Survival behavior in the cyclic Lotka-Volterra model with a randomly switching reaction rate.
Survival behavior in the cyclic Lotka-Volterra model with a randomly switching reaction rate.
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DOI：
10.1103/physreve.97.022406
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发表时间：
2017-11
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影响因子：
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通讯作者：
Robert West;M. Mobilia;A. Rucklidge
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作者：
Robert West;M. Mobilia;A. Rucklidge
我们研究了随机切换的繁殖捕食率对非空间循环Lotka-Volterra模型生存行为的影响，该模型也被称为零和石头剪刀布游戏，用于隐喻地描述三个物种之间的循环竞争。在大而有限的种群中，人口波动（内部噪声）会在有限的时间内使两个物种灭绝，而繁殖-捕食率最小的物种最有可能成为幸存者（弱者定律）。在这里，我们的模型环境（外部）噪声，假设最强的物种（最快的繁殖和捕食）在给定的静态环境中的繁殖捕食率随机切换两个值之间对应的更多和更少的有利的外部条件。我们研究了环境噪声和人口噪声对物种生存概率和平均灭绝时间的联合影响。特别是，我们调查的生存概率是否遵循最弱的法律，并分析其依赖于外部噪声强度和开关率。值得注意的是，当平均而言，有一个有限数量的开关灭绝之前，生存概率的捕食者的物种的反应速率开关通常随外部噪声强度的非单调变化（最佳生存约一个临界噪声强度）。我们还概述了所有的反应速率切换在显着不同的时间尺度的情况下的关系。
We study the influence of a randomly switching reproduction-predation rate on the survival behavior of the nonspatial cyclic Lotka-Volterra model, also known as the zero-sum rock-paper-scissors game, used to metaphorically describe the cyclic competition between three species. In large and finite populations, demographic fluctuations (internal noise) drive two species to extinction in a finite time, while the species with the smallest reproduction-predation rate is the most likely to be the surviving one (law of the weakest). Here we model environmental (external) noise by assuming that the reproduction-predation rate of the strongest species (the fastest to reproduce and predate) in a given static environment randomly switches between two values corresponding to more and less favorable external conditions. We study the joint effect of environmental and demographic noise on the species survival probabilities and on the mean extinction time. In particular, we investigate whether the survival probabilities follow the law of the weakest and analyze their dependence on the external noise intensity and switching rate. Remarkably, when, on average, there is a finite number of switches prior to extinction, the survival probability of the predator of the species whose reaction rate switches typically varies nonmonotonically with the external noise intensity (with optimal survival about a critical noise strength). We also outline the relationship with the case where all reaction rates switch on markedly different time scales.