The ability of random environmental variation to stabilize competitor coexistence was pointed out long ago and, in recent years, has received considerable attention. Analyses have focused on variations in the log-abundances of species, with mean logarithmic growth rates when rare, E[r], used as metrics for persistence. However, invasion probabilities and the times to extinction are not single-valued functions of E[r] and, in some cases, decrease as E[r] increases. Here, we present a synthesis of stochasticity-induced stabilization (SIS) phenomena based on the ratio between the expected arithmetic growth µ and its variance g. When the diffusion approximation holds, explicit formulas for invasion probabilities and persistence times are single valued, monotonic functions of µ/g. The storage effect in the lottery model, together with other well-known examples drawn from population genetics, microbiology and ecology (including discrete and continuous dynamics, with overlapping and non overlapping generations), are placed together, reviewed, and explained within this new, transparent theoretical framework. We also clarify the relationships between life-history strategies and SIS, and study the dynamics of extinction when SIS fails.

中文翻译：

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生态学和进化中的随机性引起的稳定性：一种新的综合

随机环境变化稳定竞争者共存的能力很久以前就被指出，近年来受到了相当多的关注。分析集中在物种对数丰度的变化上，稀有时的平均对数增长率 E[r] 用作持久性的度量。然而，入侵概率和灭绝时间不是 E[r] 的单值函数，在某些情况下，随着 E[r] 的增加而减少。在这里，我们基于预期算术增长 μ 与其方差 g 之间的比率，综合了随机性引起的稳定 (SIS) 现象。当扩散近似成立时，入侵概率和持续时间的显式公式是 μ/g 的单值单调函数。彩票模型中的存储效应，与从种群遗传学、微生物学和生态学（包括离散和连续动态，具有重叠和非重叠世代）中提取的其他著名例子一起，在这个新的、透明的理论框架内被放在一起、审查和解释。我们还阐明了生活史策略与 SIS 之间的关系，并研究了 SIS 失败时灭绝的动态。