# Synchronization in ecological systems by weak dispersal coupling with time delay

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## Abstract

One of the most salient spatiotemporal patterns in population ecology is the synchronization of fluctuating local populations across vast spatial extent. Synchronization of abundance has been widely observed across a range of spatial scales in relation to the rate of dispersal among discrete populations. However, the dependence of synchrony on patterns of among-patch movement across heterogeneous landscapes has been largely ignored. Here, we consider the duration of movement between two predator–prey communities connected by weak dispersal and its effect on population synchrony. More specifically, we introduce time-delayed dispersal to incorporate the finite transmission time between discrete populations across a continuous landscape. Reducing the system to a phase model using weakly connected network theory, it is found that the time delay is an important factor determining the nature and stability of phase-locked states. Our analysis predicts enhanced convergence to stable synchronous fluctuations in general and a decreased ability of systems to produce in-phase synchronization dynamics in the presence of delayed dispersal. These results introduce delayed dispersal as a tool for understanding the importance of dispersal time across a landscape matrix in affecting metacommunity dynamics. They further highlight the importance of landscape and dispersal patterns for predicting the onset of synchrony between weakly coupled populations.

## Keywords

Synchronization Phase model Dispersal Time delay## Notes

### Acknowledgments

E. Wall is grateful to the McGill University Biology Department for a Science Undergraduate Research Award. F. Guichard and A.R. Humphries thank the Natural Sciences and Engineering Research Council of Canada for funding through the Discovery Grants Program.

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