Natural populations are regulated by ecological factors operating at different spatiotemporal scales and thus exhibit scale-dependent dynamics. Spectral approaches (e.g. Fourier transform, wavelet analysis, etc.) provide useful tools to reveal the timescale-specific features of population dynamics, which provide new opportunities to disentangle the drivers of population variability and synchrony. That said, the timescale-specific approach has yet been used in understanding the role of biotic processes in variability and synchrony, both theoretically and empirically. Here we combine a metapopulation model and spectral decomposition approach to understand how dispersal affect population variability and synchrony across timescale. We mostly focus on under-compensatory cases (i.e. populations are under weak regulations, low intrinsic growth rate). The methods include analytical solution of the spectral matrix, numerical simulation with different time lengths, and simulation of the metapopulation experiment.
Results/Conclusions
While dispersal decreases local population variability and increases spatial synchrony at long timescales, it increases local population variability and decreases spatial synchrony at short timescales. The latter counterintuitive result is explained by the statistical averaging effect of dispersal. Such contrasting effects between short and long timescale translate into opposite patterns of dispersal-variability/synchrony relationships derived from short and long time series data. Specifically, if we obtain sufficiently long time series, local population variability decreases, and spatial synchrony increase, with dispersal. If we obtain very short time series, local population variability increases, and spatial synchrony decreases, with dispersal. Our findings have important implications for experimental design, in particular determining the critical length required to reveal the expected effect of dispersal. With simulated data, we provide recommendations on the critical length for different scenarios (about 100 for one repeat, and 18 for six repeats).