TY - JOUR

T1 - Universal Evolutionary Model for Periodical Species

AU - Goles, Eric

AU - Slapničar, Ivan

AU - Lardies, Marco A.

N1 - Publisher Copyright:
© 2021 Eric Goles et al.

PY - 2021

Y1 - 2021

N2 - Real-world examples of periodical species range from cicadas, whose life cycles are large prime numbers, like 13 or 17, to bamboos, whose periods are large multiples of small primes, like 40 or even 120. The periodicity is caused by interaction of species, be it a predator-prey relationship, symbiosis, commensalism, or competition exclusion principle. We propose a simple mathematical model, which explains and models all those principles, including listed extremal cases. This rather universal, qualitative model is based on the concept of a local fitness function, where a randomly chosen new period is selected if the value of the global fitness function of the species increases. Arithmetically speaking, the different interactions are related to only four principles: given a couple of integer periods either (1) their greatest common divisor is one, (2) one of the periods is prime, (3) both periods are equal, or (4) one period is an integer multiple of the other.

AB - Real-world examples of periodical species range from cicadas, whose life cycles are large prime numbers, like 13 or 17, to bamboos, whose periods are large multiples of small primes, like 40 or even 120. The periodicity is caused by interaction of species, be it a predator-prey relationship, symbiosis, commensalism, or competition exclusion principle. We propose a simple mathematical model, which explains and models all those principles, including listed extremal cases. This rather universal, qualitative model is based on the concept of a local fitness function, where a randomly chosen new period is selected if the value of the global fitness function of the species increases. Arithmetically speaking, the different interactions are related to only four principles: given a couple of integer periods either (1) their greatest common divisor is one, (2) one of the periods is prime, (3) both periods are equal, or (4) one period is an integer multiple of the other.

UR - http://www.scopus.com/inward/record.url?scp=85118102667&partnerID=8YFLogxK

U2 - 10.1155/2021/2976351

DO - 10.1155/2021/2976351

M3 - Article

AN - SCOPUS:85118102667

VL - 2021

JO - Complexity

JF - Complexity

SN - 1076-2787

M1 - 2976351

ER -