循环竞争中流动种群的自组织

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摘要翻译：
失衡模式的形成是空间扩展的、生物多样性的生态系统的一个特征。有趣的例子是物种的循环竞争，正如“石头-纸-剪刀”游戏所比喻的那样。实验和理论上都发现，这种非传递的相互作用将静态个体的自组织诱导成嘈杂的、不规则的集群。然而，对这种模式的深刻理解和刻画仍然缺乏。在这里，我们从理论上研究了个体流动性对岩石-纸-剪刀游戏中出现的空间结构的影响。我们设计了一种定量的方法来分析随机时间演化过程中自形成的空间模式。对于最初由May和Leonard提出的一个范式模型，在相互作用粒子方法中，我们证明了系统的行为--在适当的连续介质极限--是由一组随机偏微分方程恰当地捕捉的。系统的随机动力学导致了纠缠旋转螺旋波的出现。虽然螺旋波的波长和传播速度可以通过一个确定性的复Ginzburg-Landau方程精确地预测，但它们的纠缠是系统固有的随机性的结果。这些发现和我们的方法对于理解噪声模式的形成有重要的应用，例如在生态和进化的背景下，以及生物化学反应的动力学。
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英文标题：
《Self-Organization of Mobile Populations in Cyclic Competition》
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作者：
Tobias Reichenbach, Mauro Mobilia, and Erwin Frey
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最新提交年份：
2008
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分类信息：

一级分类：Quantitative Biology        数量生物学
二级分类：Populations and Evolution        种群与进化
分类描述：Population dynamics, spatio-temporal and epidemiological models, dynamic speciation, co-evolution, biodiversity, foodwebs, aging; molecular evolution and phylogeny; directed evolution; origin of life
种群动力学；时空和流行病学模型；动态物种形成；协同进化；生物多样性；食物网；老龄化；分子进化和系统发育；定向进化；生命起源
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：Adaptation and Self-Organizing Systems        自适应和自组织系统
分类描述：Adaptation, self-organizing systems, statistical physics, fluctuating systems, stochastic processes, interacting particle systems, machine learning
自适应，自组织系统，统计物理，波动系统，随机过程，相互作用粒子系统，机器学习
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一级分类：Physics        物理学
二级分类：Biological Physics        生物物理学
分类描述：Molecular biophysics, cellular biophysics, neurological biophysics, membrane biophysics, single-molecule biophysics, ecological biophysics, quantum phenomena in biological systems (quantum biophysics), theoretical biophysics, molecular dynamics/modeling and simulation, game theory, biomechanics, bioinformatics, microorganisms, virology, evolution, biophysical methods.
分子生物物理、细胞生物物理、神经生物物理、膜生物物理、单分子生物物理、生态生物物理、生物系统中的量子现象（量子生物物理）、理论生物物理、分子动力学/建模与模拟、博弈论、生物力学、生物信息学、微生物、病毒学、进化论、生物物理方法。
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英文摘要：
  The formation of out-of-equilibrium patterns is a characteristic feature of spatially-extended, biodiverse, ecological systems. Intriguing examples are provided by cyclic competition of species, as metaphorically described by the `rock-paper-scissors' game. Both experimentally and theoretically, such non-transitive interactions have been found to induce self-organization of static individuals into noisy, irregular clusters. However, a profound understanding and characterization of such patterns is still lacking. Here, we theoretically investigate the influence of individuals' mobility on the spatial structures emerging in rock-paper-scissors games. We devise a quantitative approach to analyze the spatial patterns self-forming in the course of the stochastic time evolution. For a paradigmatic model originally introduced by May and Leonard, within an interacting particle approach, we demonstrate that the system's behavior - in the proper continuum limit - is aptly captured by a set of stochastic partial differential equations. The system's stochastic dynamics is shown to lead to the emergence of entangled rotating spiral waves. While the spirals' wavelength and spreading velocity is demonstrated to be accurately predicted by a (deterministic) complex Ginzburg-Landau equation, their entanglement results from the inherent stochastic nature of the system.These findings and our methods have important applications for understanding the formation of noisy patterns, e.g., in ecological and evolutionary contexts, and are also of relevance for the kinetics of (bio)-chemical reactions.
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PDF链接：
https://arxiv.org/pdf/801.1798

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关键词：自组织 Organization Quantitative Evolutionary Biodiversity scissors theoretically 组织 rock 系统