Periodical Cicadas

With a length of approximately one inch (2.5 cm) and a wingspan of three inches (7 cm), cicadas are a feast for many predators. When they emerge, they face predation from various animals. However, their sheer numbers mean that even if many are consumed, enough remain to ensure the continuation of their species.

What's particularly fascinating about periodical cicadas is their mathematical defense against predators. Their life cycle is nothing short of extraordinary. As entomologist Joe Ballenger from the University of Wyoming explains:

"The life cycle of periodical cicadas begins in the trees. Parents lay eggs on tree branches, and the young hatch and burrow down to the roots, where they feed on tree sap until they mature."

Interestingly, the broodlings develop at different rates underground. If one were to dig for cicada nymphs a decade after they burrowed, they would discover nymphs of various sizes and stages. However, by year 16, all cicada nymphs reach the same developmental stage. Remarkably, the faster-developing nymphs seem to wait for the slower ones to catch up.

When the soil temperature reaches 64°F (17.8°C) in year 17, they emerge, filling the air with their calls and clumsily flying around, seeking mates. This synchronized emergence is a survival strategy known as predator satiation, where the sheer volume of cicadas ensures that some will survive to reproduce.

With only a few weeks to mate and reproduce before dying, they are driven by instinct. After 17 years of dormancy, they are eager to find companionship. So, if you're nearby during their emergence, you might want to cover your drink and find some shelter!

Choosing a prime number as their cycle length has evolutionary advantages. Many birds, for instance, do not live long enough to adapt their hunting skills to cicadas' periodicity. Thus, cicadas cleverly evade potential predators.

Understanding Prime Numbers

Prime numbers hold a significant place in mathematics. Defined as numbers greater than 1 that can only be divided by 1 and themselves, they cannot be evenly distributed into multiple groups. For example, 101 is a prime number, as it cannot be arranged into equal groups.

The sequence of prime numbers begins with 2, 3, 5, 7, 11, and has intrigued mathematicians since ancient Greece. Euclid demonstrated that there are infinitely many primes, utilizing a clever technique known as "proof by contradiction."

Despite centuries of study, prime numbers were not initially connected to practical applications. That changed with the advent of the internet, where secure communication relies on prime numbers and cryptography. While Euclid didn't foresee this application, it highlights the importance of fundamental research.

The Role of Mathematics in Cicada Survival

Interestingly, there are cicadas with a 13-year cycle. So, why do they opt for prime numbers like 17 instead of higher numbers like 18? To comprehend this choice, we need to consider the cicadas’ strategy against cyclic predators.

If a predator had an 8-year cycle, cicadas with an 18-year period would encounter it every 72 years. However, by choosing a 17-year cycle, they avoid the predator for 136 years. The goal is to maximize the least common multiple (LCM) between their cycle and that of any potential predators, while keeping their cycle length manageable.

Primes are advantageous in this context. For any prime number p, the LCM between n and p equals np. This property allows cicadas to extend the time between encounters with predators.

As for the 17-year brood, known as Brood X, they emerged in 1987—the year I was born. Coincidentally, they appear in years that are multiples of 17, serving as a memorable connection.

If you have any questions or thoughts, feel free to reach out to me on LinkedIn:

Kasper Müller - Senior Consultant, Data and Analytics, FS, Technology Consulting - EY | LinkedIn

Programming, mathematics, and teaching are among my passions. Data science, machine learning, and programming are my fields of interest.

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