Detecting cyclicity in ecological time series

Cyclic population dynamics are of central interest in ecology. Reliably identifying and quantifying the cyclicity of populations is valuable for the understanding of regulatory mechanisms and their variability across spatiotemporal scales. Cyclicity can be detected using periodogram analysis of time series. The statistical significance of periodogram peaks is commonly evaluated against the null hypothesis of uncorrelated fluctuations, also known as white noise. Here, we show that this null hypothesis is inadequate for cycle detection in ecosystems with non-negligible correlation times. As an alternative null hypothesis we propose the so-called Ornstein-Uhlenbeck state-space (OUSS) model, which generalizes white noise to allow for temporal correlations. We justify its use on mechanistic principles and demonstrate its advantages using numerical simulations of simple population models. We show that merely contrasting cyclicity against white noise greatly increases the false cycle detection rate and can lead to wrong conclusions even for simple systems. A comparative statistical analysis of the Global Population Dynamics Database using both null hypotheses suggests that a significant number of populations might have been misinterpreted as cyclic in the past. Our proposed methods for cycle detection are available as an R package (peacots).