one species emerges every 13 years, and another every 17 years, then these two species will only overlap every 221 years (13 x 17), which is a considerably long period of time. Now, consider if the periods were 3 and 5 years. The overlapping period would now be only 15 years, which is a relatively short amount of time. This is bad for the cicadas, which have thus adapted for longer life cycles.
In conclusion, we now have an explanation for the apparent ‘intelligence’ that appears in magicicada life cycles, and as to why their emergence periods tend to be prime numbers. Turns out there is no actual intelligence involved, but rather the unique circumstances in the cicadas’ ecosystem, coupled with the self-adjusting hand of natural selection, had managed to produce a clever defense mechanism that is rather unique in the animal world.
𝐅𝐮𝐫𝐭𝐡𝐞𝐫 𝐫𝐞𝐚𝐝𝐢𝐧𝐠 :
http://www.abc.net.au/science/articles/2001/11/27/421251.htm
