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A stochastic model is developed to analyze the equilibrium spatial pattern of population synchrony, the correlation of temporal fluctuations in population density between localities. The expected population dynamics and the distribution of individual dispersal distance are homogeneous in space. Environmental stochasticity is caused by temporal fluctuations in the intrinsic rate of increase and/or carrying capacity of local populations that are correlated in space (but not time), the environmental correlation decreasing with distance. We analyze a linearized model for small fluctuations. Employing the standard deviation of a function in a given direction as a measure of scale, the spatial scale of population synchrony, l, is related to the spatial scales of environmental correlation, l, and individual dispersal, l, by the simple general formula [Formula: see text], where m is the individual dispersal rate and γ is the strength of population density regulation (or rate of return to equilibrium, [Formula: see text] in the logistic model). Relative to environmental correlation (the Moran effect), the contribution of individual dispersal to the spatial scale of synchrony is magnified by the ratio of the individual dispersal rate to the strength of density regulation. Thus, even if the scale of individual dispersal is smaller than that of environmental correlation, dispersal can substantially increase the scale of population synchrony for weakly regulated populations.

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Predicting the effects of an expected climatic change requires estimates and modeling of stochastic factors as well as density-dependent effects in the population dynamics. In a population of a small songbird, the dipper (Cinclus cinclus), environmental stochasticity and density dependence both influenced the population growth rate. About half of the environmental variance was explained by variation in mean winter temperature. Including these results in a stochastic model shows that an expected change in climate will strongly affect the dynamics of the population, leading to a nonlinear increase in the carrying capacity and in the expected mean population size.