Detection of imperfect population synchrony in an uncertain world

1. We propose the method of 'phase analysis' for studying the spatio-temporal fluctuations of animal populations, and use this method for helping identify remarkable synchronized population fluctuations that may sometimes be found over very large spatial domains. 2. The method requires decomposing the observed time series of population fluctuations into two components-one that quantifies the changing phase of the signal, and the other that quantifies the changing amplitude. 3. Two populations are considered to be 'phase synchronized' if there is locking or synchrony between their phase components, while their associated amplitudes may nevertheless remain largely uncorrelated. 4. Since environmental noise often masks population synchrony, a null hypothesis approach is used to detect whether the phase variables are locked more than would be expected by chance alone. 5. The technique is thus particularly appropriate for ecological analyses where it is often important to study evidence of weak interactions in irregular non-stationary and noisy time series. Because climatic patterns (and predicted climate changes) almost certainly influence population dynamics, the approach appears particularly relevant for analysing the potential links between climatic fluctuations and population abundance.