Universal Evolutionary Model for Periodical Species

Goles, Éric; Slapničar, Ivan; Lardies, Marco A.

doi:10.1155/2021/2976351

Cited by 5 publications

(3 citation statements)

References 28 publications

(39 reference statements)

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“…Te present research also provides a basis for future work to consider whether nondeliberate processes can produce Ulam's spiral, thus providing an assessment of whether an allocation of cooperators in the fashion depicted in this paper is empirically plausible. Past research has shown how physical [97,98], biological [1,[99][100][101][102][103][104][105][106][107], and social phenomena [2,3] can draw attention to the prime numbers and foundational studies in this avenue of research have considered how prime-generating patterns might infuence the spatial organization of entities [1]. Te present paper underscores the importance of such work and it calls for further investigation into how or whether Ulam's spiral can emerge in reality-not just on the theoretician's page-as a spatial distribution of organisms capable of stimulating cooperation.…”

Section: Discussionmentioning

confidence: 99%

Seeding the Spatial Prisoner’s Dilemma with Ulam’s Spiral

Johnson

2023

Complexity

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Ulam’s spiral reveals patterns in the prime numbers by presenting positive integers in a right-angled whorl. The classic spatial prisoner’s dilemma (PD) reveals pathways to cooperation by presenting a model of agents interacting on a grid. This paper brings these tools together via a deterministic spatial PD model that distributes cooperators at the prime-numbered locations of Ulam’s spiral. The model focuses on a narrow boundary game variant of the PD for ease of comparison with early studies of the spatial PD. Despite constituting an initially small portion of the population, cooperators arranged in Ulam’s spiral always grow to dominance when (i) the payoff to free-riding is less than or equal to 8/6 (≈1.33) times the payoff to mutual cooperation and (ii) grid size equals or exceeds 23 × 23. As in any spatial PD model, particular formations of cooperators spur this growth and here these formations draw attention to rare configurations in Ulam’s spiral.

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Section: Discussionmentioning

confidence: 99%

Seeding the Spatial Prisoner’s Dilemma with Ulam’s Spiral

Johnson

2023

Complexity

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“…Por lo tanto, los ciclos de floración parecen estar agrupados estrechamente en números que se pueden factorizar en pequeños números primos (Goles et al 2021). Veller et al (2015) propusieron un modelo matemático simple para explicar la evolución de los intervalos de floraciones masivas de los bambúes.…”

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Muerte por reproducción sexual: El caso (sin resolver) de la floración de los bambúes

Guerreiro

Vega

2023

Ecol. Austral

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R��.Los bambúes pertenecen a la familia de los pastos (o Poaceae). Existen 1698 especies de bambúes leñosos y herbáceos distribuidos alrededor del mundo en selvas y en bosques tropicales, subtropicales y templados. En nuestro país habitan cinco géneros y 23 especies de bambúes leñosos nativos. El aspecto más desconocido de los bambúes leñosos es su fenología reproductiva. Aunque se han descripto cuatro tipos de floración principales, las especies de bambúes más interesantes son las que poseen un patrón de floración masivo y cíclico luego de un período largo de crecimiento vegetativo. Dichos eventos de floración masiva ocurren a intervalos aproximadamente regulares, y luego de ellos, los individuos que florecen, mueren. El objetivo de esta revisión es proporcionar una muestra informativa del conocimiento actual de la floración de los bambúes, con énfasis en las especies nativas de la Argentina. Al día de hoy se conoce la duración aproximada del ciclo de vida de la mayoría de las especies de bambúes leñosos de nuestro país, sobre la base de una extensa búsqueda bibliográfica y de una revisión de las colecciones de los principales herbarios nacionales e internacionales. En la mayoría de las especies, los ciclos de vida medios son múltiplos de 15-16 años, y el ciclo de 30 años es el más habitual. En este trabajo se describen las principales hipótesis sobre las fuerzas evolutivas que conducen a los bambúes a florecer, producir semillas y morir de forma sincrónica. Asimismo, se discuten los factores ambientales, genéticos y la combinación de ambos, propuestos como posibles 'causas' de este atípico patrón de floración. Finalmente, se enumeran las consecuencias ambientales y sociales de este fenómeno.[Palabras clave: ciclos de vida, consecuencias ambientales y sociales, determinantes ambientales, determinantes genéticos, sincronía reproductiva] A��. Death by sexual reproduction: The (unsolved) case of bamboo flowering. Bamboos belong to the grass family (or Poaceae). There are 1698 bamboo species distributed around the world in tropical, subtropical and temperate jungles and forests. In our country, there are five native genera that comprise 23 species. The least known characteristic of the woody bamboos is their flowering phenology. Four main types of flowering pa�erns have been described. However, the most interesting are those bamboo species that show a massive and cyclical flowering pa�ern, after a long period of vegetative growth. Such mass flowering events occur at roughly regular intervals and are followed by the death of the flowering individuals. The goal of this review is to provide an informative sample of the current knowledge of bamboo flowering, with an emphasis on the species native to Argentina. Currently, the approximate duration of the life cycle of most woody bamboo species in our country is known, based on a review of the collections of the most important national and international herbaria and an extensive bibliographic search. In most species, the average life cycles are multiples of 15-16 ...

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“…Recent theoretical models [ 35 , 36 ] add both to this list of ways that cooperation can evolve and to the academic variety of this research area. The models show that cyclical behaviour on prime-number period lengths (as observed in predator–prey models predicting prime-valued prey life cycles [ 37 , 38 ]) can instigate cooperation’s evolution by allowing cooperators to evade defectors who spread themselves across a large number of composite time points [ 35 , 36 ]. Such findings establish how a formative mathematical construct (the prime numbers) connects to models of cooperation as foreshadowed in past research [ 37 ], thus branching off from a more general line of inquiry that studies the mathematical underpinnings of moral behaviour (i.e.…”

Section: Introductionmentioning

confidence: 99%

Empirically testing a relationship between cooperation and the prime numbers

Johnson

2024

R. Soc. Open Sci.

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Theoretical models suggest a relationship between cooperation and the prime numbers. In environments where agents play multiple one-shot prisoner’s dilemma games per generation, cooperators evolve to fixation more frequently when cooperating on a cyclical schedule with a prime-number period length. This finding parrots classic predator–prey models showing selection for prime-number prey life cycles. Here, I report an empirical test of the former models using previously published data concerning humans playing one-shot public goods games across multiple time points—i.e. an analogue to multiple one-shot prisoner’s dilemma games. I find very modest evidence of cyclicality at prime-numbered time intervals, though results indicate rough agreement between theoretical predictions and observed rates of full cooperation across time points. Analyses of individual decisions find increased contributions to the public good at prime-number time points and separate placebo tests indicate a 4-in-1000 chance of spuriously estimating this effect. However, when exploratory analyses exclude low-value prime-numbered time points, the magnitude of the estimated effect decreases and the hypothesis of no effect cannot be rejected, implying that low-value, prime-number time points drive estimates, contrary to theoretical model predictions. These findings cast doubt on the hypothesis of increased cooperation at prime-number time points—at least among humans playing public goods games.

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Universal Evolutionary Model for Periodical Species

Cited by 5 publications

References 28 publications

Seeding the Spatial Prisoner’s Dilemma with Ulam’s Spiral

Seeding the Spatial Prisoner’s Dilemma with Ulam’s Spiral

Muerte por reproducción sexual: El caso (sin resolver) de la floración de los bambúes

Empirically testing a relationship between cooperation and the prime numbers

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