Global attractors and extinction dynamics of cyclically competing species.
Global attractors and extinction dynamics of cyclically competing species.
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DOI：
10.1103/physreve.87.052710
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发表时间：
2013-05
期刊：
影响因子：
--
通讯作者：
S. Rulands;A. Zielinski;Erwin Frey
中科院分区：
文献类型：
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作者：
S. Rulands;A. Zielinski;Erwin Frey
在非平衡物理和生态学中，向吸收态的过渡具有重要的基础意义。在生态学中，吸收状态对应于物种的灭绝。本文研究了三种循环相互作用物种的空间种群动态。相互作用机制既包括Lotka-Volterra循环模型中物种之间的直接竞争，也包括May-Leonard模型中分离的选择和繁殖过程。研究表明，导致生物多样性短暂维持的动态过程与总体物种浓度非线性动态的吸引子密切相关。这些全局吸引子的特征在一定的流动性阈值下发生了质的变化，这取决于物种之间不同类型竞争的相对强度。它们提供了关于灭绝时间与系统规模的比例的信息，从而提供了生物多样性的稳定性。我们将有效自由能定义为系统在达到吸收态之前处于特定全局状态的概率的负对数。然后，全球吸引子对应于这种有效能量景观的最小值，并确定物种全球浓度的最可能值。与平衡热力学一样，有效自由能的质变表明并表征了潜在的非平衡相变。我们提供了完整的种群动态阶段图，并对各个阶段的时空动态和灭绝路径进行了全面分析。
Transitions to absorbing states are of fundamental importance in nonequilibrium physics as well as ecology. In ecology, absorbing states correspond to the extinction of species. We here study the spatial population dynamics of three cyclically interacting species. The interaction scheme comprises both direct competition between species as in the cyclic Lotka-Volterra model, and separated selection and reproduction processes as in the May-Leonard model. We show that the dynamic processes leading to the transient maintenance of biodiversity are closely linked to attractors of the nonlinear dynamics for the overall species' concentrations. The characteristics of these global attractors change qualitatively at certain threshold values of the mobility and depend on the relative strength of the different types of competition between species. They give information about the scaling of extinction times with the system size and thereby the stability of biodiversity. We define an effective free energy as the negative logarithm of the probability to find the system in a specific global state before reaching one of the absorbing states. The global attractors then correspond to minima of this effective energy landscape and determine the most probable values for the species' global concentrations. As in equilibrium thermodynamics, qualitative changes in the effective free energy landscape indicate and characterize the underlying nonequilibrium phase transitions. We provide the complete phase diagrams for the population dynamics and give a comprehensive analysis of the spatio-temporal dynamics and routes to extinction in the respective phases.