Abstract
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.
Highlights
Life-history diversity is a remarkable feature of living species and underlies fundamental evolutionary questions [1]
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. e periodicity is caused by interaction of species, be it a predator-prey relationship, symbiosis, commensalism, or competition exclusion principle
By analyzing the ecological factors that shape development, reproduction, and survival, the life-history theory seeks to explain the evolution of the major features of life cycles [21]
Summary
Life-history diversity is a remarkable feature of living species and underlies fundamental evolutionary questions [1]. Some authors have proposed a very simple model for cicadas prime life cycles by assuming the existence of a periodical predator [20]. In this context, it was proved that the fixed points for the nonextinct periodical cicadas are necessarily prime numbers. We propose a universal qualitative framework for species with synchronic periodical cycles, which is based on local fitness functions and the evolution of species interaction evaluating the extinction probability of species. (vi) For v16, the couples (c1, c2) such that c2 ∣ c1 are global fixed points, and there exist infinitely many local ones. (viii) For v18, the couples (c1, c2) such that c1 ∣ c2 are global fixed points, and there exist infinitely many local ones. There exist other infinite families of local fixed points
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
