A new variance ratio metric to detect the timescale of compensatory dynamics

Authors: Lei Zhao, Shaopeng Wang, Lauren M. Hallett, Andrew L. Rypel, Lawrence W. Sheppard, Max C. N. Castorani, Lauren G. Shoemaker, Kathryn L. Cottingham, Katharine Suding, and Daniel C. Reuman

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.

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