Prime number selection of cycles in a predator‐prey model

Goles, Éric; Schulz, O.; Markus, Mario

doi:10.1002/cplx.1040

Cited by 47 publications

(57 citation statements)

References 22 publications

(19 reference statements)

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“…Although a simple spatially extended model has been proposed recently to describe the cicadas behavior [9], the formulation considers that the predators also exhibit a periodical life cycle and have similar dynamics as those of the preys. In this manner, the selection of life cycles concerns the optimal way to make the emergence of preys do not coincide with 4 the emergence of predators.…”

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confidence: 99%

Emergence of Prime Numbers as the Result of Evolutionary Strategy

et al. 2004

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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.

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confidence: 99%

Emergence of Prime Numbers as the Result of Evolutionary Strategy

et al. 2004

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“…Baker refers to two studies providing an explanation for this phenomenon, namely Yoshimura (1997) and Goles et al (2001). Here I will focus on the latter, which is the only one making a systematic use of mathematics.…”

Section: Baker's Examplementioning

confidence: 98%

“…Here I will focus on the latter, which is the only one making a systematic use of mathematics. Goles et al (2001) describes a hypothetical setting in which both the cicadas and their predators are present, with life cycles of fixed lengths Y, X respectively. Mutant cicadas and mutant predators having different life-cycles may emerge and supersede the existing ones just in case they are fitter to survival in a sense to be specified.…”

Section: Baker's Examplementioning

confidence: 99%

Magicicada, Mathematical Explanation and Mathematical Realism

Rizza

2010

Erkenn

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Baker (2005) claims to provide an example of mathematical explanation of an empirical phenomenon which leads to ontological commitment to mathematical objects. This is meant to show that the positing of mathematical entities is necessary for satisfactory scientific explanations and thus that the application of mathematics to science can be used, at least in some cases, to support mathematical realism. In this paper I show that the example of explanation Baker considers can actually be given without postulating mathematical objects and thus cannot be used by the mathematical realist. I also show that, despite this, mathematics keeps playing an important methodological role in the explanation and does not reduce to a merely computational or descriptive framework.

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“…But of course we can ask about just how this happens to come about. Indeed several mathematical models relating to the prime numbers 13 and 17 have been developed, well after Banneker's lifetime, in order to explain why periodical cicadas may have evolved prime number cycles [2,7,10,13,18,26]. 1 "An insect population is said to be periodical if the life cycle has a fixed length of k years (k > 1) and if the adults do not appear every year but only every kth year" [4].…”

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confidence: 99%