A Five Species Cyclically Dominant Evolutionary Game with Fixed Direction: A New Way to Produce Self-Organized Spatial Patterns

Kang, Yibin; Pan, Qiuhui; Wang, Xueting; He, Mingfeng

doi:10.3390/e18080284

Cited by 10 publications

(5 citation statements)

References 42 publications

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“…Important issues are those of coexistence of all available species or extinction of some species. See Park and Jang [18] and Kang et al [10,11] for studies of coexistence of 5 species in a spatial version of RSPLS. Choices for the invasion and reproduction rates leading to the coexistence of some but not all the original 5 species appear in the work of Vukov et al [25] who extend the work of [10] to contemplate more invasion rates and find that two species become extinct while the remaining three coexist.…”

Section: Introductionmentioning

confidence: 99%

Stability of cycles in a game of Rock-Scissors-Paper-Lizard-Spock

Castro¹,

Garrido-da-Silva²,

Ferreira³

et al. 2021

Preprint

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We study a system of ordinary differential equations in R 5 that is used as a model both in population dynamics and in game theory, and is known to exhibit a heteroclinic network formed by three types of elementary heteroclinic cycles. We show the asymptotic stability of the network for parameter values in a range compatible with the two interpretations of the equations. We obtain estimates of the relative attractiveness of each one of the cycles by computing their stability indices. For the parameter values ensuring the asymptotic stability of the network we show that if one of the cycles has a weak form of attractiveness, then the other two are completely unstable. We also show the existence of an open region in parameter space where all three cycles are completely unstable and the network is asymptotically stable, giving rise to intricate dynamics that has been observed numerically by other authors.

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Section: Introductionmentioning

confidence: 99%

Stability of cycles in a game of Rock-Scissors-Paper-Lizard-Spock

Castro¹,

Garrido-da-Silva²,

Ferreira³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Generalizations of the RPS model involving additional species and interactions, have also been investigated in recent years [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Complex dynamical spatial structures (such as spirals with an arbitrary number of arms [16,27,31], domain interfaces, with or without non-trivial internal dynamics [32], and string networks, with or without junctions [33,34]), diverse scaling laws [16,25], and phase transitions [35][36][37][38][39][40][41][42][43] have been shown to naturally emerge in some of these scenarios.…”

Section: Introductionmentioning

confidence: 99%

Predominance of the weakest species in Lotka-Volterra and May-Leonard formulations of the rock-paper-scissors model

2019

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We revisit the problem of the predominance of the 'weakest' species in the context of Lotka-Volterra and May-Leonard implementations of a spatial stochastic rock-paper-scissors model in which one of the species has its predation probability reduced by 0 < Pw < 1. We show that, despite the different population dynamics and spatial patterns, these two implementations lead to qualitatively similar results for the late time values of the relative abundances of the three species (as a function of Pw), as long as the simulation lattices are sufficiently large for coexistence to prevail -the 'weakest' species generally having an advantage over the others (specially over its predator). However, for smaller simulation lattices, we find that the relatively large oscillations at the initial stages of simulations with random initial conditions may result in a significant dependence of the probability of species survival on the lattice size and total simulation time.

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“…However, the adaptation and evolution of organisms to the environment is unpredictable due to the sophisticated changes and the lengthy processes, but fortunately, we can make meaningful estimates of those processes by some means [ 1 , 2 ]. Monte Carlo simulation algorithm is one of the most important method to study the temporal and spatial characteristics of large-scale ecosystem [ 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 ]. Compared with the traditional population dynamics algorithm, the Monte Carlo simulation in two-dimensional space can reveal more details and spatio-temporal characteristics.…”

Section: Introductionmentioning

confidence: 99%

Deep-Reinforcement Learning-Based Co-Evolution in a Predator–Prey System

Wang

Cheng

Wang

2019

Entropy

Self Cite

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Understanding or estimating the co-evolution processes is critical in ecology, but very challenging. Traditional methods are difficult to deal with the complex processes of evolution and to predict their consequences on nature. In this paper, we use the deep-reinforcement learning algorithms to endow the organism with learning ability, and simulate their evolution process by using the Monte Carlo simulation algorithm in a large-scale ecosystem. The combination of the two algorithms allows organisms to use experiences to determine their behavior through interaction with that environment, and to pass on experience to their offspring. Our research showed that the predators' reinforcement learning ability contributed to the stability of the ecosystem and helped predators obtain a more reasonable behavior pattern of coexistence with its prey. The reinforcement learning effect of prey on its own population was not as good as that of predators and increased the risk of extinction of predators. The inconsistent learning periods and speed of prey and predators aggravated that risk. The co-evolution of the two species had resulted in fewer numbers of their populations due to their potentially antagonistic evolutionary networks. If the learnable predators and prey invade an ecosystem at the same time, prey had an advantage. Thus, the proposed model illustrates the influence of learning mechanism on a predator-prey ecosystem and demonstrates the feasibility of predicting the behavior evolution in a predator-prey ecosystem using AI approaches.

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A Five Species Cyclically Dominant Evolutionary Game with Fixed Direction: A New Way to Produce Self-Organized Spatial Patterns

Cited by 10 publications

References 42 publications

Stability of cycles in a game of Rock-Scissors-Paper-Lizard-Spock

Stability of cycles in a game of Rock-Scissors-Paper-Lizard-Spock

Predominance of the weakest species in Lotka-Volterra and May-Leonard formulations of the rock-paper-scissors model

Deep-Reinforcement Learning-Based Co-Evolution in a Predator–Prey System

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