Spatial synchrony of oscillating populations has been observed in various ecological systems, and identifying its causes has attracted the interest of ecologists. The synchrony of a spatial population has been shown to be detrimental to its persistence because all local populations may go extinct simultaneously. Previous studies have shown that three main hypotheses can explain this phenomenon. First, it may be due to synchronous environmental forcing-the so-called Moran effect or Moran theorem. Second, migration or dispersal of individuals is liable to cause population synchrony, and third, nomadic predators have been proposed as a synchronizing mechanism. In this paper, we focus on the first explanation.Moran's theorem suggests that if two(or more) populations sharing a common linear density-dependence in the renewal process are disturbed with correlated noise, they will become synchronized with a correlation that matches the noise correlation. Four conditions are needed for the Moran theorem to be applicable:linear density-dependence structure, identical density dependence structure, no dynamical coupling, and spatially correlated white environmental noise. However, there is mounting evidence that population dynamics may differ geographically within a given species. Moreover, various climatic variables in nature are known to demonstrate positive temporal autocorrelation. These violate the assumptions that the dynamics of the populations are identical and environmental noise is white. Therefore, the classical Moran theorem needs to be extended to cope with these situations.In this paper, we make the assumption that population dynamics can be described by linear and stationary autoregressive processes, and that they are affected by spatially correlated colored environmental noise. The noise color refers to the temporal correlation in the time series data of the environmental noise and is expressed as the degree of(first-order) autocorrelation for autoregressive noise. The level of synchrony can be measured as the correlation between two populations. We show that(1) the observed spatial synchrony between two populations can be split into two multiplicative components:the demographic component that depends on the values of the autoregressive coefficients and the environmental noise color, and the correlation of the environmental noise. The Moran theorem still holds in spatial synchrony accounted for by the correlated red noise between homogeneous populations described by linear processes.(2) Spatial variability in population dynamics may substantially contribute to the spatial variability of population synchrony. However, it is complex. No obvious connection is found between the values of the autoregressive coefficients and the demographic component of spatial synchrony.(3) The synchronizing potential of correlated red noise has two characteristics:the correlation between red noises can contribute to the spatial synchrony, and the coefficient of noise color can contribute to the spatial synchrony by affecting the density dependent structure of population dynamics. However, we cannot obtain a discernible pattern between the demographic component of spatial synchrony and the environmental noise color. Environmental noise color intensifies or diminishes the Moran effect when population dynamics are spatially heterogeneous, and this effect depends strongly on the values of the three new combined parameters that we consider in this paper. These results should improve our understanding of the mechanism underlying population synchrony. They should also help develop conservation management plans and improve the control of pest species.