Classic approaches to studying synchrony of the dynamics of multiple populations of the same species in different locations (called spatial synchrony) focused on correlations between population time series in pairs of locations, often plotting how correlation declines with distance between the sampling locations. Classic approaches to studying patterns of synchrony and compensatory dynamics of species within the same community (called community synchrony and compensation) often used the variance ratio, which is based on variances and covariances of species population time series. Such covariance approaches have certainly advanced our understanding, but they conceal more than they reveal because the correlation of two time series is only one small aspect of their relationship, and declines in correlation with distance and the variance ratio are only unidimensional summary aspects of the full relationships between population dynamics occurring in different places or species.
Results/Conclusions
Over the past ~10 years, a variety of new statistical approaches have been developed to study synchrony and asynchrony both across space and within a community. These approaches have led to major advances, revealing three new dimensions of spatial synchrony and community synchrony/compensation. First, approaches based on Fourier analysis and wavelets have: 1) revealed the timescale specificity of synchrony, and 2) changes in synchrony through time, and 3) have greatly improved inferences of causes of synchrony. Second, geographic approaches to spatial synchrony have: 1) revealed major new phenomena on large spatial scales, and 2) have also improved inferences of causes. Third, recent work, still in its infancy, has used an approach to synchrony and compensatory dynamics based on the statistical concept of the “copula”, which provides a complete description of the dependence between variables. Copulas have begun to reveal important new aspects of how time series combine across a community or across space to influence community or metacommunity stability. We will summarize some of the new approaches, including where software can be found implementing these approaches, and what has been achieved with the approaches that used to be difficult.