Highly diverse ecosystems exhibit a broad distribution of population sizes and species turnover, where species at high and low abundances are exchanged over time. We show that these two features generically emerge in the fluctuating phase of many-variable model ecosystems with disordered species interactions, when species are supported by migration from outside the system at a small rate. We show that these and other phenomena can be understood through the existence of a scaling regime in the limit of small migration, in which large fluctuations and long timescales emerge. We construct an exact analytical theory for this asymptotic regime that provides scaling predictions on timescales and abundance distributions that are verified exactly in simulations. In this regime, a clear separation emerges between rare and abundant species at any given time, despite species moving back and forth between the rare and abundant subsets. The number of abundant species is found to lie strictly below a well-known stability bound, maintaining the system away from marginality. At the same time, other measures of diversity, which also include some of the rare species, go above this bound. In the asymptotic limit where the migration rate goes to zero, trajectories of individual species abundances are described by non-Markovian jump-diffusion processes, which proceeds as follows: A rare species remains so for some time, then experiences a jump in population sizes after which it becomes abundant (a species turnover event) and later sees its population size gradually decreasing again until rare, due to the competition with other species. The asymmetry of abundance trajectories under time reversal is maintained at a small but finite migration rate. These features may serve as fingerprints of endogenous fluctuations in highly diverse ecosystems.

中文翻译：

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多物种生态波动是濒临灭绝的跳跃过程

高度多样化的生态系统表现出广泛的种群规模和物种更替分布，其中高丰度和低丰度的物种随着时间的推移而交换。我们表明，这两个特征通常出现在具有无序物种相互作用的多变量模型生态系统的波动阶段，此时物种受到来自系统外部的小速率迁移的支持。我们表明，这些现象和其他现象可以通过在小迁移的限制下存在缩放机制来理解，其中出现大的波动和长的时间尺度。我们为这种渐近状态构建了精确的分析理论，提供了时间尺度和丰度分布的缩放预测，并在模拟中得到了精确验证。在这种情况下，尽管物种在稀有和丰富的子集之间来回移动，但在任何给定时间稀有和丰富的物种之间都会出现明显的分离。人们发现丰富的物种数量严格低于众所周知的稳定界限，从而使系统远离边缘化。与此同时，其他多样性指标（也包括一些稀有物种）超出了这一界限。在迁移率趋于零的渐近极限下，个体物种丰度的轨迹由非马尔可夫跳跃扩散过程描述，其过程如下：稀有物种保持这种状态一段时间，然后在之后经历种群规模的跳跃。它变得丰富（物种更替事件），然后由于与其他物种的竞争，其种群规模再次逐渐减少直至稀少。时间反转下丰度轨迹的不对称性保持在较小但有限的迁移速率下。这些特征可能是高度多样化的生态系统中内生波动的指纹。