Understanding the mechanisms governing ecological stability—why a property such as primary productivity is stable in some communities and variable in others—has long been a focus of ecology. Compensatory dynamics, in which anti‐synchronous fluctuations between populations buffer against fluctuations at the community level, are a key theoretical mechanism of stability. Classically, compensatory dynamics have been quantified using a variance ratio approach that compares the ratio between community variance and aggregate population variance, such that a lower ratio indicates compensation and a higher ratio indicates synchrony among species fluctuations. However, population dynamics may be influenced by different drivers that operate on different timescales, and evidence from aquatic systems indicates that communities can be compensatory on some timescales and synchronous on others. The variance ratio and related metrics cannot reflect this timescale specificity, yet have remained popular, especially in terrestrial systems. Here, we develop a timescale‐specific variance ratio approach that formally decomposes the classical variance ratio according to the timescales of distinct contributions. The approach is implemented in a new R package, called tsvr, that accompanies this paper. We apply our approach to a long‐term, multisite grassland community dataset. Our approach demonstrates that the degree of compensation vs. synchrony in community dynamics can vary by timescale. Across sites, population variability was typically greater over longer compared to shorter timescales. At some sites, minimal timescale specificity in compensatory dynamics translated this pattern of population variability into a similar pattern of greater community variability on longer compared to shorter timescales. But at other sites, differentially stronger compensatory dynamics at longer compared to shorter timescales produced lower‐than‐expected community variability on longer timescales. Within every site, there were plots that exhibited shifts in the strength of compensation between timescales. Our results highlight that compensatory vs. synchronous dynamics are intrinsically timescale‐dependent concepts, and our timescale‐specific variance ratio provides a metric to quantify timescale specificity and relate it back to the classic variance ratio.

中文翻译：

---

一种新的方差比度量，用于检测补偿动力学的时间尺度

长期以来，了解控制生态稳定的机制（为什么某些社区的基本生产力是稳定的，而另一些社区却是可变的）却一直是生态学的重点。补偿动力学是种群之间的反同步波动抵御社区水平波动的缓冲，是稳定的重要理论机制。传统上，补偿性动态已使用方差比方法进行了量化，该方法比较了社区方差和总体种群方差之间的比率，因此较低的比率表示补偿，较高的比率表示物种波动之间的同步。但是，人口动态可能会受到在不同时间范围内运行的不同驱动因素的影响，水生系统的证据表明，社区可以在某些时间范围内进行补偿，而在其他时间范围内则可以同步。方差比和相关指标不能反映这种时标的特异性，但仍然很受欢迎，尤其是在地面系统中。在这里，我们开发了一种特定于时标的方差比方法，该方法根据不同贡献的时标正式分解了经典方差比。该方法在本文随附的称为tsvr的新R包中实现。我们将我们的方法应用于长期的多站点草地社区数据集。我们的方法表明，社区动态中补偿程度与同步程度会随时间变化。与较短的时间尺度相比，跨站点的人口变异性通常在更长的时间内更大。在某些地方，补偿动力学中最小的时间尺度特异性将这种种群变异性模式转化为相似的模式，即与较短的时间尺度相比，更长的种群变异性更长。但是在其他地点，与较短的时间尺度相比，更长的时间上不同的补偿动态会在较长的时间尺度上产生低于预期的社区变异性。在每个站点中，都有一些图在时间尺度之间表现出补偿强度的变化。我们的结果表明，补偿动力学与同步动力学本质上是时间尺度相关的概念，而我们的时间尺度特定方差比提供了一种量化时间尺度特异性并将其与经典方差比率相关联的度量。