3

The bees have solved the problem of dividing a surface into regions of equal area with the least total perimeter (honeycomb conjecture) by trial and error. Are there any other examples of solutions of mathematical problems by biological evolution, or is there a field that studies this phenomenon?

This is conceptually similar to using a physical / mechanical approach (proofs), as described in The Mathematical Mechanic by Mark Levi.

I believe some machine learning algorithms are also conceptually similar.

curious_metazoan
  • 359

2 Answers2

2

One example, which I believe is fairly well known, is that various species of cicadas reproduce at periods of prime numbers (e.g., $13$ and $17$ for $2$ specific species) of years. As for the reasons for this, it's not completely known or understood, but Wikipedia's Predator satiation survival strategy section of their "Periodical cicadas" article says:

The emergence period of large prime numbers (13 and 17 years) was hypothesized to be a predator avoidance strategy adopted to eliminate the possibility of potential predators receiving periodic population boosts by synchronizing their own generations to divisors of the cicada emergence period.[16] Another viewpoint holds that the prime-numbered developmental times represent an adaptation to prevent hybridization between broods with different cycles during a period of heavy selection pressure brought on by isolated and lowered populations during Pleistocene glacial stadia, and that predator satiation is a short-term maintenance strategy.

Another example is how the Fibonacci numbers occur in nature in various ways. The Science article at How are Fibonacci numbers expressed in nature? explains various cases in some detail, especially on the second page, including how this also applies to honey bees.

John Omielan
  • 47,976
  • 1
    This is a great, example. Just to include the reference, numberphile also did a video on this that I thought explained it quite well. – Cade Reinberger Aug 06 '19 at 22:01
  • The first example is great. But what problem does a Fibonacci sequence solve? It appears to be arising just as a result of a procedure – curious_metazoan Aug 10 '19 at 16:11
  • 1
    @curious_metazoan You're right that in quite a few cases, the Fibonacci sequence likely occurs mainly as "just a result of a procedure". As the article says, it's not always obvious to what extent that is the case. However, as for what problems it does solve, the last $2$ sentences of the second last paragraph says "In other situations, the ratio exists because that particular growth pattern evolved as the most effective. In plants, this may mean maximum exposure for light-hungry leaves or maximum seed arrangement.". For at least those $2$ cases, this helped to solve a problem. – John Omielan Aug 10 '19 at 16:19
0

Another problem solved: is there a convex three-dimensional homogeneous body that when resting on a flat surface has just one stable and one unstable point of equilibrium?

The Indian star tortoise and two other turtle species evolved a Gömböc shaped shell: https://www.youtube.com/watch?v=rvVF5QWSYF4

curious_metazoan
  • 359