标题： 多种群生态波动作为灭绝边缘的跳跃过程 显示英文标题

标题： Many-species ecological fluctuations as a jump process from the brink of extinction

摘要： 高度多样的生态系统表现出种群大小和物种更替的广泛分布，其中高丰度和低丰度的物种随时间交换。 我们表明，这些两个特征在许多变量模型生态系统中，当物种以小速率从系统外部迁入时，在波动相中普遍出现。 我们表明，这些和其他现象可以通过在小迁移极限下的尺度规律来理解，在这种情况下会出现大的波动和长的时间尺度。 我们构建了一个精确的解析理论来描述这个渐近区域，该理论提供了关于时间尺度和丰度分布的尺度预测，并在模拟中被精确验证。 在这个区域内，尽管物种在稀有和丰富子集之间来回移动，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。 发现丰富的物种数量严格低于一个著名的稳定性界限，使系统远离临界性。 同时，其他包含一些稀有物种的多样性度量则超过这个界限。 在迁移率趋于零的渐近极限下，单个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：一个稀有物种会保持稀有一段时间，然后经历种群大小的跳跃，之后变得丰富（一个物种更替事件），随后由于与其他物种的竞争，其种群大小逐渐减少，再次变为稀有。 在小但有限的迁移率下，丰度轨迹的时间反演不对称性得以保持。 这些特征可能作为高度多样化生态系统内生波动的指纹。 显示英文摘要

摘要： 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 small but finite migration rate. These features may serve as fingerprints of endogenous fluctuations in highly-diverse ecosystems.