[论文解读] Many-species ecological fluctuations as a jump process from the brink of extinction

Thibaut Arnoulx de Pirey, Guy Bunin|arXiv (Cornell University)|Jun 23, 2023

Ecosystem dynamics and resilienceEnvironmental Science被引用 3

一句话总结

本文提出了一种非马尔可夫跳扩散框架，以解释由物种相互作用驱动的多样化生态系统中大规模生态波动，表明稀有种群在逐渐衰退前会经历突然的种群跃迁至丰度。在低迁移率极限下，系统表现出一种标度行为，其中物种更替以间歇性跳跃形式出现，其丰度分布和多样性度量偏离平衡态预测，并始终低于线性稳定性边界。

ABSTRACT

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.

研究动机与目标

• 理解在高度多样化生态系统中，仅由内部物种相互作用驱动的广泛物种丰度分布与大规模种群波动的起源。
• 识别具有杂乱相互作用的多物种生态系统在波动相中的普遍标度行为。
• 为小迁移率下的渐近 regime 建立分析框架，其中长时标与稀有事件占主导地位。
• 解释尽管持续发生更替，多样性为何仍能持续存在，且稀有种与优势种之间为何存在分离。
• 表征物种丰度轨迹的非马尔可夫特性，包括时间反演不对称性。

提出的方法

• 在迁移率趋于零的极限下，提出重标度动力学，使渐近 regime 的精确解析处理成为可能。
• 采用动力学平均场理论（DMFT）自洽求解相互作用强度与种群轨迹的统计特性。
• 应用非马尔可夫跳扩散过程来建模单个物种种群丰度的演化：长期处于稀有状态后突然跃迁至丰度高峰。
• 推导出丰度分布与时间尺度的标度预测，并通过大规模模拟精确验证。
• 引入一种筛选程序，基于入侵增长速率与动态稳定性识别优势物种，将其与瞬时波动区分开来。
• 对具有随机相互作用与小迁移率的完整 Lotka-Volterra 模型进行数值模拟，并与 DMFT 结果进行验证。

实验结果

研究问题

• RQ1 在仅存在内部物种相互作用的多样化生态系统中，大规模种群波动与广泛丰度分布是如何产生的？
• RQ2 低迁移率在生成长时标波动与间歇性物种更替中起到何种作用？
• RQ3 为何波动相中的多样性度量超过线性稳定性边界，而优势物种种群数量却仍低于该边界？
• RQ4 物种丰度轨迹的时间反演不对称性在小迁移率极限下如何表现？
• RQ5 个体物种的动力学能否被描述为非马尔可夫跳跃过程？其行为的标度定律是什么？

主要发现

• 在小迁移率极限下，物种丰度轨迹最适宜由非马尔可夫跳扩散过程描述，稀有种群长期保持稀有，随后突然跃迁至高丰度。
• 优势物种种群数量严格低于线性稳定性边界，其值为 φ_top = 0.28，比理论边界 φ = 0.31 低 1%。
• 渐近丰度分布与瞬时分布以及固定点相中观察到的截断正态分布均不同，证实存在一个独特的动力学相。
• 即使在小但非零的迁移率下，系统仍保持物种丰度轨迹的时间反演不对称性，表明其为内生的非平衡动力学。
• 基于 DMFT 的分析框架准确预测了时间尺度与丰度分布的标度律，经大规模系统模拟（S = 20,000）验证。
• 基于入侵增长速率与动态稳定性筛选物种，可恢复接近渐近分布的分布，证实了在波动相中优势物种识别的稳健性。