Spatial scale of population synchrony: Environmental correlation versus dispersal and density regulation

A stochastic model is developed to analyze the equilibrium spatial pattern of population synchrony, the correlation of temporal fluctuations in popula tion density between localities. The expected population dynamics and the d istribution of individual dispersal distance are homogeneous in space. Envi ronmental stochasticity is caused by temporal fluctuations in the intrinsic rate of increase and/or carrying capacity of local populations that are co rrelated in space (but not time), the environmental correlation decreasing with distance. We analyze a linearized model for small fluctuations. Employ ing the standard deviation of a function in a given direction as a measure of scale, the spatial scale of population synchrony, l(rho), is related to the spatial scales of environmental correlation, l(r), and individual dispe rsal, l, by the simple general formula l(rho)(2) = l(e)(2) + ml(2)/gamma, w here m is the individual dispersal rate and gamma is the strength of popula tion density regulation (or rate of return to equilibrium, (r) over bar in the logistic model). Relative to environmental correlation (the Moran effec t), the contribution of individual dispersal to the spatial scale of synchr ony is magnified by the ratio of the individual dispersal rate to the stren gth of density regulation. Thus, even if the scale of individual dispersal is smaller than that of environmental correlation, dispersal can substantia lly increase the scale of population synchrony for weakly regulated populat ions.