Evolutionary Maths

by Jack Dry

Maths in nature seems slightly unnatural to me. Shouldn’t nature be free from the same maths which has been used to design carbon dioxide belching factories, noisy cars and nuclear bombs? So, when I first learnt that there was maths ingrained in nature, it confirmed my hunch that maths really was everywhere.

Cicadas are insects. More specifically they are locust-like insects which have red eyes and are a wooden brown colour. Their colouring is clever since it allows them to blend into the trees which they peacefully sit on. This makes it more difficult for predators to see them and so they are eaten less often. Coincidentally, this is why a large proportion of insects are darker, tree-like, colours. This is called an adaptation. An adaptation is where an organism has changed over time to become more suitable for the environment in which it lives. Adaptations are a product of natural selection, the phenomenon which Darwin coined. Although their colouring is a clever adaptation, it’s by far their finest.

Before explaining the genius behind the cicada’s development cycle, it is necessary to clarify what a prime number is. A prime number is a number which is only divisible by itself and one. Take the number 5, for example. In making a rectangle with five beads the only way it is possible is if they were arranged into a straight line. This is a trait of prime numbers. If you had six beads, however, a rectangle could be made from two columns of 3 next to each other or a straight line of six beads. Therefore the number six is not a prime number. 

Now I shall act as Gauss’ lens and convey the mathematical genius of the cicadas. All organisms have a period in which they develop. During this period, very few of the organisms inhabit their typical environment, if any at all.  They are undergoing a period of development where they are preparing to swarm the lands in vast numbers, albeit for a very short period of time. The cicada’s period of development is a rather lengthy seventeen years. All insects also have predators. The cicada’s predator is typically the aptly named cicada killer wasp. The wasp’s period of development is four years. This means that only every 68 years will the wasps and cicadas occupy the same environment. Only every 68 years will the cicadas be killed by the wasps. If the cicada’s period of development was two years less - 16 years - the cicadas would be eaten by the wasps every time they developed. If this were the case then the cicadas would quickly become extinct. In this way the cicadas are able to survive and reproduce more successfully with a prime number period of development- the aim of all organisms.

The mathematics in evolution would remain obliquely hidden behind the scenes had it not been for a small Brazilian research group. It is likely that there are millions of other phenomenon with maths ingrained in it, like in this example, which is why, if we want to understand our world better, we have to make a huge effort to promoting the study of mathematics.