涨落环境中Logistic种群的综合相图
A comprehensive phase diagram for logistic populations in fluctuating environment
摘要：
种群动力学反映了一个基本的出生-死亡过程，其中与不同事件相关的速率可能取决于外部环境条件和种群密度。一系列简单而流行的确定性模型（如逻辑增长）支持灭绝阶段和活跃阶段之间的跨临界分叉点。在这里，我们提供了一个全面的分析，该系统的阶段，同时考虑到内生的人口噪音（随机出生和死亡事件）和环境随机性的影响，导致出生率和死亡率的变化。确定了三个阶段：在非活跃期，平均灭绝时间$T$与种群的承载力$N$无关，与种群初始大小成比例关系。在幂律阶段$T \sim N^q$和指数阶段$T \sim exp(αN)$。所有这三个阶段和它们之间的过渡进行了详细的研究。连续近似的故障内确定的幂律阶段，并伴随着下降模式的变化进行了分析。的适用性的新兴图片的生态时间序列的分析和保护工作的管理进行了简要的讨论。
英文摘要：
Population dynamics reflects an underlying birth-death process, where the rates associated with different events may depend on external environmental conditions and on the population density. A whole family of simple and popular deterministic models (like logistic growth) support a transcritical bifurcation point between an extinction phase and an active phase. Here we provide a comprehensive analysis of the phases of that system, taking into account both the endogenous demographic noise (random birth and death events) and the effect of environmental stochasticity that causes variations in birth and death rates. Three phases are identified: in the inactive phase the mean time to extinction $T$ is independent of the carrying capacity $N$, and scales logarithmically with the initial population size. In the power-law phase $T \sim N^q$ and the exponential phase $T \sim exp(αN)$. All three phases and the transitions between them are studied in detail. The breakdown of the continuum approximation is identified inside the power-law phase, and the accompanied changes in decline modes are analyzed. The applicability of the emerging picture to the analysis of ecological timeseries and to the management of conservation efforts is briefly discussed.
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