A randomly interacting N-species Lotka-Volterra system in the presence of a Gaussian multiplicative noise is analyzed. The investigation is focused on the role of this external noise into the statistical properties of the extinction times of the populations. The distributions show a Gaussian shape for each noise intensity value investigated. A monotonic behavior of the mean extinction time as a function of the noise intensity is found, while a nonmonotonic behavior of the width of the extinction time probability distribution characterizes the dynamical evolution.
We study diffusion-controlled two-species annihilation with a finite number of particles. In this stochastic process, particles move diffusively, and when two particles of opposite type come into contact, the two annihilate. We focus on the behavior in three spatial dimensions and for initial conditions where particles are confined to a compact domain. Generally, one species outnumbers the other, and we find that the difference between the number of majority and minority species, which is a conserved quantity, controls the behavior. When the number difference exceeds a critical value, the mino…
Cyclic dominance between species may yield spiral waves that are known to provide a mechanism enabling persistent species coexistence. This observation holds true even in presence of spatial heterogeneity in the form of quenched disorder. In this work we study the effects on spatio-temporal patterns and species coexistence of structured spatial heterogeneity in the form of habitats that locally provide one of the species with an advantage. Performing extensive numerical simulations of systems with three and six species we show that these structured habitats destabilize spiral waves. Analyzing …
Invading activity fronts or near-critical clusters may stabilize vulnerable excitable systems against stochastic trajectories terminating in an absorbing state
Virginia Tech（弗吉尼亚理工大学）；Faculty of Health Sciences, Virginia Tech（弗吉尼亚理工大学健康科学学院）
Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model
物种的循环优势已被确定为维持生物多样性的一种潜在机制，见例如B。Kerr，M. a.莱利，M。W. Feldman和B. J. M. Bohannan [Nature {\bf 418}，171（2002）]和B. Kirkup和M. a. Riley [Nature {\bf 428}，412（2004）].通过数值模拟支持的分析方法，我们解决了这个问题，通过研究一个典型的非空间三种群随机系统，即"石头剪刀布"或循环洛特卡-沃尔泰拉模型的属性。虽然确定性的方法（速率方程）预测的物种的共存导致定期（但中性稳定）振荡的人口密度，我们表明，在系统中产生的波动与\emph{finite number of agents}大大改变了这一局面，并负责灭绝：经过足够长的时间后，三个物种中的两个灭绝。作为主要发现，我们提供了在给定时间的灭绝概率的解析估计和数值计算。我们还讨论了我们的研究结果的影响，一类广泛的竞争人口系统。
Dispersal diversity buffers species vulnerability to local extinction
University of Padova（帕多瓦大学）；National Biodiversity Future Center（国家生物多样性未来中心）；The Abdus Salam International Centre for Theoretical Physics（阿卜杜斯·萨拉姆国际理论物理中心）；University of Lausanne（洛桑大学）；Princeton University（普林斯顿大学）；CMCC Foundation, Euro Mediterranean Center on Climate Change（欧洲地中海气候变化中心基金会）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
Models of many-species ecosystems, such as the Lotka-Volterra and replicator equations, suggest that these systems generically exhibit near-extinction processes, where population sizes go very close to zero for some time before rebounding, accompanied by a slowdown of the dynamics (aging). Here, we investigate the connection between near-extinction and aging by introducing an exactly solvable many-variable model, where the time derivative of each population size vanishes both at zero and some finite maximal size. We show that aging emerges generically when random interactions are taken between…
Cyclic dominance is frequently believed to be a mechanism that maintains diversity of competing species. But this delicate balance could also be fragile if some of the members is weakened because an extinction of a species will involve the annihilation of its predator hence leaving only a single species alive. To check this expectation we here introduce a fourth species which chases exclusively a single member of the basic model composed by three cyclically dominant species. Interestingly, the coexistence is not necessarily broken and we have detected three consecutive phase transitions as we …
我们详细研究了由Amaral和Meyer提出的营养网模型[Phys. Rev. Lett. 82，652（1999）]。我们关注的是与真实生物食物网相关的小规模系统，波动在其中发挥着重要作用。我们表明，使用Monte Carlo模拟，这样的网络可以是不可行的，导致所有物种在小和/或弱耦合系统的灭绝。并给出了灭绝时间和生存机会的估计。我们发现，在灭绝之前，高度连接的物种（“杂食动物”）的比例正在增加。有活力的食物网呈现金字塔结构，在较低的营养级，被占据的生态位密度较高，而且相邻层次的职业密切相关。我们还证明了食物链〈动〉<动>的长度分布具有指数特征，并且随模型参数的变化很弱。相反，灭绝物种的雪崩大小的分布强烈依赖于网络的连通性。对于松散连接的系统，我们恢复幂律类型的行为与在早期的研究中发现的相同的指数，而密集连接的网络的分布是不是幂律类型。
We study the influence of a randomly switching reproduction-predation rate on the survival behavior of the non-spatial 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 th…
