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Emergence of Prime Numbers as the Result of Evolutionary Strategy

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Posted by: Richard Phillips

A recent paper is:

Emergence of Prime Numbers as the Result of Evolutionary Strategy, Phys. Rev. Lett.

Excerpts: We investigate by means of a simple theoretical model the emergence of prime numbers as life cycles, as those seen for some species of cicadas. The cicadas, more precisely the Magicicadas, spend most of their lives below the ground and then emerge and die in a short period of time. The Magicicadas display an uncommon behavior: their emergence is synchronized and these periods are usually prime numbers. In the current work, we develop a spatially extended model at which preys and predators coexist and can change their evolutionary dynamics through the occurrence of mutations. We verified that prime numbers as life cycles emerge as a result of the evolution of the population. Our results seem to be a first step in order to prove that the development of such strategy is selectively advantageous, especially for those organisms that are highly vulnerable to attacks of predators.

Emergence of Prime Numbers as the Result of Evolutionary Strategy, Paulo R. A. Campos, Viviane M. de Oliveira, Ronaldo Giro, Douglas S. Galvão, Phys. Rev. Lett. 93, 098107, 04/08/27



My understanding of this is that if different species compete for a resource, and each species needs that resource only periodically then a given species is less likely to conflict with others if the time cycle on which it needs the resource is relatively prime (as in number theory) to the time cycles of the other species. Therefore it is advantageous that that time cycle be a (reasonably large) prime number.

Perhaps this is an example of a simple program (that does a simple thing) being evolved.


Posted by: Ned Porter

Interesting.

Another possible theory that might be the evolution of a simple program is to avoid cold mating seasons:

Washington Post, May 3, 2004 p A08:
"Randel T. Cox of the University of Memphis and C.E. Carlton of the University of Arkansas calculated the odds of survival of populations of cicadas of different life-cycle lengths over a 1,500-year period in which 1 of every 50 summers was fatally cold. Cicadas with six-year life cycles had a 4 percent chance of surviving. Those with an 11-year cycle had a 51 percent chance. Those with a 17-year cycle had a 96 percent chance."

The other thing I find interesting about these bugs is that the broods do not overlap, except in some small areas, geographically.

http://www.cicadas.info/m.htm

Hope this helps


Posted by: Jason Cawley

Seems unlikely it is just a "2% cold" effect. That would favor a longer cycle without much regard for its number theoretic properties - yes 17 would be better than 11, but 18 or 25 would also be better than 17. You are just taking fewer chances over the 1500 year fixed period.

Favoring primes will come only from interacting cycles, "striking out" common factors. Whereas an 18 year cycle would often "hit" a competitor with a 2, 3, or 6 year cycle repeatedly, a 17 year cycle would "hit" them only on multiples of both. Note that the interaction need not come from a predator. Another species that competes for the same resources would suffice.


Posted by: Ned Porter

>Note that the interaction need not come from a predator. Another species that competes for the same resources would suffice.

An important point, Thanks Jason.

Everything was eating 17-year cicadas: birds, snakes, dogs, cats, even some humans. Their survival depends on their numbers (over a million per acre--an estimated one trillion emerged this year!).

The species that it may have competed with was probably non-prime cicadas.

ned




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