Ecological synchrony has become a central phenomenon to predict the persistence of population, as well as to infer mechanisms driving species coexistence and ecosystem function. Metrics of synchrony includes statistical correlation between random variables and the relation between phases of periodic signals. However, deviation from synchrony, or asynchrony, remains weakly defined in ecology. For example, negative correlation or coherence (or the lack thereof) is not a robust measure of asynchrony between time series with a periodic component. Also, asynchrony is often used to refer to periodic time series that are simply not in-phase. We will start from synchrony defined by the stability of a fixed phase difference between time series, thus including in-phase or any phase-locked state. We will then study asynchrony as the loss of stability of these synchronous states. We adopted the Rosenzweig-MacArthur predator-prey model to derive the minimum conditions for self-sustained ecological asynchrony driven by dispersal in a trophic metacommunity. The model was analysed using phase dynamic equations for weakly coupled oscillators and numerical simulations of the full metacommunity model.
Results/Conclusions
Our analysis demonstrates that the loss of synchrony among homogeneous and weakly coupled communities is only possible in systems of at least 3 patches. More specifically, we show that pulse-relaxation predator-prey dynamics leading to stable phase-locked dynamics between 2 patches switch to asynchronous dynamics in a 3-patch metacommunity where dispersal causes the frequency of oscillations in each patch to fluctuate through time. This leads to shifts between apparent in-phase and out of phase dynamics between communities. Our simulations were able to show the robustness of this result to increasing dispersal rate, and to a broad range of predator and prey traits. Our theory of self-sustained ecological asynchrony provides a novel and testable set of predictions as a starting point for studying deviations from synchrony. It also provides a new interpretation of ecological data that exhibit shifts in either statistical correlation or in phase dynamics among locations or species.