Ecological stability refers to a family of concepts used to describe how systems of interacting species vary through time and respond to disturbances. Because observed ecological stability depends on sampling scales and environmental context, it is notoriously difficult to compare measurements across sites and systems. Here, we apply stochastic dynamical systems theory to derive general statistical scaling relationships across time, space, and ecological level of organisation for three fundamental stability aspects: resilience, resistance, and invariance. These relationships can be calibrated using random or representative samples measured at individual scales, and projected to predict average stability at other scales across a wide range of contexts. Moreover deviations between observed vs. extrapolated scaling relationships can reveal information about unobserved heterogeneity across time, space, or species. We anticipate that these methods will be useful for cross-study synthesis of stability data, extrapolating measurements to unobserved scales, and identifying underlying causes and consequences of heterogeneity.

中文翻译：

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生态系统稳定性的一般统计尺度定律

生态稳定性是指一系列概念，用于描述相互作用物种的系统如何随时间变化并对干扰做出反应。由于观察到的生态稳定性取决于采样规模和环境背景，众所周知，很难对不同地点和系统的测量结果进行比较。在这里，我们应用随机动力系统理论来推导出跨时间、空间和组织生态水平的一般统计尺度关系，用于三个基本稳定性方面：弹性、阻力和不变性。这些关系可以使用在单个尺度上测量的随机或代表性样本进行校准，并预测以预测在广泛背景下其他尺度的平均稳定性。此外，观察到的与 外推的比例关系可以揭示有关跨时间、空间或物种未观察到的异质性的信息。我们预计这些方法将有助于稳定性数据的交叉研究综合、将测量值外推到未观察到的尺度以及确定异质性的潜在原因和后果。